Three-dimensional preliminary results of the MOOD method: A Very High-Order Finite Volume method for Conservation Laws.

Steven Diot (1) , Stéphane Clain (1, 2) , Raphaël Loubère (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 DMA - Departamento de Matemática e Aplicaçoes

The Multi-dimensional Optimal Order Detection (MOOD) method has been designed by authors in [5] and extended in [7] to reach Very-High-Order of accuracy for systems of Conservation Laws in a Finite Volume (FV) framework on 2D unstructured meshes. In this paper we focus on the extension of this method to 3D unstructured meshes. We present preliminary results for the three-dimensional advection equation which confirm the good behaviour of the MOOD method. More precisely, we show that the scheme yields up to sixth-order accuracy on smooth solutions while preventing oscillations from appearing on discontinuous profiles.

Mots clés: MOOD; 3D; high-order; finite volume; hexahedral; tetrahedral mesh; advection.; advection

Domaines: Modélisation et simulation; Physique mathématique [math-ph]

Steven Diot, Stéphane Clain, Raphaël Loubère. Three-dimensional preliminary results of the MOOD method: A Very High-Order Finite Volume method for Conservation Laws.. 2012. ⟨hal-00658481v2⟩