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Numerical treatment of two-dimensional interfaces for acoustic and elastic waves. (English) Zbl 1087.76079

Summary: We present a numerical method to take into account 2D arbitrary-shaped interfaces in classical finite difference schemes, on a uniform Cartesian grid. This work extends the ”explicit simplified interface method” (ESIM), previously proposed by the authors in 1D [J. Comput. Phys. 168, 227–248 (2001; Zbl 0991.76053)]. The physical problem under study concerns the linear hyperbolic systems of acoustics and elastodynamics, with stationary interfaces. Our method maintains, near the interfaces, properties of the schemes in homogeneous medium, such as the order of accuracy and the stability limit. Moreover, it enforces the numerical solution to satisfy the exact interface conditions. Lastly, it provides subcell geometrical features of the interface inside the meshing. The ESIM can be coupled automatically with a wide class of numerical schemes (Lax–Wendroff, flux-limiter schemes, etc.) for a negligible additional computational cost. Throughout the paper, we focus on the challenging case of an interface between a fluid and an elastic solid. In numerical experiments, we provide comparisons between numerical solutions and original analytic solutions, showing the efficiency of the method.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S20 Finite difference methods applied to problems in solid mechanics

Citations:

Zbl 0991.76053
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References:

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