Grid overlapping for implicit parallel computation of compressible flows. (English) Zbl 0960.76062
Summary: We investigate the suitability of applying the overlapping grid method to parallel computation of steady and unsteady compressible inviscid flows with three-point block-tridiagonal implicit schemes. An easily usable interface treatment is constructed and analyzed for both steady and unsteady problems. The performance of the method, such as convergence rate and time accuracy, can be controlled through the overlapping width. The method needs no iteration at each time step or modification of Thomas algorithm for the solution of the implicit parts. In both steady and unsteady cases, we demonstrate good absolute parallel efficiency for two-dimensional subsonic and transonic flow computations.
MSC:
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 76N15 | Gas dynamics (general theory) |
| 65Y05 | Parallel numerical computation |
Keywords:
overlapping interface condition; subsonic flow; overlapping grid method; parallel computation; compressible inviscid flows; three-point block-tridiagonal implicit schemes; convergence rate; accuracy; transonic flowSoftware:
CMPGRDReferences:
| [1] | Berger, M., On conservation at grid interfaces, SIAM J. Numer. Anal., 24, 967 (1987) · Zbl 0633.65086 |
| [2] | Chan, T. F.; Goovearts, D., Schwarz-Schur, Overlapping versus Non-overlapping Domain Decomposition (1988) |
| [3] | Chesshire, G.; Henshaw, D., Composite overlapping meshes for the solution of partial differential equations, J. Comput. Phys., 90, 1 (1990) · Zbl 0709.65090 |
| [4] | Chesshire, G.; Henshaw, D., A scheme for conservative interpolation on overlapping grids, SIAM J. Sci. Comput., 15, 819 (1994) · Zbl 0805.65086 |
| [5] | De-Spiegeleer, G.; Lerat, A.; N. Wu, Z., Implicit multidomain computation of compressible flows with a large number of subdomains, Comput. Fluid Dynam. J., 7, 245 (1998) |
| [6] | Gustafsson, B.; Kreiss, H.-O.; Sundström, A., Stability theory of difference approximations for initial boundary value problems, II, Math. Comput., 26, 649 (1972) · Zbl 0293.65076 |
| [7] | Gustafsson, B., The Euler and Navier-Stokes equations: Wellposedness, stability and composite grids, Computational Fluid Dynamics (February 18-22, 1991) |
| [8] | Gustafsson, B., The choice of numerical boundary conditions for hyperbolic systems, J. Comput. Phys., 48, 270 (1982) · Zbl 0495.65045 |
| [9] | Gustafsson, B., The convergence rate for difference approximations to general mixed initial boundary value problem, SIAM J. Numer. Anal., 18, 179 (1981) · Zbl 0469.65068 |
| [10] | Keyes, D. E., Domain Decomposition: A Bridge between Nature and Parallel Computers (1992) |
| [11] | Kreiss, H.-O; Lorenz, J., Initial-Boundary Value Problems and the Navier-Stokes Equations (1989) · Zbl 0689.35001 |
| [12] | Lerat, A., Multidimensional centered schemes of the Lax-Wendroff type, CFD Review, 124 (1995) · Zbl 0875.76363 |
| [13] | Lerat, A.; Sidès, J., Numerical simulation of unsteady transonic flows using the Euler equations in integeral form, Israel J. Tech., 17, 302 (1979) · Zbl 0458.76047 |
| [14] | Lerat, A.; Wu, Z. N., Stable conservative multidomain treatments for implicit Euler solvers, J. Comput. Phys., 123, 45 (1996) · Zbl 0839.76065 |
| [15] | Osher, S., Stability of difference equations of dissipative type for mixed initial-boundary value problems, I, Math. Comput., 23, 235 (1969) · Zbl 0177.20403 |
| [16] | Pärt-Enander, E.; Sjögreen, B., Conservative and nonconservative interpolation between overlapping grids for finite volume solutions of hyperbolic problems, Comput. & Fluids, 23, 551 (1994) · Zbl 0813.76071 |
| [17] | Roose, D.; Driessche, R. V., Parallel computers and parallel algorithms for CFD: An introduction, AGARD-R-807, 1 (1995) |
| [18] | Sawley, M. L.; Tegnér, J. K., A comparison of parallel programming models for multiblock flow computations, J. Comput. Phys., 122, 280 (1995) · Zbl 0839.76070 |
| [19] | Thuné, M., Stability of Difference Approximations of Hyperbolic Systems on Substructured Domains (December 1986) |
| [20] | Wang, H., A parallel solver for tridiagonal solvers, ACM Trans. Math. Software, 7, 170 (1981) · Zbl 0473.65010 |
| [21] | Wu, Z. N., Convergence study of an implict multidomain method for compressible flow computations, Comput. & Fluids, 25, 181 (1996) · Zbl 0869.76060 |
| [22] | Wu, Z. N., Uniqueness of steady state solutions for difference equations on overlapping grids, SIAM J. Numer. Anal., 33, 1336 (1996) · Zbl 0859.65090 |
| [23] | Wu, Z. N., Steady and unsteady shock waves on overlapping grids, SIAM J. Sci. Comput., 20, 1851 (1999) · Zbl 0940.65096 |
| [24] | Zhang, H. X.; Zhuang, F. G., NND schemes and their applications to numerical simulations of two- and three-dimensional flows, Adv. Appl. Mech., 29, 193 (1992) · Zbl 0749.76050 |
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.
