Structure-preserving schemes for drift-diffusion systems on general meshes: DDFV vs HFV

TL;DR

This paper compares two finite volume schemes, DDFV and HFV, for drift-diffusion models on complex meshes, focusing on their positivity preservation and performance on various tests.

Contribution

It provides a detailed comparison of DDFV and HFV schemes for drift-diffusion systems, highlighting their differences on general meshes.

Findings

Both schemes ensure positivity of discrete densities.

The schemes exhibit different behaviors on various test cases.

The comparison informs the choice of scheme based on mesh and boundary conditions.

Abstract

We made a comparison between a Discrete Duality Finite Volume (DDFV) scheme and a Hybrid Finite Volume (HFV) scheme for a drift-diffusion model with mixed boundary conditions on general meshes. Both schemes are based on a nonlinear discretisation of the convection-diffusion fluxes, which ensures the positivity of the discrete densities. We investigate the behaviours of the schemes on various numerical test cases.