Advances in Computational Methods for Free-Surface Flows

• Abbott, J. P. 1978. An efficient algorithm for the determination of certain bifurcation points. J. Comput. Appl. Math. 4:19–27.

  Article  Google Scholar 

• Addessio, F. L., Carroll, D. E., Dukowicz, J. K., Harlow, F. H., Johnson, J. N., Kashiwa, B. A., Maltrud, M. E. and Ruppel, H. M. 1986. CAVEAT: a computer code for fluid dynamics problems with large distortion and internal slip. Los Alamos National Laboratory Report: LA-10613-MS.

  Google Scholar 

• Ahmed, A. and Alexandrou, A. N. 1992. Compression molding using a generalized Eulerian—Lagrangian formulation with automatic remeshing. Adv. Polym. Technol. 11:203–211.

  Article  CAS  Google Scholar 

• Ahn, Y. C. and Ryan, M. E. 1991. A finite-difference analysis of the extrudate swell problem. Int. J. Numer. Meth. Fluids. 13: 1289–1310.

  Article  CAS  Google Scholar 

• Amsden, A. A. 1966. The particle-in-cell method for the calculation of the dynamics of compressible fluids. Los Alamos Scientific Laboratory Report. LA-3466.

  Google Scholar 

• Amsden, A. A., Ruppel, H. M. and Hirt, C. W. 1980. SALE: A simplified ALE computer program for fluid flow at all speeds. Los Alamos Scientific Laboratory Report. LA-8095.

  Google Scholar 

• Anturkar, N. R., Papanastasiou, T. C. and Wilkes, J. O.1991. Stability of coextrusion through converging dies. J. Non-Newt. Fluid Mech. 41: 1–25.

  Article  CAS  Google Scholar 

• Aston, B. M. and Thomas, J. W. 1982. An implicit scheme for water wave problems. Appl. Math. Comput. 10–11:809–818.

  Article  Google Scholar 

• Babuska, B. 1971. Error bounds for finite element method. Numer. Meth. 16:322–333.

  Article  Google Scholar 

• Bach, P. and Hassager, O. 1985. An algorithm for the use of the Lagrangian specification in Newtonian fluid mechanics and applications to free-surface flow. J. Fluid Mech. 152: 173–190.

  Article  Google Scholar 

• Bach, P. and Villadsen, J. 1984. Simulation of the vertical flow of a thin, wavy film using a finite-element method. Int. J. Heat Mass Trans. 37:815–827.

  Article  Google Scholar 

• Bapat, C. N. and Batra, R. C. 1984. Finite plane strain deformation of nonlinear viscoelastic rubber-covered rolls. Int. J. Numer. Meth. Eng. 20: 1911–1927.

  Article  Google Scholar 

• Barr, P. K. and Ashurst, W. T. 1984. An interface scheme for turbulent flame propagation. Sandia National Laboratories Report. 82–8773.

  Google Scholar 

• Bathe, K.-J. 1982. Finite Element Procedures in Engineering Analysis. Englewood Cliffs, NJ: Prentice Hall.

  Google Scholar 

• Behrens, R. A., Crochet, M. J., Denson, C. D. and Metzner, A. B. 1987. Transient free-surface flows: motion of a fluid advancing in a tube. AIChE J. 33: 1178–1186.

  Article  CAS  Google Scholar 

• Belytschko, T., Kennedy, J. M. and Schoeberle, D. F. 1980. Quasi-Eulerian finite-element formulation for fluid-structure interaction. ASME J. Pressure Vessel Technol. 102: 62--69.

  Article  CAS  Google Scholar 

• Bercovier, M. and Engelman, M. S. 1980. A finite element method for incompressible non-Newtonian flow. J. Comput. Phys. 36: 313--326.

  Article  Google Scholar 

• Beris, A. N., Tsamopoulos, J. A., Armstrong, R. C. and Brown, R. A. 1985. Creeping motion of a sphere through a Bingham plastic. J. Fluid Mech. 158: 219–244.

  Article  CAS  Google Scholar 

• Bird, R. B. 1976. Useful non-Newtonian models. Ann. Rev. Fluid Mech. 8: 13--26.

  Article  Google Scholar 

• Bird, R. B., Armstrong, R. C. and Hassager, O. 1987. Dynamics of Polymeric Liquids - Volume 1: Fluid Dynamics,2nd edn. New York: Wiley.

  Google Scholar 

• Bixler, N. E. 1982. Stability of coating flow. PhD thesis, University of Minnesota, Minneapolis.

  Google Scholar 

• Boris, J. P. 1989. New directions in computational fluid dynamics. Ann. Rev. Fluid Mech. 21: 345–385.

  Article  Google Scholar 

• Brackbill, J. U., Kothe, D. B. and Zemach, C. 1992. A continuum method for modeling surface tension. J. Comput. Phys. 100: 335--354.

  Article  CAS  Google Scholar 

• Brackbill, J. U. and Saltzman, J. S. 1982a. Adaptive zoning for singular problems in two dimensions. J. Comput. Phys. 46: 342–368.

  Article  Google Scholar 

• Brackbill, J. U. and Saltzman, J S 1982b. Applications and generalizations of variational methods for generating adaptive meshes. Appt. Math. Comput. 10--11: 865–884.

  Google Scholar 

• Brandt, A. 1977. Multi-level adaptive solutions to boundary-value problems. Math. Comput. 31: 333–390.

  Article  Google Scholar 

• Brezzi, F. 1974. On the existence, uniqueness and approximation of saddle point problems arising with Lagrange multipliers. RAIRO, Serie Rouge. 8 R-2: 129–151.

  Google Scholar 

• Brooks, A. N. and Hughes, T. J. R. 1982. Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier - Stokes equations. Comput. Meth. Appl. Mech. Eng. 32: 199--259.

  Article  Google Scholar 

• Burket, R. S., Conaghan, B. F. and Hirshburg, R. I. 1984. Coating method. US Patent 4,443,504.

  Google Scholar 

• Bush, M. B., Milthorpe, J. F. and Tanner, R. I. 1984. Finite element and boundary element methods for extrusion computations. J. Non-Newt. Fluid Mech. 16: 37--51.

  Article  Google Scholar 

• Bush, M. B. and Tanner, R. I. 1983. Numerical solution of viscous flows using integral equation methods. Int. J. Numer. Meth. Fluids. 3: 71--92.

  Article  Google Scholar 

• Bussmann, H., Hoffmann, H. and Beck, D. 1992. Frequency response in slide coaters: FE calculations and measurements. Paper read at AIChE Spring National Meeting, New Orleans, LA, March 29-April 2.

  Google Scholar 

• Carey, G. F., Wang, K. C. and Joubert, W. D. 1989. Performance of iterative methods for Newtonian and generalized Newtonian flows. Int. J. Numer. Meth. Fluids. 9: 127–150.

  Article  Google Scholar 

• Carvalho, M. S. and Scriven, L. E. 1993. Effect of deformable roll cover on roll coating. In Proc. 1993 TAPPI Polymers, Laminations and Coatings Conference, Chicago, IL, August 29-September 2, Book 2, pp. 451–460. Atlanta, GA: TAPPI.

  Google Scholar 

• Chan, R. K.-C. and Street, R. L. 1970. A computer study of finite-amplitude water waves. J. Comput. Phys. 6: 68–94.

  Article  Google Scholar 

• Chern, I.-L., Glimm, J., McBryan, O., Plohr, B. and Yaniv, S. 1986. Front tracking for gas dynamics. J. Comput. Phys. 62: 83–110.

  Google Scholar 

• Chorin, A. J. 1980. Flame advection and propagation algorithms. J. Comput. Phys. 35: 1–11.

  Article  Google Scholar 

• Chorin, A. J. 1985. Curvature and solidification. J. Comput. Phys. 58: 472–490.

  Article  Google Scholar 

• Christodoulou, K. N. 1990. Computational physics of slide coating. PhD thesis, University of Minnesota, Minneapolis.

  Google Scholar 

• Christodoulou, K. N., Scofield, D. F. and Scriven, L. E. 1990. Stability of multilayer coating flows to three-dimensional disturbances. Paper read at AIChE Spring National Meeting, Orlando, FL, March 18–22.

  Google Scholar 

• Christodoulou, K. N. and Scriven, L. E. 1984. The physics of slide coating, dynamic wetting, and air entrainment. Paper read at AIChE Annual Meeting, San Francisco, CA, November 25–30.

  Google Scholar 

• Christodoulou, K. N. and Scriven, L. E. 1988. Finding leading modes of a viscous free surface flow: an asymmetric generalized eigenproblem. J. Sci. Comput. 3: 355–406.

  Article  Google Scholar 

• Christodoulou, K. N. and Scriven, L. E. 1989. The fluid mechanics of slide coating. J. Fluid Mech. 208: 321–354.

  Article  CAS  Google Scholar 

• Christodoulou, K. N. and Scriven, L. E. 1990. Singular elements at dynamic wetting line (unpublished)

  Google Scholar 

• Christodoulou, K. N. and Scriven, L. E. 1992. Discretization of free surface flows and other moving boundary problems. J. Comput. Phys. 99: 39–55.

  Article  Google Scholar 

• Christov, C. I. and Volkov, P. K. 1984. Numerical investigation of the steady viscous flow past a stationary deformable bubble. J. Fluid Mech. 158: 341–364.

  Article  Google Scholar 

• Chung, K. Y. 1985. Shape optimization and free boundary problems with grid adaptation. PhD thesis, University of Michigan.

  Google Scholar 

• Cliffe, K. A. 1983. Numerical calculations of two-cell and single-cell Taylor flows. J. Fluid Mech. 135: 219–233.

  Article  Google Scholar 

• Cliffe, K. A. and Spence, A. 1984. The calculation of high-order singularities in the finite Taylor problem. In Numerical Methods for Birfurcation Problems,Intl. Series Numer. Math., Vol. 70, ed. T. Kuepper, H. D. Mittelmann and H. Weber, pp. 129–144. Basel, and Boston, MA: Birkhaeuser.

  Google Scholar 

• Coates, P. J., Armstrong, R. C. and Brown, R. A. 1992. Calculation of steady-state viscoelastic flow through axisymmetric contractions with the EEME formulation. J. Non-Newt. Fluid Mech. 42: 141–188.

  Article  CAS  Google Scholar 

• Couniot, A. and Crochet, M. J. 1986. Finite-elements for the numerical simulation of injection molding. In Proc. 2nd Intl. Conf. Numerical Methods in Industrial Forming Processes: NUMIFORM 86. Gothenburg, Sweden, August 25–29, pp. 165–170. Rotterdam, Netherlands, and Boston, MA: A. A. Balkema.

  Google Scholar 

• Cox, R. G. 1986. The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech. 168: 169.

  Article  CAS  Google Scholar 

• Coyle, D. J. 1984. The fluid mechanics of roll coating: steady flows, stability, and rheology. PhD thesis, University of Minnesota, Minneapolis.

  Google Scholar 

• Coyle, D. J. 1988. Forward roll coating with deformable rolls: a simple one-dimensional elastohydrodynamic model. Chem. Eng. Sci. 43: 2673–2684.

  Article  CAS  Google Scholar 

• Coyle, D. J. 1990. Nonlinear theory of squeeze-roll coating. Paper read at AIChE Spring National Meeting, Orlando, FL, March 19–22.

  Google Scholar 

• Coyle, D. J. 1992. Roll coating. In Modern Coating and Drying Technology, eds E. D. Cohen and E. B. Gutoff, pp. 63–116. Weinheim, Germany: VCH Publishers.

  Google Scholar 

• Coyle, D. J., Macosko, C. W. and Scriven, L. E. 1987. Film-splitting flows of shear-thinning liquids in forward roll coating. AIChE J. 33: 741–746.

  Article  CAS  Google Scholar 

• Coyle, D. J., Macosko, C. W. and Scriven, L. E. 1990. Stability of film splitting between counter-rotating cylinders. J. Fluid Mech. 216: 437–458.

  Article  Google Scholar 

• Crochet, M. J. 1989. Numerical simulation of viscoelastic flow: a review. Rubber Chem. Technol. 62: 426–455.

  Article  Google Scholar 

• Crochet, M. J. and Legat, V. 1992. The consistent streamline-upwind/Petrov-Galerkin method for viscoelastic flow revisited. J. Non-Newt. Fluid Mech. 42: 283–299.

  Article  CAS  Google Scholar 

• Crowley, W. P. 1971. FLAG: a free-Lagrange method for numerically simulating hydrodynamic flows in two dimensions. Lecture Notes in Physics. 8: 37–43.

  Article  Google Scholar 

• Crowley, W. P. 1985. Free-Lagrange methods for compressible hydrodynamics in two space dimensions. Lecture Notes in Physics. 238: 1–21.

  Article  Google Scholar 

• Cuvelier, C. and Schulkes, R. M. S. 1990. Some numerical methods for the computation of capillary free boundaries governed by the Navier-Stokes equations. SIAM Review. 32: 355–423.

  Article  Google Scholar 

• Dahlquist, G. and Björk, A. 1974. Numerical Methods. Englewood Cliffs: Prentice Hall.

  Google Scholar 

• Daly, B. J. 1967. Numerical study of two fluid Rayleigh-Taylor instability. Phys. Fluids. 10: 297–307.

  Article  CAS  Google Scholar 

• Dandy, D. S. and Leal, L. G. 1989. A Newton’s scheme for solving free-surface flow problems. Int. J. Numer. Meth. Fluids. 9: 1469–1486.

  Article  Google Scholar 

• Daripa, P., Glimm, J., Lindquist, B.,Maesumi, M. and McBryan, O. 1988. On the simulation of heterogeneous petroleum reservoirs. In Numerical Simulation of Oil Recovery,ed. E. M. Wheeler, pp. 89–100. New York: Springer.

  Chapter  Google Scholar 

• Davey, A. 1962. The growth of Taylor vortices in flow between rotating cylinders. J. Fluid Mech. 14: 336–368.

  Article  Google Scholar 

• de Santos, J. M. 1991. Two-phase co-current downflow through constricted passages. PhD thesis, University of Minnesota, Minneapolis.

  Google Scholar 

• Demkowicz, L. and Oden, J. T. 1986. On a mesh optimization method based on a minimization of interpolation error. Int. J. Eng. Sci. 24: 55–68.

  Article  Google Scholar 

• Dhatt, G., Gao, D. M. and Ben Cheikh, A. 1990. A finite-element simulation of metal flow in molds. Int. J. Numer. Meth. Eng. 30: 821–831.

  Article  Google Scholar 

• Dheur, J. and Crochet, M. J. 1987. Newtonian stratified flow through a sudden expansion. Rheol. Acta. 26: 401–413.

  Article  CAS  Google Scholar 

• Dheur, J. and Crochet, M. J. 1989. Stratified flows of Newtonian and viscoelastic fluids. J. Non-Newt. Fluid Mech. 32: 1–18.

  Article  CAS  Google Scholar 

• DiPrima, R. C. and Rogers, E. H. 1969. Computing problems in nonlinear hydrodynamic stability. Phys. Fluids Suppl. П: 165–170.

  Google Scholar 

• Do, D. V. and Christodoulou, K. N. 1992. Multilayer curtain coating flows: stability and sensitivity to small 3-D disturbances. Paper read at AIChE Spring National Meeting, New Orleans, LA, March 29-April 2.

  Google Scholar 

• Donea, J. 1983. Arbitrary Lagrangian-Eulerian finite element methods. In Computational Methods for Transient Analysis, eds T. Belytschko and T. R. J. Hughes, pp. 473–516. Amsterdam: North-Holland.

  Google Scholar 

• Drazin, P. G. and Reed, W. H. 1981. Hydrodynamic Stability. New York: Cambridge University Press.

  Google Scholar 

• Duff, I. S. 1984. Design features of a frontal code for solving sparse unsymmetric linear systems outof-core. SIAM J. Sci. Stat. Comput. 5: 270–280.

  Article  Google Scholar 

• Duff, I. S., Erisman, A. M. and Reid, J. K. 1986. Direct Methods for Sparse Matrices. New York: Oxford University Press.

  Google Scholar 

• Dukowicz, J. 1981. Lagrangian fluid dynamics using Voronoi-Delauny mesh. In Numerical Methods for Coupled Problems, eds E. Hinton, P. Bettes and R. W. Lewis, pp. 82–104. Swansea, UK: Pineridge Press.

  Google Scholar 

• Dukowicz, J. 1984. Conservative rezoning (remapping) for general quadrilateral meshes. J. Comput. Phys. 54: 411–424.

  Article  Google Scholar 

• Dupret, F. 1982. A method for the computation of viscous flow by finite elements with free boundaries and surface tension. In Finite Element Flow Analysis, Proc. 4th Intl. Symp. FEM Flow Problems, Tokyo, 26–29 July 1982, ed. T. Kawai, pp. 495–502. Tokyo: University of Tokyo Press.

  Google Scholar 

• Durst, F., Haas, R., Peric, M., Scheurer, G. and Wagner, H.-G. 1991. Numerische Simulation zweidimensionaler Schlitzdüsenströmungen bei der Fliesserbeschichtung. Coating 2/91: 52–54, 3/91: 90–92, 7/91: 259–263, and 10/91: 360–366.

  Google Scholar 

• Dutta, A. and Ryan, M. E. 1982. Dynamics of a creeping Newtonian jet with gravity and surface tension - a finite difference technique for solving steady free-surface flows using orthogonal curvilinear coordinates. AIChE J. 28: 220–232.

  Article  CAS  Google Scholar 

• Edwards, W. S., Tuckerman, L. S., Friesner, R. A. and Sorensen, D. C. 1994. Krylov methods for the incompressible Navier-Stokes equations. J. Comput. Phys. 110: 82–102.

  Article  Google Scholar 

• Einset, E. and Jensen, K. F. 1992. A finite element solution of three-dimensional mixed convection gas flows in horizontal channels using preconditioned iterative matrix methods. Int. J. Numer. Meth. Fluids. 14: 817–841.

  Article  CAS  Google Scholar 

• Eiseman, P. R. 1982. Orthogonal grid generation. Appl. Math. Comput. 10–11: 193–233.

  Article  Google Scholar 

• Ellwood, K. R. J., Papanastasiou, T. C. and Wilkes, J. O. 1992. Three-dimensional streamlined finite elements - design of extrusion dies. Int. J. Numer. Meth. Fluids. 14: 13–24.

  Article  Google Scholar 

• Engelman, M. S.1982. Quasi-Newton methods in fluid dynamics. In The Mathematics of Finite Element Applications, Vol. IV, ed. J. R. Whiteman, pp.479–487. London: Academic Press.

  Google Scholar 

• Engelman, M. S. and Hasbani, I. 1990. Matrix-free solution algorithms in a finite-element context. Fluid Dynamics International Technical Report 88–1.

  Google Scholar 

• Engelman, M. S. and Sani, R. L. 1983. Finite element simulation of incompressible fluid flows with a free/moving surface. In Numerical Methods in Laminar and Turbulent Flow (Proc. 3rd Intl. Conf. Seattle, WA), eds C. Taylor, J. A. Johnson and W. R. Smith, pp.47–74. Swansea, UK: Pineridge Press.

  Google Scholar 

• Esmail, M. N. and Markov, V. V. 1989. Numerical simulation of dynamic contact angles. Trans. Math. Inst. Acad. Sci. USSR (English Trans.) 186:203–208.

  Google Scholar 

• Ettouney, H. M. and Brown, R. A. 1983. Finite-element methods for steady solidification problems. J. Comput. Phys. 49: 118–150.

  Article  CAS  Google Scholar 

• Fatemi, E. A. and Kistler, S. F. 1992. Finite-difference discretization of viscous free-surface flows. Paper read at AIChE Spring National Meeting, New Orleans, LA, March 29-April 2.

  Google Scholar 

• Finnicum, D. S., Weinstein, S. J. and Ruschak, K. J. 1993. The effect of applied pressure on the shape of a two-dimensional liquid curtain falling under the influence of gravity. J. Fluid Mech. 255: 647–665.

  Article  CAS  Google Scholar 

• Floryan, J. M. and Rasmussen, H. 1989. Numerical methods for viscous flows with free/moving boundaries. Applied Mechanics Reviews. 42: 323–341.

  Article  Google Scholar 

• Fortin, M. and Fortin, A. 1985. A generalisation of Uzawa’s algorithm for the solution of the NavierStokes equations. Comm. Appl. Numer. Meth. 1 : 205–210.

  Article  Google Scholar 

• Fortin, M. and Glowinski, R. 1983. The Augmented Lagrangian Method. Amsterdam: North-Holland.

  Google Scholar 

• Francis, D. C., Christodoulou, K. N., Scofield, D. F. and Lang, C. 1990. Fundamental studies of slot coating. Paper read at AIChE Spring National Meeting,Orlando, FL, March 18–22.

  Google Scholar 

• Frank, R. M. and Lazarus, R. B. 1964. Mixed Eulerian-Lagrangian methods. Methods in Computational Physics. 3: 117–179.

  Google Scholar 

• Frederiksen, C. S. and Watts, A. M. 1981. Finite-element method for time-dependent incompressible free surface flow. J. Comput. Phys. 39: 282–304.

  Article  CAS  Google Scholar 

• Fritts, M. J. and Boris, J. P. 1979. The Lagrangian solution of transient problems in hydrodynamics. J. Comput. Phys. 31: 173–215.

  Article  Google Scholar 

• Fritts, M. J., Crowley, W. P. and Trease, H. E. (eds). 1985. The Free Lagrange Method. Lecture Notes in Physics, Volume 238. New York: Springer Verlag.

  Google Scholar 

• Fromm, J. 1981. Finite-difference computation of the capillary jet free surface problem. Lecture Notes in Physics. 141: 188–193.

  Article  Google Scholar 

• Fromm, J. 1986. Free-surface calculation of capillary spreading. Lecture Notes in Physics. 264: 283–289.

  Article  Google Scholar 

• Fuller, G. G., Cathey, C. A., Hubbard, B. and Zebrowski, B. B. 1987. Extensional viscosity measurements for low-viscosity fluids. J. Rheol. 31: 235–249.

  Article  CAS  Google Scholar 

• Fyfe, D. E., Oran, E. S. and Fritts, M. J. 1988. Surface tension and viscosity with Lagrangian hydrodynamics on a triangular mesh. J. Comput. Phys. 76: 349–384.

  Article  CAS  Google Scholar 

• Gartling, D. K. and Phan-Thien, N. 1984. A numerical simulation of a plastic fluid in a parallel-plate plastometer. J. non-Newt. Fluid Mech. 14: 347–360.

  Article  Google Scholar 

• Gaster, M. 1962. A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. J. Fluid. Mech. 14: 222–224.

  Article  Google Scholar 

• Geller, A. S., Lee, S. H. and Leal, L. G. 1986. The creeping motion of a spherical particle normal to a deformable interface. J. Fluid Mech. 169: 27–69.

  Article  CAS  Google Scholar 

• Glimm, J., Grove, J., Lindquist, B., McBryan, O. A. and Tryggvason, G. 1988. The bifurcation of tracked scalar waves. SIAM J. Sci. Stat. Comput. 9: 61–79.

  Article  Google Scholar 

• Glimm, J. and McBryan, O. A. 1985. A computational model for interfaces. Adv. Appl. Math. 6: 422–435.

  Article  Google Scholar 

• Glimm, J., McBryan, O., Menikoff, R. and Sharp, D. H. 1986. Front tracking applied to Rayleigh-Taylor instability. SIAM J. Sci. Stat. Comput. 7: 230–251.

  Article  Google Scholar 

• Goenaga, A. and Higgins, B. G. 1990. Analysis of free surface flow problems by the boundary element method. Paper read at AIChE Spring National Meeting,Orlando, FL, March 18–22.

  Google Scholar 

• Golafshani, M. 1988. A simple numerical technique for transient creep flows with free surface. Int. J. Numer. Meth. Fluids. 8: 897–912.

  Article  Google Scholar 

• Goldhirsch, I., Orszag, S. A. and Maulik, B. K. 1987. An efficient method for computing leading eigenvalues of large asymmetric matrices. J. Sci. Comput. 2:33–58.

  Article  Google Scholar 

• Goodwin, R. and Horsy, G. M. 1991. Viscous flow down a slope in the vicinity of a contact line. Phys. Fluids A - Fluid Dynamics 3: 515–528.

  Article  CAS  Google Scholar 

• Gordon, W. J. and Hall, C. A. 1973. Construction of curvilinear coordinate systems and applications to mesh generation. Int. J. Numer. Meth. Eng. 7: 461–477.

  Article  Google Scholar 

• Grald, E. W., Chakrabarti, M., Subbiah, S. and Gephart, J. 1994. The spectral element method and its application to modeling coating flows. Paper read at AIChE Spring National Meeting, Atlanta, GA, April 17–21.

  Google Scholar 

• Gresho, P.M. 1991. Some current CFD issues relevant to the incompressible Navier-Stokes equations. Comput. Meth. Appl. Mech. Eng. 87: 201–252.

  Article  Google Scholar 

• Gresho, P. M. and Chan, S. T. 1990. On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite-element method that also introduces a nearly consistent mass matrix. Part 2: Implementation. Int. J. Numer. Meth. Fluids. 11: 621--660.

  Article  Google Scholar 

• Gresho, P. M., Lee, R. L. and Sani, R. L. 1980. On the time-dependent solution of the incompressible Navier-Stokes equations in two and three dimensions. In Recent Advances in Numerical Methods in Fluids, eds C. Taylor and K. Morgan, pp. 27–75. Swansea, UK: Pineridge Press.

  Google Scholar 

• Gresho, P. M. and Sani, R. L. 1987. On pressure boundary conditions for the incompressible Navier-Stokes equations. Int. J. Numer. Meth. Fluids. 7: 1111–1145.

  Article  Google Scholar 

• Griewank, A. and Corliss, G. F. 1992. Automatic Differentiation of Algorithms. Philadelphia: SIAM.

  Google Scholar 

• Habashi, W. G., Nguyen, V.-N. and Bhat, M. V. 1991. Efficient direct solvers for large-scale computational fluid dynamics problems. Comput. Meth. Appl. Mech. Eng. 87: 253–265.

  Article  Google Scholar 

• Hackler, M. A., Christodoulou, K. N., Hirschburg, R. I. and Lightfoot, E. J. 1992. Frequency response of coating flows to small three-dimensional disturbances by supercomputer-aided analysis. Paper read at AIChE Spring National Meeting,New Orleans, LA, March 29-April 2.

  Google Scholar 

• Haftka, T. and Grandhi, R. V. 1986. Structural shape optimization - a survey. Comput. Meth. Appl. Mech. Eng. 57: 91–106.

  Article  Google Scholar 

• Hansen, E. B. 1987. Stokes flow down a wall into an infinite pool. J. Fluid Mech. 178: 243–256.

  Article  CAS  Google Scholar 

• Hansen, E. B. 1991. Stokes flow of a fluid layer over an obstacle on a tilted plane. Math. Comput. Modeling. 15: 185–193.

  Article  Google Scholar 

• Harlow, F. 1964. The particle-in-cell computing method for fluid dynamics. Methods in Computational Physics. 3: 313–343.

  Google Scholar 

• Harlow, F. H. and Amsden, A. A. 1971. Numerical fluid dynamics. In Fluid Dynamics, Los Alamos Scientific Laboratory Report LA--4700.

  Google Scholar 

• Harlow, F. H. and Welch, J. E. 1965. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids. 8: 2182–2189.

  Article  Google Scholar 

• Haroutunian, V., Engelman, M. S. and Hasbani, I. 1993. Segregated finite element algorithms for the numerical solution of large-scale incompressible flow problems. Int. J. Numer. Meth. Fluids. 17: 323–348.

  Article  CAS  Google Scholar 

• Hasbani, Y. and Engelman, M. 1979. Out-of-core solution of linear equations with non-symmetric coefficient matrix. Comput. Fluids. 7: 13–31.

  Article  Google Scholar 

• Haussling, H. J. 1982. Solution of nonlinear water wave problems using boundary-fitted coordinate systems. Appt. Math. Comput. 10-11: 385–407.

  Article  Google Scholar 

• Hayes, R. E., Dannelongue, H. H. and Tanguy, P. A. 1991. Numerical simulation of mold filling in reaction injection molding. Polym. Eng. Sci. 31: 842–848.

  Article  CAS  Google Scholar 

• Heijer, C. D. and Rheinboldt, W. C. 1981 On steplength algorithms for a class of continuation methods. SIAM J. Numer. Anal. 18: 925–948.

  Article  Google Scholar 

• Higgins, B. G. 1980. Capillary hydrodynamics and coating beads. PhD thesis, University of Minnesota, Minneapolis.

  Google Scholar 

• Hill, G. A., Shook, C. A. and Esmail, M. N. 1981. Finite-difference simulation of die-swell for a Newtonian fluid. Canad. J. Chem. Eng. 58: 100–108.

  Article  Google Scholar 

• Hirt, C. W., Amsden, A. A. and Cook, J. L. 1974. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comput. Phys. 14: 227–253.

  Article  Google Scholar 

• Hirt, C. W., Cook, J. L. and Butler, T. D. 1970. A Lagrangian method for calculating the dynamics of an incompressible fluid with free surface. J. Comput. Phys. 5: 103–124.

  Article  Google Scholar 

• Hirt, C. W., Korzekwa, D. R., Rollet, A. D. and Wilde, P. 1990. Planar flow casting: modeling and understanding. Flow Science (Flow Science Inc., Los Alamos, NM) Report FSI-90–00–4.

  Google Scholar 

• Hirt, C. W. and Nichols, B. D. 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39: 210–225.

  Article  Google Scholar 

• Hirt, C. W., Nichols, B. D. and Romero, N. C. 1975. SOLA - a numerical solution algorithm for transient flows. Los Alamos Scientific Laboratory Report LA-5852.

  Book  Google Scholar 

• Hirt, C. W. and Shannon, J. P. 1968. Free-surface stress conditions for incompressible flow calculations. J. Comput. Phys. 2: 403–411.

  Article  Google Scholar 

• Ho, L.-W. and Patera, A. T. 1990. A Legendre spectral element method for simulation of unsteady incompressible free-surface flows. Comput. Meth. Appl. Mech. Eng. 80: 355–366.

  Article  Google Scholar 

• Ho, L.-W. and Patera, A. T. 1991. Variational formulation of three-dimensional free-surface flows. Natural imposition of surface tension boundary conditions. Int. J. Numer. Meth. Fluids. 13: 691–698.

  Article  CAS  Google Scholar 

• Hood, P. 1976. Frontal solution program for unsymmetric matrices. Int. J. Numer. Meth. Eng. 10: 379–399.

  Article  Google Scholar 

• Hood, P. 1977. Correction. Int. J. Numer. Meth. Eng 11: 1055.

  Article  Google Scholar 

• Howard, D., Connolley, W. M. and Rollet, J. S. 1990. Unsymmetric conjugate gradient methods and sparse direct methods in finite element flow simulations. Int. J. Numer. Meth. Fluids. 10: 925–945.

  Article  Google Scholar 

• Huerta, A. and Liu, W. K. 1988. Viscous flows with large free surface motion. Comput. Meth. Appl. Mech. Eng. 69: 277–324.

  Article  Google Scholar 

• Hughes, T. J. R., Liu, W. K. and Zimmerman, T. K. 1981. Lagrangian-Eulerian finite-element formulation for incompressible viscous flows. Comput. Meth. Appl. Mech. Eng. 29: 329–349.

  Article  Google Scholar 

• Huh, K. Y., Golay, M. W. and Manno, V. P. 1986. A method for reduction of numerical diffusion in the donor treatment of convection. J. Comput. Phys. 63: 201–221.

  Article  Google Scholar 

• Hurez, P. and Tanguy, P. A. 1990. Finite element analysis of dip coating with Bingham fluids. Polym. Eng. Sci. 30: 1125–1132.

  Article  CAS  Google Scholar 

• Hurez, P., Tanguy, P. A. and Bertrand, F. H. 1991. A finite element analysis of die swell with pseudoplastic and viscoplastic fluids. Comput. Meth. Appl. Mech. Eng. 86: 97–103.

  Article  Google Scholar 

• Huyakorn, P. S., Taylor, C., Lee, R. L. and Gresho, P. M. 1978. A comparison of various mixed interpolation finite elements in the velocity-pressure formulation of the Navier-Stokes equations. Comput. Fluids. 6: 25–35.

  Article  Google Scholar 

• Hyman, J. M. 1984. Numerical methods for tracking interfaces. Physica. 12D: 396–407.

  Google Scholar 

• Hyun, J. C. and Ballman, R. L. 1978. Isothermal melt spinning - Lagrangian and Eulerian viewpoints. J. Rheol. 22: 349–380.

  Article  Google Scholar 

• Isaacson, E. and Keller, H. B. 1966. Analysis of Numerical Methods. New York: Wiley.

  Google Scholar 

• Jackson, C. P. 1987. A finite-element study of the onset of vortex shedding in flow past variously shaped bodies. J. Fluid Mech. 182: 23–45.

  Article  CAS�� Google Scholar 

• Jackson, C. P. and Robinson, P. C. 1985. A numerical study of various algorithms related to the preconditioned conjugate gradient method. Int. J. Numer. Meth. Eng. 21: 1315–1338.

  Article  Google Scholar 

• Jackson, C. P. and Winters, K. H. 1984. A finite-element study of the Bénard problem using parameter-stepping and bifurcation search. Int. J. Numer. Meth. Fluids. 4: 127–145.

  Article  Google Scholar 

• Johnson, M., Kamm, R. D., Ho, L.-W., Shapiro, A. and Pedley, T. J. 1991. The nonlinear growth of surface-tension-driven instabilities of a thin annular film. J. Fluid. Mech. 233: 141–156.

  Article  CAS  Google Scholar 

• Joseph, D. D. 1990. Fluid Dynamics of Viscoelastic Liquid. New York: Springer.

  Google Scholar 

• Kaneko, N. and Scriven, L. E. 1988. Transient analysis of a curtain coating flow. Paper read at AIChE Spring National Meeting, New Orleans, LA, March 6–10.

  Google Scholar 

• Karagiannis, A., Hrymak, A. N. and Vlachopoulos, J. 1988. Three-dimensional extrudate swell of creeping Newtonian jets. AIChE J. 34: 2088–2094.

  Article  CAS  Google Scholar 

• Karagiannis, A., Mavridis, H., Hrymak, A. N. and Vlachopoulos, J. 1989. A finite element convergence clustered element-by-element technique. In Domain decomposition methods for partial ffегепtiaI equations, eds R. Glowinski et al., pp. 140–150. Philadelphia, PA: SIAM.

  Google Scholar 

• Liu, J.-J., Yu, T.-A. and Cheng, 5.-H. 1991. Finite-difference solution of a Newtonian jet swell problem. Int. J. Numer. Meth. Fluids. 12: 125–142.

  Article  CAS  Google Scholar 

• Loh, C. Y. and Rasmussen, H. 1987. A numerical procedure for viscous free surface flows. App’. Numer. Math. 3 : 479–495.

  Article  Google Scholar 

• Longuet-Higgins, M. S. and Cokelet, E. D. 1976. The formation of steep surface waves on water. Part 1: a numerical method of computation. Proc. Roy. Soc. Lond., Ser. A. 350: 1–26.

  Article  Google Scholar 

• Lowndes, J. 1980. The numerical simulation of the steady movement of a fluid meniscus in a capillary tube. J. Fluid Mech. 101: 631–646.

  Article  CAS  Google Scholar 

• Lu, W. Q. and Chang, H. C. 1988. An extension of the biharmonic boundary integral method to free-surface flow in channels. J. Comput. Phys. 77: 340–360.

  Article  CAS  Google Scholar 

• Luo, X.-L. and Mitsoulis, E. 1990. An efficient algorithm for strain history tracking in finite-element computations of non-Newtonian fluids with integral constitutive equations. Int. J. Numer. Meth. Fluids. 11: 1015–1031.

  Article  Google Scholar 

• Luo, X.-L. and Tanner, R. I. 1988. Finite-element simulation of long and short circular die experiments using integral models. Int. J. Numer. Meth. Eng. 25: 9–22.

  Article  Google Scholar 

• Lynch, D. R. 1982. Unified approach to simulation on deforming elements with application to phase change problems. J. Comput. Phys. 47:387–411.

  Article  Google Scholar 

• Maday, Y. and Patera, A. T. 1989. Spectral element methods for the Navier-Stokes equations. In State-of-the-art Surveys in Computational Mechanics, eds J. T. Oden, and A. K. Noor. New York: ASME.

  Google Scholar 

• Malamataris, N. T. and Papanastasiou, T. C. 1991. Unsteady free surface flows on truncated domains. Ind. Eng. Chem. Res. 30: 2211–2219.

  Article  CAS  Google Scholar 

• (Manteuffel, T. A. 1977. The Tchebychev iteration for non-symmetric linear systems. Numer. Math. 28: 307–327.

  Article  Google Scholar 

• Marchal, M. and Crochet, M. J. 1987. A new mixed finite-element method for calculating viscoelastic flow. J. Non-Newt. Fluid Mech. 26: 77–114.

  Article  CAS  Google Scholar 

• Margolin, L. G. and Nichols, B. D. 1983. Momentum control volumes for finite-difference codes. In Numerical Methods in Laminar and Turbulent Flows (Proc. 3rd Intl. Conf, Seattle, WA), eds C. Taylor, J. A. Johnson and W. R. Smith, pp.411–421. Swansea, UK: Pineridge Press.

  Google Scholar 

• Matsuhiro, I., Shiojima, T., Shimazaki, Y. and Daiuji, H. 1990. Numerical analysis of polymer injection moulding process using finite element method with marker particles. Int. J. Numer. Meth. Eng. 30: 1569–1575.

  Article  Google Scholar 

• McKibben, J. F. and Aidun, C. K. 1991. Computational visualization of three-dimensional free surface flows. In Proc. TAPPI Engineering Conference (Nashville, TN, Sept. 30-Oct. 3), Book 2, pp. 711–718. Atlanta, GA: TAPPI Press.

  Google Scholar 

• Melhem, R. G. and Rheinboldt, W. C. 1982. A comparison of methods of determining turning points of nonlinear equations. Computing. 29: 201–226.

  Article  Google Scholar 

• Meyer, K. A. 1969. Three dimensional study of flow between concentric rotating cylinders. Phys. Fluids. Suppl. II: 155–165.

  Google Scholar 

• Mittal, S. and Tezduyar, T. E. 1992. Space-time finite element computations of incompressible flows involving oscillating cylinders. Int. J. Numer. Meth. Fluids. 15: 1073–1118.

  Article  Google Scholar 

• Miura, H. and Aidun, C. K. 1992. Pressure fluctuations and coat-weight nonuniformities in blade coating. In Proc. 1992 TAPPI Coating Conference, pp. 193–216. Atlanta: TAPPI Press.

  Google Scholar 

• Miyamoto, K. 1992. On the mechanism of air entrainment. Ind. Coating Res. 1: 71–88.

  Google Scholar 

• Miyata, H. 1986. Finite-difference simulation of breaking waves. J. Comput. Phys. 65: 179–214.

  Article  Google Scholar 

• Moffat, H. K. 1964. Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18: 1–18.

  Article  Google Scholar 

• Monaghan, J. J. 1985. Particle methods for hydrodynamics. Comput. Phys. Rep. 3: 71–124.

  Article  Google Scholar 

• Morice, P. 1983. Numerical generation of boundary-fitted coordinate systems with optimal control of orthogonality. In Advances in Grid Generation (Proc. ASME Applied Mechanics, Bioengineering, and Fluids Engineering Conference; Houston), FED-Vol. 5, eds K. N. Ghia and U. Ghia, pp. 71–78. New York: ASME.

  Google Scholar 

• Miles, W., Hens, J. and Boiy, L. 1989. Observation of dynamic wetting process with laser-Doppler velocimetry. AIChE J. 35: 1521–1526.

  Article  Google Scholar 

• Mulder, W., Osher, S. and Sethian, J. A. 1992. Computing interface motion in compressible gas dynamics. J. Comput. Phys. 100: 209–228.

  Article  Google Scholar 

• Muttin, F., Coupez, T., Bellet, M. and Chenot, J. L. 1991. Newtonian fluid computations in Lagrangian variables with a remeshing technique. Application to the filling stage of the diecasting process. In Proc. 1st Intl. Conf. Computational Modelling of Free and Moving Boundary Problems (Southampton, England, July 2–4), eds L. C. Wrobel and C. A. Brebbia, pp. 207–221. Southampton, England: Computational Mechanics Publications.

  Google Scholar 

• Natarajan, R. 1992. An Arnoldi-based iterative scheme for nonsymmetric matrix pencils arising in finite element stability problems. J. Comput. Phys. 100: 128–142.

  Article  Google Scholar 

• Nelson, N. K., Kistler, S. F. and Olmsted, R. D. 1990. A generalized viscous model for the steady shear rheology of magnetic dispersions. Paper read at 62nd Annual Meeting of the Society of Rheology, Santa Fe, NM, October 21–25.

  Google Scholar 

• Nichols, B. D. and Hirt, C. W. 1971. Improved free surface boundary conditions for numerical incompressible-flow calculations. J. Comput. Phys. 8: 434–448.

  Article  Google Scholar 

• Nichols, B. D. and Hirt, C. W. 1973. Calculating three-dimensional free surface flows in the vicinity of submerged and exposed structures. J. Comput. Phys. 12: 234–246.

  Article  Google Scholar 

• Nichols, B. D. and Hirt, C. W. 1975. Methods for calculating multi-dimensional transient free surface flows past bodies. In Proc. First Intl. Conf. Numer. Methods Ship Hydrodynamics,Gaithersburg, Maryland, pp. 253–277.

  Google Scholar 

• Nichols, B. D., Hirt, C. W. and Hotchkiss, R. S. 1980. SOLA-VOF - a solution algorithm for transient fluid flow with multiple free boundariesLos Alamos Scientic Laboratory ReportLA-8355.

  Google Scholar 

• Nickell, R. E., Tanner, R. I. and Caswell, B. 1974. The solution of viscous incompressible jet and free surface flows using finite-element methods. J. Fluid Mech. 65: 189–206.

  Article  Google Scholar 

• Noh, W. F. and Woodward, P. 1976. SLIC (simple line interface calculation). Lecture Notes in Physics. 59: 330–340.

  Article  Google Scholar 

• Oran, E. S. and Boris, J. P. 1987. Numerical Simulation of Reactive Flow. New York: Elsevier.

  Google Scholar 

• Ortega, J. M. and Rheinboldt, W. C. 1970. Iterative Solution of Nonlinear Equations in Several Variables. New York: Academic Press.

  Google Scholar 

• Osher, S. and Sethian, J. A. 1988. Fronts propagating with curvature-dependent speed: algorithms based on Hamiltonian-Jacobi formulation. J. Comput. Phys. 79: 12–49.

  Article  Google Scholar 

• Papanastasiou, T. C. 1987. Flows of material with yield. J. Rheol. 31: 385–404.

  Article  CAS  Google Scholar 

• Papanastasiou, T. C., Macosko, C. W. and Scriven, L. E. 1985. Streamlined finite-elements and transit times. In Finite Elements in Fluids, Vol. 6,eds R. H. Gallagher, G. F. Carey, J. T. Oden and O. C. Zienkiewicz, pp. 263–278. New York: Wiley.

  Google Scholar 

• Papanastasiou, T. C., Scriven, L. E. and Macosko, C. W. 1987. A finite element method for liquid with memory. J. Non-Newt. Fluid Mech. 22: 271–288.

  Article  CAS  Google Scholar 

• Parlett, B. and Saad, Y. 1985. Complex shift and invert

  Google Scholar 

• strategies for real matrices. Yale University, Computer Science Dept. Tech. Report YALEU/DCS-RR-424.

  Google Scholar 

• Patera, A. T. 1984. A spectral element method for fluid flow: laminar flow in a channel expansion. J. Comput. Phys. 54: 468–488.

  Article  Google Scholar 

• Pavelle, R. and Wang, P. S. 1985. MACSYMA from F to G. J. Symbol. Comput. 1:69–100.

  Article  Google Scholar 

• Pearson, J. R. A. 1960. The instability of uniform viscous flow under rollers and spreaders. J. Fluid Mech. 7: 481–500.

  Article  Google Scholar 

• Peitgen, H. and Pruefer, M. 1984. Global aspects of Newton’s method for nonlinear boundary value problems. In Numerical Methods for Bifurcation Problems,Intl. Series Numer. Math., Vol. 70, eds T. Kuepper, H. D. Mittelmann and H. Weber, pp. 352–368. Basel: Birkhauser.

  Google Scholar 

• Peskin, C. S. 1977. Numerical analysis of blood flow in the heart. J. Comput. Phys. 25: 220–252.

  Article  Google Scholar 

• Petzold, L. R. 1982. A description of DASSL: A differential/algebraic system solver. Sandia National Laboratory Report SAND82–8637.

  Google Scholar 

• Petzold, L. R. 1982. Differential/algebraic equations are not ODE’s. SIAM J. Sci. Stat. Comput. 3: 367–384.

  Article  Google Scholar 

• Pilitsis, S. and Beris, A. N. 1989. Calculation of steady-state viscoelastic flow in an undulating tube. J. Non-Newt. Fluid Mech. 31: 231--287.

  Article  CAS  Google Scholar 

• Pitts, E. and Greiller, J. 1961. The flow of thin liquid films between rollers. J. Fluid Mech. 11: 33–50.

  Article  Google Scholar 

• Poenisch, G. D. and Schwetlick, H. H. 1981. Computing turning points of curves implicitly defined by nonlinear equations depending on a parameter. Computing. 26: 107–121.

  Article  Google Scholar 

• Potter, D. E. and Tuttle, G. H. 1973. The construction of discrete orthogonal coordinates. J. Comput. Phys. 13: 483--501.

  Article  Google Scholar 

• Pozrikidis, C. 1988. The flow of a liquid film along a periodic wall. J. Fluid Mech. 188: 275–300.

  Article  CAS  Google Scholar 

• Pozrikidis, C. and Thoroddsen, S. T. 1991. The deformation of a liquid film flowing down an inclined plane wall over a small particle arrested on the wall. Phys. Fluids A - Fluid Dynamics. 3:2546–2558.

  Article  CAS  Google Scholar 

• Pracht, W. E. 1971. A numerical method for calculating transient creep flows. J. Comput. Phys. 7: 46–60.

  Article  Google Scholar 

• Pranckh, F. R. and Scriven, L. E. 1989. Elastohydrodynamics of membrane coating. University of Minnesota Supercomputer Institute Report UMSI 89/83.

  Google Scholar 

• Pranckh, F. R. and Scriven, L. E. 1990a. The elastohydrodynamics of blade coating. AIChE J. 36: 587–597.

  Article  CAS  Google Scholar 

• Pranckh, F. R. and Scriven, L. E. 1990b. The physics of blade coating of a deformable substrate. TAPPI J. 73(1): 163–173.

  CAS  Google Scholar 

• Rajagopalan, D., Armstrong, R. C. and Brown, R. A. 1990. Finite element methods for calculation of steady, viscoelastic flow using constitutive equations with a Newtonian viscosity. J. Non-Newt. Fluid Mech. 36: 159–192.

  Article  CAS  Google Scholar 

• Rajagopalan, D., Armstrong, R. C. and Brown, R. A. 1993. Comparison of computational efficiency of flow simulations with multimode constitutive equations: integral and differential models. J. Non-Newt. Fluid Mech. 46: 243–273.

  Article  CAS  Google Scholar 

• Rajagopalan, D., Philips, R. J., Armstrong, R. C. and Brown, R. A. 1992. The influence of viscoelasticity on the existence of steady solutions in two-dimensional rimming flow. J. Fluid Mech. 235: 611–642.

  Article  CAS  Google Scholar 

• Ramaswamy, B. 1990. Numerical simulation of unsteady viscous free-surface flow. J. Comput. Phys. 90: 396–430.

  Article  CAS  Google Scholar 

• Ramshaw, J. D. 1985. Conservative rezoning algorithm for generalized two-dimensional meshes. J. Comput. Phys. 59: 193–199.

  Article  Google Scholar 

• Rao, R. R. and Finlayson, B. A. 1991. Adaptive refinement of a viscoelastic flow problem with the explicitly elliptic momentum equation. J. Non-Newt. Fluid Mech. 38: 223--246.

  Article  CAS  Google Scholar 

• Reddy, M. P. and Reddy, J. N. 1991. Finite element simulation of mold filling processes. In Advances in Finite Deformation Problems in Materials Processing and Structures, AMD-Vol. 125, pp. 65–74. New York: ASME.

  Google Scholar 

• Reid, J. K. 1981. Frontal methods for solving finite-element systems of linear equations. In Sparse Matrices and their Uses,ed. I. S. Duff, pp. 275–281. New York: Academic Press.

  Google Scholar 

• Rheinboldt, W. C. and Burkardt, J. V. 1983. A locally parametrized continuation process. ACM Trans. Math. Software. 9: 215–235.

  Article  Google Scholar 

• Rosenberg, J. and Keunings, R. 1991. Numerical integration of differential viscoelastic models. J. Non-Newt. Fluid Mech. 39: 269–290.

  Article  CAS  Google Scholar 

• Ruschak, K. J. 1978. Flow of a falling film into a pool. AIChE J. 24: 705–709.

  Article  Google Scholar 

• Ruschak, K. J. 1980. A method for incorporating free boundaries with surface tension in finite element fluid flow simulators. Int. J. Numer. Meth. Eng. 15:639–648.

  Article  Google Scholar 

• Ruschak, K. J. 1983. A three-dimensional linear stability analysis for two-dimensional free boundary flows by the finite element method. Comput. Fluids. 11: 391–401.

  Article  Google Scholar 

• Ruschak, K. J. 1985. Coating flows. Ann. Rev. Fluid Mech. 17: 65–89.

  Article  Google Scholar 

• Ryskin, G. and Leal, L. G. 1983. Orthogonal mapping. J. Comput. Phys. 50: 71–100.

  Article  Google Scholar 

• Ryskin, G. and Leal, L. G. 1984. Numerical solution of free-boundary problems in fluid mechanics. Part 1. The finite-difference technique. J. Fluid Mech. 148: 1–17.

  Article  CAS  Google Scholar 

• Saad, Y. 1980. Variations on Arnoldi’s method for computing eigenelements of large unsymmetric matrices. Linear Algeb. Appl. 34: 269–295.

  Article  Google Scholar 

• Saad, Y 1989. Numerical solution of large nonsymmetric eigenvalue problems. Comput. Phys. Commun. 53: 71–90.

  Article  Google Scholar 

• Saad, Y. and Schultz, M. 1986. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7: 856–869.

  Article  Google Scholar 

• Sackinger, P. A., Schunk, P. R. and Rao, R. R. 1996. A Newton-Raphson pseudo-solid domain mapping technique for free and moving boundary problems: a finite element implementation. J. Corp. Phys., 125: 83–103.

  Article  CAS  Google Scholar 

• Saeger, R. B., Davis, H. T. and Scriven, L. E. 1990. Adaptive elliptic grid generation for 3-D elemental structures. Univ. of Minnesota Supercomputer Institute Report UMSI 90/73.

  Google Scholar 

• Saito, H. and Scriven, L. E. 1981. Study of a coating flow by the finite element method. J. Comput. Phys. 42: 53–76.

  Article  Google Scholar 

• Salamon, T. R., Armstrong, R. C. and Brown, R. A. 1992. Modification of inertial film instability by viscoelasticity. In Theoretical and Applied Rheology (Proc. XIth Intl. Congr. Rheology, Brussels, Belgium, August 17–21, 1992), eds P. Moldenaers and R. Keunings, pp.213–215. Amsterdam: Elsevier.

  Google Scholar 

• Savage, M. D. 1977a. Cavitation in lubrication. Part 1. On boundary conditions and cavity-fluid interfaces. J. Fluid Mech. 80: 743–755.

  Article  Google Scholar 

• Savage, M. D. 1977b. Cavitation in lubrication. Part 2. Analysis of wavy interfaces. J. Fluid Mech. 80: 757–767.

  Article  Google Scholar 

• Scanlan, D. J. 1990. Two-slot coater analysis: inner layer separation issues in two-layer coating. MS thesis, University of Minnesota, Minneapolis.

  Google Scholar 

• Schunk, P. R. 1989. Surfactant and polymer effects in coating and related flows. PhD thesis, University of Minnesota, Minneapolis.

  Google Scholar 

• Schunk, P. R. and Scriven, L. E. 1990. Constitutive equation for modeling mixed extension and shear in polymer solution processing. J. Rheol. 34: 1085–1119.

  Article  Google Scholar 

• Schwetlick, H. 1984. Algorithms for finite-dimensional turning point problems from viewpoint to relationships with constrained optimization methods. In Numerical Methods for Bifurcation Problems, Intl. Series Numer. Math., Vol. 70, eds T. Kuepper, H. D. Mittelmann and H. Weber, pp.459–479. Basel: Birkhaeuser.

  Google Scholar 

• Sethian, J. 1984. Turbulent combustion in open and closed vessels. J. Comput. Phys. 54: 425–456.

  Article  Google Scholar 

• Sethian, J. A. and Strain, J. 1992. Crystal growth and dendritic solidification. J.Comput.Phys. 98:231–253.

  Article  CAS  Google Scholar 

• Shanks, S. P. and Thompson, J. F. 1977. Numerical solution of the Navier-Stokes equations for 2D hydrofoils in or below a free surface. In Proc. 2nd Intl. Conf Numerical Ship Hydrodynamics, pp. 202–220. Berkeley: Univ. of Calif. Extension Publ.

  Google Scholar 

• Shokoohi, F. and Elrod, H. G. 1987. Numerical investigation of the disintegration of liquid jets. J. Comput. Phys. 71: 324–341.

  Article  CAS  Google Scholar 

• Shopov, P. J. and Bazhlekov, I. B. 1991. Numerical method for viscous hydrodynamic problems with dynamic contact lines. Comput. Meth. Appl. Mech. Eng. 91: 1157–1174.

  Article  Google Scholar 

• Shopov, P. J., Minev, P. D. and Bazhlekov, I. B. 1992. Numerical method for unsteady viscous hydrodynamical problems with free boundaries. Int. J. Numer. Meth. Fluids. 14: 681--705.

  Article  CAS  Google Scholar 

• Sicilian, J. M. and Hirt, C. W. 1984. HYDR-3D: a solution algorithm for transient 3D flows. Flow Science (Flow Science Inc., Los Alamos, NM) Report FSI-81–00–1.

  Google Scholar 

• Silliman, W. J. and Scńven, L. E. 1980. Separating flow near a static contact line: slip at a wall and shape of a free surface. J. Comput. Phys. 34: 287–313.

  Article  CAS  Google Scholar 

• Smith, R. E. 1982. Algebraic grid generation. Appl. Math. Comput. 10-11: 137–170.

  Article  Google Scholar 

• Sonneveld, P. 1989. CGS: a fast, Lanczos-type solver for nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 10: 36–52.

  Article  Google Scholar 

• Sonneveld, P., Wesseling, P. and de Zeeuw, P. M. 1985. Multigrid and conjugate gradient methods as convergence acceleration techniques. In Multigrid Methods for Integral and Differential Equations, eds D. J. Paddon and H. Holstein, pp. 117–167. Oxford: Clarendon Press.

  Google Scholar 

• Soulaïmani, A., Fortin, M., Dhatt, G. and Quellet, Y. 1991. Finite element simulation of two-and three-dimensional free-surface flows. Comput. Meth. Appl. Mech. Eng. 86: 265–296.

  Article  Google Scholar 

• Souvaliotis, A. and Beris, A. N. 1992. Application of domain decomposition spectral collocation methods in viscoelastic flows through model porous media. J. Rheol. 36: 1417–1453.

  Article  CAS  Google Scholar 

• Stewart, G. W. 1978. SRRIT - a FORTRAN subroutine to calculate the dominant invariant subspaces of a real matrix. University of Maryland Computer Science Center (College Park) Technical Report TR-514, ONR-N00014–76-C-0391.

  Google Scholar 

• Strang, G. and Fix, G. 1973. An Analysis of the Finite Element Method. Englewood Cliffs, NJ: Prentice Hall.

  Google Scholar 

• Strigberger, J., Baruzzi, G., Habashi, W. and Fortin, M. 1993. Some special purpose preconditioners for conjugate gradient-like methods applied to CFD. Int. J. Numer. Meth. Fluids. 16: 581--596.

  Article  Google Scholar 

• Subbiah, S., Trafford, D. L. and Güçeri, S. I. 1989. Non-isothermal flow of polymers into two-dimensional, thin cavity molds: a numerical grid-generation approach. Int. J. Heat Mass Transfer. 32: 415–434.

  Article  CAS  Google Scholar 

• Tabata, M. and Morishita, A. 1989. Fractional step finite element scheme for free boundary problems. Theor. Appl. Mech. 39: 251–257.

  Google Scholar 

• Tanner, R. I. and Milthorpe, J. F. 1983. Numerical simulation of the flow of fluid with yield stresses. In Numerical Methods in Laminar and Turbulent Flow (Proc. 3rd Intl. Conf), eds C. Taylor, J. A. Johnson and W. R. Smith, pp.680–690. Swansea: Pineridge Press.

  Google Scholar 

• Tanzosh, J., Manga, M. and Stone, H. A. 1992. Boundary integral methods for viscous free-boundary problems: deformation of single and multiple fluid-fluid interfaces. In Proc. 7th Intl. Conf. Boundary Element Technology, Vol. VII, eds C. A. Brebbia and M. S. Ingber, pp.19–39. Southampton, England: Computational Mechanics Publications.

  Google Scholar 

• Tezduyar, T. E., Behr, M. and Liou, J. 1992. A new strategy for finite-element computations involving moving boundaries and interfaces - the deformingspatial-domain/space-time procedure: I. The concept and the preliminary numerical tests. Comput. Meth. Appl. Mech. Eng. 94: 339–351.

  Article  Google Scholar 

• Tezduyar, T. E., Behr, M., Mittal, S. and Liou, J. 1992. A new strategy for finite-element computations involving moving boundaries and interfaces - the deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows and flows with drifting cylinders. Comput. Meth. Appl. Mech. Eng. 94: 353--371.

  Article  Google Scholar 

• Thomas, P. D. 1982. Composite three-dimensional grids generated by elliptic systems. AIAA J. 20: 1195–1202.

  Article  Google Scholar 

• Thomas, P. D. and Brown, R. A. 1987. LU decomposition of matrices with augmented dense constraints. Int. J. Numer. Meth. Eng. 24: 1451–1459.

  Article  Google Scholar 

• Thomas, P. D. and Middlecoff, J. F. 1980. Direct control of the grid point distribution in meshes generated by elliptic equations. AIAA J. 18: 652–656.

  Article  Google Scholar 

• Thompson, E. G. 1986. Use of pseudo-concentrations to follow creeping viscous flow during transient analysis. Int. J. Numer. Meth. Fluids. 6: 749–761.

  Article  Google Scholar 

• Thompson, J. F., Thomas, F. C. and Mastin, C. W. 1974. Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies. J. Comput. Phys. 15: 299–319.

  Article  Google Scholar 

• Thompson, J. F., Warsi, U. A. and Mastin, C. W. 1982. Boundary-fitted coordinate systems for numerical solution of partial differential equations - a review. J. Comput. Phys. 47: 1–108.

  Article  Google Scholar 

• Thompson, J. F., Warsi, Z. U. A. and Mastin, W. C. 1985. Numerical Grid Generation. New York: Elsevier.

  Google Scholar 

• Tilton, J. N. 1988. The steady motion of an interface between two viscous liquids in a capillary tube. Chem. Eng. Sci. 43: 1371–1384.

  Article  CAS  Google Scholar 

• Torrey, M. D., Cloutman, L. D., Mjolsness, R. C. and Hirt, C. W. 1985. NASA-VOF2D: A computer program for incompressible flows with free surfaces. Los Alamos National Laboratory Report. LA-10612-MS.

  Google Scholar 

• Tran-Cong, T. and Phan-Tien, N. 1988a. Three-dimensional study of extrusion processes by boundary element method. I. An implementation of high-order elements and some Newtonian results. Rheol. Acta. 27: 21–30.

  Article  CAS  Google Scholar 

• Tran-Cong, T. and Phan-Thien, N. 1988b. Three-dimensional study of extrusion processes by boundary element method. II. Extrusion of a viscoelastic fluid. Rheol. Acta. 27: 639–648.

  Article  CAS  Google Scholar 

• Tryggvason, G. 1988. Numerical simulation of the Rayleigh-Taylor instability. J. Comput. Phys. 75:253–282.

  Article  CAS  Google Scholar 

• Tsiveriotis, K. and Brown, R. A. 1992. Boundary-conforming mapping applied to computations of highly deformed solidification interfaces. Int. J. Numer. Meth. Fluids. 14: 981–1003.

  Article  CAS  Google Scholar 

• Tsiveriotis, K. and Brown, R. A. 1993. Solution of free-boundary problems using finite-element/Newton methods and locally refined grids: application to analysis of solidification microstructure. Int. J. Numer. Meth. Fluids. 16: 827–843.

  Article  CAS  Google Scholar 

• Ungar, L. H. and Brown, R. A. 1982. The dependence of the shape and stability of rotating captive drops on multiple parameters. Philos. Trans. Roy. Soc. Lond. A306: 457–480.

  Google Scholar 

• Ungar, L. H. and Brown, R. A. 1985. Cellular interface morphologies in directional solidification. IV. The formation of deep cells. Phys. Rev. B. 31: 5931–5940.

  Article  CAS  Google Scholar 

• Ungar, L. H., Ramprasad, N. and Brown, R. A. 1988. Finite element methods for unsteady solidification problems arising in prediction of morphological structure. J. Sci. Comput. 3: 77–108.

  Article  Google Scholar 

• Unverdi, S. O. and Tryggvason, G. 1992. A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100: 25–37.

  Article  Google Scholar 

• Van Abbenyen, W., Christodoulou, K. N. and Scriven, L. E. 1989. Frequency response of a coating flow: predictions for slide coating. University of Minnesota Supercomputer Center Report UMSI 89/40.

  Google Scholar 

• Van Abbenyen, W., Goetmaeckers, B., Van de Vijver, H., Bussmann, H. and Beck, D. 1990. Experimental verification of the calculated frequency response of a multilayer slide-coating operation. Paper read at AIChE Spring National Meeting,Orlando, FL, March 19–22.

  Google Scholar 

• Van der Vorst, H. A. 1992. Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13: 631–644.

  Article  Google Scholar 

• Visbal, M. and Knight, D. 1982. Generation of orthogonal and nearly orthogonal coordinates with grid control near boundaries. AIAA J. 20: 305–306.

  Article  Google Scholar 

• Voinov, O. V. 1976. Hydrodynamics of wetting. Fluid Dynamics. 11: 714–721.

  Article  Google Scholar 

• Wambersie, D. and Crochet, M. J. 1992. Transient finite element method for calculating steady state three-dimensional free surface flows. Int. J. Numer. Meth. Fluids. 14: 343–360.

  Article  CAS  Google Scholar 

• Wang, H. P. and Lee, H. S.1989. Numerical techniques for free and moving boundary problems. In Funda-mentals of Computer Modeling for Polymer Processing, ed. C. L. Tucker, pp. 369–401. Munich, Vienna and New York: Hanser Publishers.

  Google Scholar 

• Wang, H. P. and McLay, R. T. 1986. Automatic remeshing scheme for modeling hot forming process. J. Fluid Eng. (ASME) 108: 465–469.

  Article  Google Scholar 

• Weatherburn, C. E. 1927. Differential Geometry of Three Dimensions. London: Cambridge Univ. Press.

  Google Scholar 

• Werner, B. and Spence, A. 1984. The computation of symmetry-breaking bifurcation points. SIAM J. Numer. Anal. 2: 388–399.

  Article  Google Scholar 

• Wilkinson, J. H. 1965. The Algebraic Eigenvalue Problem. Oxford: Clarendon Press.

  Google Scholar 

• Winslow, A. M. 1967. Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh. J. Comput. Phys. 2: 149–172.

  Google Scholar 

• Winters, K. H., Cliffe, K. A. and Jackson, C. P. 1987. The prediction of instabilities using bifurcationtheory. In Numerical Methods for Transient and Coupled Problems, eds R. W. Lewis, E. Hinton, P. Bettess and B. A. Schrefler, pp. 179–198. New York: Wiley.

  Google Scholar 

• Yiantsios, S. G. and Higgins, B. G. 1989. study for shear-thinning flow problems. Int. J. Numer. Meth. Fluids 8: 121–133.

  Google Scholar 

• Katagiri, Y. 1992. Analysis of edge effects in curtain coating. Paper read at AIChE Spring National Meeting, New Orleans, LA, March 29-April 2.

  Google Scholar 

• Katagiri, Y. and Scriven, L. E. 1986. Supercomputer-aided analysis of transient response of a coating operation. Paper read at AIChE Annual Meeting, Miami Beach, FL, November 2–7.

  Google Scholar 

• Keller, H. B. 1977. Numerical solution of bifurcation and nonlinear eigenvalue problems. In Applications of Bifurcation Theory,ed. P. H. Rabinowitz, pp. 45–52. New York: Academic Press.

  Google Scholar 

• Kelmanson, M. A. 1983. Boundary integral equation solution of viscous flows with free surfaces. J. Eng. Math. 17: 329–343.

  Article  Google Scholar 

• Keunings, R. 1986. An algorithm for the simulation of transient viscoelastic flows with free boundaries. J. Comput. Phys. 62: 199–220.

  Article  Google Scholar 

• Keunings, R. 1989. Simulation of viscoelastic flow. In Fundamentals of Computer Modeling for Polymer Processing, ed. C. L. Tucker, pp.403–469. Munich: Hanser.

  Google Scholar 

• Keunings, R. 1991. Progress and challenges in computational rheology. Rheol. Acta. 29: 556–570.

  Article  Google Scholar 

• Kheshgi, H. S. and Scriven, L. E. 1984. Penalty finite-element analysis of unsteady free-surface flows. In Finite Elements in Fluids, Volume 5, eds R. H. Gallagher, J. T. Oden, O. C. Zienkiewicz, T. Kawai and M. Kawahara, pp. 393–434. New York: John Wiley.

  Google Scholar 

• Kheshgi, H. S. and Scriven, L. E. 1985. Variable penalty method for finite element analysis of incompressible flow. Int. J. Numer. Meth. Fluids. 5: 785–803.

  Article  Google Scholar 

• Kheshgi, H. S. and Scriven, L. E. 1988. The evolution of disturbances in horizontal films. Chem. Eng. Sci. 43: 793–801.

  Article  CAS  Google Scholar 

• Kikuchi, N., Chung, K. Y., Torigaki, T. and Taylor, J. E. 1986. Adaptive finite element methods for shape optimization of linearly elastic structures. Comput. Meth. Appl. Mech. Eng. 57: 67–89.

  Article  Google Scholar 

• King, R. C., Apelian, M. N., Armstrong, R. C. and Brown, R. A. 1988. Numerically stable finite element techniques for viscoelastic calculations in smooth and singular geometries. J. Non-Newt. Fluid Mech. 29: 147–216.

  Article  CAS  Google Scholar 

• Kistler, S. F. 1984. The fluid mechanics of curtain coating and other related viscous free surface flows with contact lines. PhD thesis, University of Minnesota, Minneapolis.

  Google Scholar 

• Kistler, S. F. 1993. The hydrodynamics of wetting. In Wettability, ed. J. C. Berg, pp.311–429. New York: Marcel Dekker.

  Google Scholar 

• Kistler, S. F. and Palmquist, K. E. 1990. A simple, algebraic finite-element discretization of free surface flows. Paper read at AIChE Spring National Meeting, Orlando, FL, March 18–22.

  Google Scholar 

• Kistler, S. F. and Scriven, L. E. 1983. Coating flows. In Computational Analysis of Polymer Processing, eds J. R. A. Pearson, and S. M. Richardson, pp. 243–299. London and New York: Applied Science Publishers.

  Chapter  Google Scholar 

• Kistler, S. F. and Scriven, L. E. 1984. Coating flow theory by finite-element and asymptotic analysis of the Navier-Stokes system. Int. J. Numer. Meth. Fluids. 4: 207–229.

  Article  Google Scholar 

• Kistler, S. F. and Scriven, L. E. 1994. The teapot effect: sheet forming flows with deflection, wetting, and hysteresis. J. Fluid Mech. 263: 19–62.

  Article  CAS  Google Scholar 

• Kistler, S. F. and Zvan, G. 1991. Hydrodynamic models of forced wetting in coating flows. Paper read at 44th IS&T Conference, St Paul, MN, May 12–17.

  Google Scholar 

• Kreis, R. I., Thames, F. C. and Hassan, H. A. 1986. Application of a variational method for generating adaptive grids. AIAA J. 24: 404–410.

  Article  Google Scholar 

• Kruyt, N. P., Cuvelier, C., Segal, A. and van der Zanden, J. 1988. A total linearization method for solving viscous free boundary flow problems by the finite element method. Int. J. Numer. Meth. Fluids. 8: 351–363.

  Article  Google Scholar 

• Ladyzhenskaya, O. A. 1963. The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach.

  Google Scholar 

• Lee, S. H. and Leal, L. G. 1982. The motion of a sphere in the presence of a deformable interface. II. A numerical study of the translation of a sphere normal to an interface. J. Colloid Interface Sci. 87: 81–106.

  Article  Google Scholar 

• Legat, V. and Marchal, J.-M. 1992. Prediction of three-dimensional general shape extrudates by an implicit iterative scheme. Int. J. Numer. Meth. Fluids. 14: 609–625.

  Article  CAS  Google Scholar 

• Leonard, A. 1985. Computing three-dimensional incompressible flows with vortex elements. Ann. Rev. Fluid Mech. 17: 523–559.

  Article  Google Scholar 

• Liang, P. Y. 1991. Numerical method for calculation of surface tension flows in arbitrary grids. AL4А J. 29: 161–167.

  CAS  Google Scholar 

• Lin, S. P., Lian, Z. W. and Creighton, B. J. 1990. Absolute and convective instability of a liquid sheet. J. Fluid Mech. 220: 673–689.

  Article  CAS  Google Scholar 

• Lin, S. P. and Roberts, G. 1981. Waves in a viscousliquid curtain. J. Fluid Mech. 112: 443–458.

  Article  CAS  Google Scholar 

• Liou, J. and Tezduyar, T. E. 1991. Computation of compressible and incompressible flows with the Rayleigh—Taylor instability in thin viscous films. Phys. Fluids A — Fluid Dynamics. 1: 1484–1501.

  Google Scholar 

• Yokoi, T. and Scriven, L. E. 1989.Profile extrusion analyzed and die shape designed by Galerkin’s method with streamline-adapted basis functions. University of Minnesota Supercomputer Institute Report UMSI 89/65.

  Google Scholar 

• Youngren, G. K. and Acrivos, A. 1976.On the shape of a gas bubble in a viscous extensional flow. J. Fluid Mech. 76:433–442.

  Article  Google Scholar 

• Youngs, D. L. 1982 Time-dependent multi-material flow with large fluid distortion. In Numerical Methods for Fluid Mechanics, eds K. W. Morton and M. J. Banes, pp.273–285. New York: Academic Press.

  Google Scholar 

• Yuan, Y. and Ingham, D. B. 1991. Numerical solution of viscous flows with a free surface. In Computational Modeling of Free and Moving Boundary Problems (Proc. 1st Intl. Conf.),eds L. C. Wrobel and C. A. Brebbia, pp. 325–339. Southampton, UK: Computational Mechanics Publ.

  Google Scholar 

• Zhou, M.-Y. and Sheng, P. 1990. Dynamics of immiscible-fluid displacement in a capillary tube. Phys. Rev. Lett. 64:882–885.

  Article  Google Scholar 

• Zienkiewicz, O. C. 1977. The Finite Element Method. London: McGraw-Hill.

  Google Scholar 

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