Academic Journal

Implicit Relaxed All Mach Number Schemes for Gases and Compressible Materials: Implicit relaxed all Mach number schemes for gases and compressible materials

Bibliographic Details
Title: Implicit Relaxed All Mach Number Schemes for Gases and Compressible Materials: Implicit relaxed all Mach number schemes for gases and compressible materials
Authors: Thomann, Andrea, Iollo, Angelo, Puppo, Gabriella
Contributors: Iollo, Angelo
Source: SIAM Journal on Scientific Computing. 45:A2632-A2656
Publication Status: Preprint
Publisher Information: Society for Industrial & Applied Mathematics (SIAM), 2023.
Publication Year: 2023
Subject Terms: Nonlinear elasticity, FOS: Physical sciences, Gas dynamics (general theory), [MATH] Mathematics [math], 01 natural sciences, Finite difference methods applied to problems in fluid mechanics, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.), All-speed scheme, [PHYS] Physics [physics], Eulerian elasticity, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Finite volume methods for initial value and initial-boundary value problems involving PDEs, Finite volume methods applied to problems in solid mechanics, Finite difference methods for initial value and initial-boundary value problems involving PDEs, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, relaxation method, Finite volume methods for boundary value problems involving PDEs, Fluid Dynamics (physics.flu-dyn), Finite volume methods applied to problems in fluid mechanics, Physics - Fluid Dynamics, Numerical Analysis (math.NA), all-speed scheme, Euler equations, linearly implicit higher order methods, Finite difference methods applied to problems in solid mechanics, low Mach number limit, Numerical methods for stiff equations, Hyperbolic conservation laws, linearly implicit higher order schemes
Description: 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-semi discrete 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 centred fluxes is applied. The numerical scheme is validated by applying it on a Eulerian model for non-linear 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.
Document Type: Article
File Description: application/xml; application/pdf
Language: English
ISSN: 1095-7197
1064-8275
DOI: 10.1137/21m146819x
DOI: 10.48550/arxiv.2112.14126
Access URL: http://arxiv.org/abs/2112.14126
https://zbmath.org/7749381
https://doi.org/10.1137/21m146819x
https://hal.science/hal-04375656v2
https://hal.science/hal-04375656v2/document
https://doi.org/10.1137/21m146819x
https://hdl.handle.net/11573/1706229
https://doi.org/10.1137/21M146819X
Rights: CC BY NC SA
Accession Number: edsair.doi.dedup.....f87fb80a4558ad5c5c6013b64f93a7cf
Database: OpenAIRE
Description
ISSN:10957197
10648275
DOI:10.1137/21m146819x