Accurate boundary conditions for exterior problems in gas dynamics
HTML articles powered by AMS MathViewer
- by Thomas Hagstrom and S. I. Hariharan PDF
- Math. Comp. 51 (1988), 581-597 Request permission
Abstract:
The numerical solution of exterior problems is typically accomplished by introducing an artificial, far field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that ’natural’ reflections may be important. We propose a reflecting boundary condition based on an asymptotic solution of the far field equations. We obtain nonlinear energy estimates for the truncated problem and present numerical experiments to validate our theory.References
- Alvin Bayliss and Eli Turkel, Radiation boundary conditions for wave-like equations, Comm. Pure Appl. Math. 33 (1980), no. 6, 707–725. MR 596431, DOI 10.1002/cpa.3160330603
- Bjorn Engquist and Andrew Majda, Absorbing boundary conditions for the numerical simulation of waves, Math. Comp. 31 (1977), no. 139, 629–651. MR 436612, DOI 10.1090/S0025-5718-1977-0436612-4
- Bertil Gustafsson and Heinz-Otto Kreiss, Boundary conditions for time-dependent problems with an artificial boundary, J. Comput. Phys. 30 (1979), no. 3, 333–351. MR 529999, DOI 10.1016/0021-9991(79)90119-0
- Bertil Gustafsson, Inhomogeneous conditions at open boundaries for wave propagation problems, Appl. Numer. Math. 4 (1988), no. 1, 3–19. MR 932316, DOI 10.1016/S0168-9274(88)80003-5
- Bertil Gustafsson, Far-field boundary conditions for time-dependent hyperbolic systems, SIAM J. Sci. Statist. Comput. 9 (1988), no. 5, 812–828. MR 957473, DOI 10.1137/0909054
- Thomas Hagstrom and H. B. Keller, Exact boundary conditions at an artificial boundary for partial differential equations in cylinders, SIAM J. Math. Anal. 17 (1986), no. 2, 322–341. MR 826697, DOI 10.1137/0517026
- S. I. Hariharan and Alvin Bayliss, Radiation of sound from unflanged cylindrical ducts, SIAM J. Sci. Statist. Comput. 6 (1985), no. 2, 285–296. MR 779406, DOI 10.1137/0906021
- G. W. Hedstrom, Nonreflecting boundary conditions for nonlinear hyperbolic systems, J. Comput. Phys. 30 (1979), no. 2, 222–237. MR 528200, DOI 10.1016/0021-9991(79)90100-1
- Gary A. Sod, Numerical methods in fluid dynamics, Cambridge University Press, Cambridge, 1985. Initial and initial-boundary value problems. MR 832441, DOI 10.1017/CBO9780511753138
- Kevin W. Thompson, Time-dependent boundary conditions for hyperbolic systems, J. Comput. Phys. 68 (1987), no. 1, 1–24. MR 887804, DOI 10.1016/0021-9991(87)90041-6
- G. B. Whitham, Linear and nonlinear waves, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. MR 0483954
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Math. Comp. 51 (1988), 581-597
- MSC: Primary 65M99; Secondary 76N99
- DOI: https://doi.org/10.1090/S0025-5718-1988-0935075-7
- MathSciNet review: 935075