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On boundary conditions for the numerical solution of fluid dynamic problems. (English) Zbl 0708.76045
Summary: The stability and accuracy of various boundary treatments are analyzed for a finite difference scheme proposed by the author for the numerical solution of problems in fluid dynamics. The theory of B. Gustafsson, H.-O. Kreiss and A. Sundström [Math. Comput. 26, 649-686 (1972; Zbl 0293.65076)] is used to establish stability and the theory of G. Skollermo [Math. Comput. 23, 11-35 (1979)] is used to compare the accuracy of the various methods. The accuracy predictions are compared with computed results.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
76M10 Finite element methods applied to problems in fluid mechanics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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[1] H. O. Kreiss,Stability Theory for Difference Approximations of Mixed Initial Boundary Value Problems I, Math. Comp., 22, (1968) 703–714. · Zbl 0197.13704 · doi:10.1090/S0025-5718-1968-0241010-7
[2] B. Gustafsson, H. O. Kreiss, A. Sundstrom,Stability Theory of Difference Approximations for Mixed Initial Boundary Value Problems II, Math. Comp., 26 (1972) 649–686. · Zbl 0293.65076 · doi:10.1090/S0025-5718-1972-0341888-3
[3] J. Oliger,Fourth Order Difference Methods for the Initial Boundary-Value Problem for Hyperbolic Equations, Math. Comp., 28 (1974) 15–25. · Zbl 0284.65074 · doi:10.1090/S0025-5718-1974-0359344-7
[4] C. K. Chu, A. Sereny,Boundary Conditions in Finite Difference Fluid Dynamic Codes, J. Comput. Phys., 15 (1974) 476–491. · Zbl 0286.76028 · doi:10.1016/0021-9991(74)90074-6
[5] A. Sundstrom,Note on the Paper Boundary Conditions in Finite Difference Fluid Dynamic Codes, by C. K. Chu and A. Sereny, J. Comput. Phys. 17 (1975) 450–454. · doi:10.1016/0021-9991(75)90050-9
[6] D. Gottlieb, E. Turkel,Boundary Conditions for Multistep Finite Difference Methods for Time-Dependent Equations, J. Comput. Phys., 26 (1978) 181–196. · Zbl 0388.65039 · doi:10.1016/0021-9991(78)90090-6
[7] D. M. Sloan,On Boundary Conditions for the Numerical Solution of Hyperbolic Differential Equations, Internat. J. Numer. Methods. Engrg., 15 (1980) 1113–1127. · Zbl 0457.65069 · doi:10.1002/nme.1620150802
[8] A. Murli, M. A. Pirozzi,A Numerical Model for Tsunami Generation and Propagation, Ricerche di Matematica (to appear). · Zbl 0721.76009
[9] G. Skollermo,Error Analysis of Finite Difference Schemes applied to Hyperbolic Initial Boundary Value Problems, Math. Comp., 33 (1979) 11–35. · Zbl 0403.65038 · doi:10.2307/2006025
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