Monoslope and multislope MUSCL methods for unstructured meshes

Authors:
Thierry Buffard;Stéphane Clain
Affiliations:
Université Clermont-Ferrand II, Laboratoire de Mathématiques, UMR CNRS 6620, 63177 Aubière cedex, France;Institut de Mathématiques de Toulouse, UMR CNRS 5219, 118 route de Narbonne, 31062 Toulouse cedex, France
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

We present new MUSCL techniques associated with cell-centered finite volume method on triangular meshes. The first reconstruction consists in calculating one vectorial slope per control volume by a minimization procedure with respect to a prescribed stability condition. The second technique we propose is based on the computation of three scalar slopes per triangle (one per edge) still respecting some stability condition. The resulting algorithm provides a very simple scheme which is extensible to higher dimensional problems. Numerical approximations have been performed to obtain the convergence order for the advection scalar problem whereas we treat a nonlinear vectorial example, namely the Euler system, to show the capacity of the new MUSCL technique to deal with more complex situations.