Modélisation numérique de la propagation des ondes acoustiques et élastiques en présence d'interfaces

Abstract : This thesis concerns the numerical treatment of interface for wave propagation in fluid and solid heterogeneous media. Interfaces introduce three kinds of problems. Numerically, the rate of convergence falls, and one can observe instabilities. Geometrically, a "stair-step" description of interfaces introduces numerical diffraction. Physically, classical schemes do not describe the nature of contacts. To solve these three drawbacks, we use an interface method (i.e., a scheme used at grid points near interfaces, that enforces the numerical solution to respect the same conditions than the exact solution). The study is divided into three parts. Firstly, we begin with a state-of-art about classical interface methods, such as the "Immersed Interface Method" (IIM) and their drawbacks. The equations of acoustics and elastodynamics are written as a first-order hyperbolic system. Three schemes, of increasing complexity and quality, are proposed (Lax-Wendroff, finite-volume with flux-limiter, WENO 5). Secondly, we calculate jump conditions for the exact solution and its spatial derivatives, for various interfaces : fluid-fluid, fluid-solid, solid-solid in perfect or imperfect contact (spring-mass conditions). Then, we propose a new interface method, the "Explicit Simplified Interface Method" (ESIM). Near interfaces, this easy-to-implement method maintains properties of schemes in homogeneous medium, for a negligible computational cost. Thirdly, we perform numerical experiments. Comparisons between analytical solutions and numerical solutions confirm properties deduced from the numerical analysis.
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Theses
Modeling and Simulation. Université de la Méditerranée - Aix-Marseille II, 2002. French


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Submitted on : Friday, August 5, 2005 - 2:17:25 PM
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Bruno Lombard. Modélisation numérique de la propagation des ondes acoustiques et élastiques en présence d'interfaces. Modeling and Simulation. Université de la Méditerranée - Aix-Marseille II, 2002. French. <tel-00009907>

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