Conservativity and weak consistency of a class of staggered finite volume methods for the Euler equations

Herbin, R.; Latché, J.-C.; Minjeaud, S.; Therme, N.

doi:10.1090/mcom/3575

Conservativity and weak consistency of a class of staggered finite volume methods for the Euler equations
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by R. Herbin, J.-C. Latché, S. Minjeaud and N. Therme HTML | PDF

Math. Comp. 90 (2021), 1155-1177 Request permission

Abstract:

We address here a class of staggered schemes for the compressible Euler equations; this scheme was introduced in recent papers and possesses the following features: upwinding is performed with respect to the material velocity only and the internal energy balance is solved, with a correction term designed on consistency arguments. These schemes have been shown in previous works to preserve the convex of admissible states and have been extensively tested numerically. The aim of the present paper is twofold: we derive a local total energy equation satisfied by the solutions, so that the schemes are in fact conservative, and we prove that they are consistent in the Lax-Wendroff sense.

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