THOMANN, Andrea; IOLLO, Angelo; PUPPO, Gabriella

doi:10.1137/21M146819X

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THOMANN, Andrea
Johannes Gutenberg - Universität Mainz = Johannes Gutenberg University [JGU]

IOLLO, Angelo
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
Institut de Mathématiques de Bordeaux [IMB]

PUPPO, Gabriella
Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome] [UNIROMA]

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SIAM Journal on Scientific Computing. 2023-10-05, vol. 45, n° 5, p. A2632-A2656

Society for Industrial and Applied Mathematics

Résumé en anglais

We present an implicit relaxation scheme for the simulation of compressible flows in all Mach number regimes based on a Jin–Xin relaxation approach. The main features of the proposed scheme lie in its simplicity and effectiveness. Thanks to the linearity of the flux in the relaxation system, the time semidiscrete scheme can be reformulated in linear decoupled elliptic equations resulting in the same number of unknowns as in the original system. To obtain the correct numerical diffusion in all Mach number regimes, a convex combination of upwind and centered fluxes is applied. The numerical scheme is validated by applying it on a model for nonlinear elasticity. Simulations of gas and fluid flows, as well as deformations of compressible solids are carried out to assess the performance of the numerical scheme in accurately approximating material waves in different Mach regimes.< Réduire

Mots clés en anglais

All-speed scheme

relaxation method

low Mach number limit

Eulerian elasticity

linearly implicit higher order schemes

All-speed scheme

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Implicit Relaxed All Mach Number Schemes for Gases and Compressible Materials

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Mots clés en anglais

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