A new very high-order finite volume method for the 2D convection diffusion problem on unstructured meshes

Stéphane Clain (1, 2) , Gaspar Machado (2) , Rui M. S. Pereira (2)

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

We present a new finite volume scheme based on the Polynomial Reconstruction Operator (PRO-scheme) for the linear convection diffusion problem with structured and unstructured meshes. We first design the numerical scheme for generic two-dimensional cells and introduce two kinds of polynomial reconstructions. Numerical experiences are carried out to prove the stability and the effectiveness of the method where a 6th-order convergence is reached.

Mots clés: Finite volume scheme; polynomial reconstruction; high-order scheme; convection diffusion

Domaines: Analyse numérique [math.NA]

Stéphane Clain, Gaspar Machado, Rui M. S. Pereira. A new very high-order finite volume method for the 2D convection diffusion problem on unstructured meshes. 2012. ⟨hal-00675743⟩