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Inverse Lax–Wendroff Procedure for Numerical Boundary Conditions of Hyperbolic Equations: Survey and New Developments

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Advances in Applied Mathematics, Modeling, and Computational Science

Part of the book series: Fields Institute Communications ((FIC,volume 66))

Abstract

In this paper, we give a survey and discuss new developments and computational results for a high order accurate numerical boundary condition based on finite difference methods for solving hyperbolic equations on Cartesian grids, while the physical domain can be arbitrarily shaped. The challenges result from the wide stencil of the high order interior scheme and the fact that the physical boundary does not usually coincide with grid lines. There are two main ingredients of the method. The first one is an inverse Lax-Wendroff procedure for inflow boundary conditions and the other one is a robust and high order accurate extrapolation for outflow boundary conditions. The method is high order accurate, stable under standard CFL conditions determined by the interior schemes, and easy to implement. We show applications in simulating interactions between compressible inviscid flows and rigid (static or moving) boundaries.

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Acknowledgements

Research is supported by AFOSR grant FA9550-09-1-0126 and NSF grant DMS-1112700.

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Sirui Tan & Chi-Wang Shu

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  1. Sirui Tan
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  2. Chi-Wang Shu
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Correspondence to Chi-Wang Shu .

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Editors and Affiliations

  1. , Department of Mathematics, Wilfrid Laurier University, University Avenue West 75, Waterloo, N2L 3C5, Ontario, Canada

    Roderick Melnik

  2. , Dept. of Physics and Computer Science, Wilfrid Laurier University, University Avenue West 75, Waterloo, N2L 3C5, Canada

    Ilias S. Kotsireas

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Tan, S., Shu, CW. (2013). Inverse Lax–Wendroff Procedure for Numerical Boundary Conditions of Hyperbolic Equations: Survey and New Developments. In: Melnik, R., Kotsireas, I. (eds) Advances in Applied Mathematics, Modeling, and Computational Science. Fields Institute Communications, vol 66. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-5389-5_3

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