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Absorbing boundary conditions for the linearized Euler equations in $ 2$-D


Author: Dietmar Kröner
Journal: Math. Comp. 57 (1991), 153-167
MSC: Primary 65N99; Secondary 76M25, 76N15
DOI: https://doi.org/10.1090/S0025-5718-1991-1079023-0
MathSciNet review: 1079023
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Abstract: In this paper we shall derive some approximate absorbing boundary conditions for the initial value problem for the unsteady linearized Euler equations in 2-D. Since we assume that the coefficients of the system are constant, we can describe the transformation of the system to a decoupled system of ODE's and the related absorbing boundary conditions explicitly. We shall verify the usefulness of these boundary conditions in some numerical tests for the nonlinear Euler equations in 2-D.


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  • [1] A. Bayliss and E. Turkel, Outflow boundary conditions for fluid dynamics, J. Comput. Phys. 48 (1982), 182-199. MR 683520 (83k:76003)
  • [2] B. Engquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves, Math. Comp. 31 (1977), 629-651. MR 0436612 (55:9555)
  • [3] L. Ferm, Open boundary conditions for external flow problems, preprint, 1990.
  • [4] L. Ferm and B. Gustafsson, A downstream boundary procedure for the Euler equations, Comput. Fluids 10 (1982), 261-276.
  • [5] B. Gustafsson, Inhomogeneous conditions at open boundaries for wave propagation problems, Appl. Numer. Math. 4 (1988), 3-19. MR 932316 (89b:65212)
  • [6] R. L. Higdon, Initial-boundary value problems for linear hyperbolic systems, SIAM Rev. 28 (1986), 177-217. MR 839822 (88a:35138)
  • [7] A. Harten, P. Lax, and B. van Leer, On upstream differencing and Godunov-type schemes for the hyperbolic conservation laws, SIAM Rev. 25 (1983), 35-60. MR 693713 (85h:65188)
  • [8] L. Wagatha, Approximation of pseudodifferential operators in absorbing boundary conditions for hyperbolic equations, Numer. Math. 42 (1983), 52-64. MR 716473 (85i:65117)
  • [9] R. F. Warming, R. M. Beam, and B. J. Hyett, Diagonalization and simultaneous symmetrization of the gas-dynamic matrices, Math. Comp. 29 (1975), 1037-1045. MR 0388967 (52:9799)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1991-1079023-0
Article copyright: © Copyright 1991 American Mathematical Society

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