A new interface method for hyperbolic problems with discontinuous coefficients: one-dimensional acoustic example

Abstract : A new numerical method, called the Explicit Simplified Interface Method (ESIM), is developed in the context of acoustic wave propagation in heterogeneous media. Equations of acoustics are written as a first-order linear hyperbolic system. Away from interfaces, a standard scheme (Lax-Wendroff, TVD, WENO...) is used in a classical way. Near interfaces, the same scheme is used, but it is applied on a set of modified values deduced from numerical values and from jump conditions at interfaces. It amounts to modify the scheme so that its order of accuracy is maintained at irregular points, despite the non-smoothness of the solution. This easy to implement interface method requires few additional computational resources and it can be applied to other partial differential equations.
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Submitted on : Friday, April 29, 2005 - 1:56:56 PM
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Joël Piraux, Bruno Lombard. A new interface method for hyperbolic problems with discontinuous coefficients: one-dimensional acoustic example. Journal of Computational Physics, Elsevier, 2001, 168 (1), pp.227-248. ⟨10.1006/jcph.2001.6696⟩. ⟨hal-00004811⟩

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