Distributed Lagrange multiplier methods for incompressible viscous flow around moving rigid bodies. (English) Zbl 0916.76052
Summary: We discuss the application of a distributed Lagrange multiplier based fictitious domain method to the numerical simulation of incompressible viscous flow around moving bodies modelled by the Navier-Stokes equations. We suppose that the rigid bodies motion is known a priori. The solution method combines finite element approximations, time discretization by operator splitting, and conjugate gradient algorithms for the solution of linearly constrained quadratic minimization problems coming from the splitting method. Numerical results are presented for two-dimensional flow around a moving disk.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76M30 | Variational methods applied to problems in fluid mechanics |
Keywords:
two-dimensional flow around moving disk; operator splitting; conjugate gradient algorithms; linearly constrained quadratic minimization problemsReferences:
| [1] | Glowinski, R.; Périaux, J.; Ravachol, M.; Pan, T. W.; Wells, R. O.; Zhou, X., Wavelet methods in computational fluid dynamics, (Hussainy, M. Y.; etal., Algorithmic Trends in Computational Fluid Dynamics (1993), Springer-Verlag: Springer-Verlag NY), 259-276 |
| [2] | Glowinski, R.; Pan, T. W.; Wells, R. O.; Zhou, X., Wavelet and finite element solutions for the Neumann problem using fictitious domains, J. Comput. Phys., 126, 40-51 (1996) · Zbl 0852.65098 |
| [3] | F. Collino, P. Joly and F. Millot, Fictitious domain method for unsteady problems: application to Electro-Magnetic scattering (to appear).; F. Collino, P. Joly and F. Millot, Fictitious domain method for unsteady problems: application to Electro-Magnetic scattering (to appear). · Zbl 0870.65123 |
| [4] | Glowinski, R.; Pan, T. W.; Périaux, J., A fictitious domain method for Dirichlet problems and applications, Comput. Methods Appl. Mech. Engrg., 111, 283-303 (1994) · Zbl 0845.73078 |
| [5] | Glowinski, R.; Pan, T. W.; Périaux, J., A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 112, 133-148 (1994) · Zbl 0845.76069 |
| [6] | Glowinski, R.; Pan, T. W.; Périaux, J., A Lagrange multiplier/fictitious domain method for the Dirichlet problem. Generalization to some flow problems, Japan J. Ind. Appl. Math., 12, 87-108 (1995) · Zbl 0835.76047 |
| [7] | Glowinski, R.; Kearsley, A. J.; Pan, T. W.; Périaux, J., Numerical simulation and optimal shape for viscous flow by fictitious domain method, Int. J. Numer. Methods in Fluids, 20, 695-711 (1995) · Zbl 0837.76068 |
| [8] | Astrakhantsev, G. P., Fictitious domain methods for second order elliptic equations with natural boundary conditions, Zh. Vychisl. Mat. Mat. Fiz., 18, 118-125 (1978) · Zbl 0382.35022 |
| [9] | Matsokin, A. M.; Nepomnyaschikh, S. V., The fictitious domain method and explicit continuation operators, Zh. Vychisl. Mat. Mat. Fiz., 33, 45-59 (1993) · Zbl 0803.65117 |
| [10] | Nepomnyaschikh, S. V., Fictitious space method on unstructured meshes, East-West J. Num. Math., 3, 71-79 (1995) · Zbl 0831.65116 |
| [11] | Buzbee, B. L.; Dorr, F. W.; George, J. A.; Golub, G. H., The direct solution of the discrete Poisson equation on irregular regions, SIAM J. Num. Anal., 8, 722-736 (1971) · Zbl 0231.65083 |
| [12] | Peskin, C. Y.; McQueen, D. M., A three-dimensional computational method for blood flow in the heart: I. Immersed elastic fibers in a viscous incompressible fluid, J. Comp. Phys., 81, 372-405 (1989) · Zbl 0668.76159 |
| [13] | Leveque, R.; Li, Z., The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Num. Anal., 31, 1019-1044 (1994) · Zbl 0811.65083 |
| [14] | Cahouet, J.; Chabard, J. P., Some fast 3-D finite element solvers for the generalized Stokes problem, Int. J. Numer. Methods in Fluids, 8, 869-895 (1988) · Zbl 0665.76038 |
| [15] | Bristeau, M. O.; Glowinski, R.; Périaux, J., Numerical methods for the Navier-Stokes equations. Applications to the simulation of compressible and incompressible viscous flow, Comp. Phys. Rep., 6, 73-187 (1987) |
| [16] | Glowinski, R., Finite element methods for the numerical simulation of incompressible viscous flow. Introduction to the control of the Navier-Stokes equations, (Anderson, C. R.; etal., Vortex Dynamics and Vortex Methods. Vortex Dynamics and Vortex Methods, Lectures in Applied Mathematics, 28 (1991), AMS: AMS Providence, R.I), 219-301 · Zbl 0751.76046 |
| [17] | Glowinski, R.; Le Tallec, P., Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics (1989), SIAM: SIAM Philadelphia · Zbl 0698.73001 |
| [18] | Glowinski, R., Ensuring well-posedness by analogy; Stokes problem and boundary control for the wave equation, J. Comp. Phys., 103, 189-221 (1989) · Zbl 0763.76042 |
| [19] | Glowinski, R.; Pironneau, O., Finite element methods for Navier-Stokes equations, Annu. Rev. Fluid Mech., 24, 167-204 (1992) · Zbl 0743.76051 |
| [20] | Turek, S., A comparative study of time-stepping techniques for the incompressible Navier-Stokes equations: From fully implicit non-linear schemes to semi-implicit projection methods, Int. J. Numer. Math. in Fluids, 22, 987-1011 (1996) · Zbl 0864.76052 |
| [21] | Amiez, G.; Gremaud, P. A., On a penalty method for the Navier-Stokes problem in regions with moving boundaries, Comp. Appl. Math., 12, 113-122 (1993) · Zbl 0803.76027 |
| [22] | Marchuk, G. I., Splitting and alternate direction methods, (Ciarlet, P. G.; Lions, J. L., Handbook of Numerical Analysis, Vol. I (1990), North-Holland: North-Holland Amsterdam), 197-462 · Zbl 0875.65049 |
| [23] | Glowinski, R., Numerical Methods for Nonlinear Variational Problems (1984), Springer-Verlag: Springer-Verlag New York · Zbl 0575.65123 |
| [24] | Glowinski, R.; Hesla, T.; Joseph, D. D.; Pan, T. W.; Périaux, J., Distributed Lagrange multiplier methods for particulate flows, (Périaux, J., Computational Science for the 21st Century (1997), John Wiley & Sons: John Wiley & Sons Chichester), to appear · Zbl 0919.76077 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
