A Positive MUSCL Scheme for Triangulations

Abstract : In this paper, we link together and extend some results that have previously been given about positive schemes in the approximation of compressible flows. We mainly turn here to bidimensional problems and spatially high-order schemes ( at least second-order ) of MUSCL type, defined on unstructured triangulations, for an explcit time discretization. In the case of the scalar advection equation, we derive a scheme preserving the positivity of the advected quantity. Moreover, if the advection velocity is divergence free, our scheme is LED. Then, we manage to preserve the positivity of density when solving the Euler equations and, in the multi-component case, we also preserve the maximum principle for mass fractions.
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  • HAL Id : inria-00073225, version 1

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Paul-Henry Cournède, Christophe Debiez, Alain Dervieux. A Positive MUSCL Scheme for Triangulations. RR-3465, INRIA. 1998. ⟨inria-00073225⟩

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