Monoslope and Multislope MUSCL Methods for unstructured meshes

Thierry Buffard (1) , Stéphane Clain (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 MIP - Mathématiques pour l'Industrie et la Physique

We present new MUSCL techniques associated with cell-centered Finite Volume method on triangular meshes. The first reconstruction consists in calculating a 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 edges) 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 complexe situations.

Mots clés: High-order scheme; Finite Volume; multislope method; unstructured mesh; conservation laws

Domaines: Analyse numérique [math.NA]

Thierry Buffard, Stéphane Clain. Monoslope and Multislope MUSCL Methods for unstructured meshes. Journal of Comptutational Physics, 2010, 229, pp.3745-3776. ⟨10.1016/j.jcp.2010.01.026⟩. ⟨hal-00323691⟩