Very high-order finite volume scheme for 1D convection diffusion problem: the implicit case

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

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

We present a fourth-order in space, second-order in time finite volume scheme for transient convection diffusion problem based on the Polynomial Reconstruction Operator and a Crank-Nicholson method. A detailed description of the scheme is provided and we perform numerical tests to highlight the performance of the method in comparison with the classical Patankar method.

Mots clés: Finite Volume; very high-order; transient convection-diffusion; Polynomial Reconstruction Operator (PRO)

Domaines: Analyse numérique [math.NA]

Gaspar Machado, Stéphane Clain, Rui M. S. Pereira. Very high-order finite volume scheme for 1D convection diffusion problem: the implicit case. 2012. ⟨hal-00675736⟩