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A Non-Overlapping Schwarz Domain Decomposition Method with High-Order Finite Elements for Flow Acoustics

Abstract : A non-overlapping domain decomposition method is proposed to solve large-scale finite element models for the propagation of sound with a background mean flow. An additive Schwarz algorithm is used to split the computational domain into a collection of sub-domains, and an iterative solution procedure is formulated in terms of unknowns defined on the interfaces between sub-domains. This approach allows to solve large-scale problems in parallel with only a fraction of the memory requirements compared to the standard approach which is to use a direct solver for the complete problem. While domain decomposition techniques have been used extensively for Helmholtz problems, this is the first application to aero-acoustics. The optimized Schwarz formulation is extended to the linearized potential theory for sound waves propagating in a potential base flow. A high-order finite element method is used to solve the governing equations in each sub-domain, and well-designed interface conditions based on local approximations of the Dirichlet-to-Neumann map are used to accelerate the convergence of the iterative procedure. The method is assessed on an academic test case and its benefit demonstrated on a realistic turbofan engine intake configuration.
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Soumis le : mardi 19 novembre 2019 - 16:55:01
Dernière modification le : mercredi 2 décembre 2020 - 11:21:19

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Alice Lieu, Philippe Marchner, Gwenael Gabard, Hadrien Beriot, Xavier Antoine, et al.. A Non-Overlapping Schwarz Domain Decomposition Method with High-Order Finite Elements for Flow Acoustics. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2020, ⟨10.1016/j.cma.2020.113223⟩. ⟨hal-02371050⟩

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