A sixth-order finite volume method for multidomain convection–diffusion problem with discontinuous coefficients

• Sixth-order finite volume method for 2D convection–diffusion problem.
• Polynomial reconstructions for unstructured meshes.
• Discontinuous diffusion coefficient and velocity.
• Numerical experiences M-matrix preservation, positivity preservation.

A sixth-order finite volume method is proposed to solve the bidimensional linear steady-state convection–diffusion equation. A new class of polynomial reconstructions is proposed to provide accurate fluxes for the convective and the diffusive operators. The method is also designed to compute accurate approximations even with discontinuous diffusion coefficient or velocity and remains robust for large Peclet numbers. Discontinuous solutions deriving from the linear heat transfer Newton law are also considered where a decomposition domain technique is applied to maintain an effective sixth-order approximation. Numerical tests covering a large panel of situations are addressed to assess the performances of the method.