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Article Dans Une Revue Computers and Fluids Année : 2018

A MUSCL-type segregated – explicit staggered scheme for the Euler equations

Résumé

We present a numerical scheme for the solution of Euler equations based on staggered discretizations and working either on structured schemes or on general simplicial or tetra-hedral/hexahedral meshes. The time discretization is performed by a fractional-step or segregated algorithm involving only explicit steps. The scheme solves the internal energy balance, with cor-rective terms to ensure the correct capture of shocks, and, more generally, the consistency in the Lax-Wendroff sense. To keep the density, the internal energy and the pressure positive, conditionally positivity-preserving convection operators for the mass and internal energy balance equations are designed by a MUSCL-like procedure: first, second-order in space fluxes are computed, then a limiting procedure is applied. This latter is purely algebraic: it does not require any geometric argument and thus works on quite general meshes; moreover, it keeps the pressure constant at contact discontinu-ities. The construction of the fluxes does not need any Riemann or approximate Riemann solver, and yields thus a particularly simple algorithm. Artificial viscosity is added in order to reduce the oscillations of the scheme. Numerical tests confirm the accuracy of the scheme.
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Dates et versions

hal-01811266 , version 1 (08-06-2018)

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L Gastaldo, R Herbin †, Jean-Claude Latché, N Therme. A MUSCL-type segregated – explicit staggered scheme for the Euler equations. Computers and Fluids, 2018, 175, pp.91-110. ⟨10.1016/j.compfluid.2018.06.013⟩. ⟨hal-01811266⟩
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