Monotonic Diamond and DDFV Type Finite-Volume Schemes for 2D Elliptic Problems (Communications in Computational Physics, 2023)
The DDFV (Discrete Duality Finite Volume) method is a finite volume schememainly dedicated to diffusion problems, with some outstanding properties. This schemehas been found to be one of the most accurate finite volume methods for diffusionproblems. In the present paper, we propose a new monotonic extension of DDFV,which can handle discontinuous tensorial diffusion coefficient. Moreover, we compare its performance to a diamond type method with an original interpolation methodrelying on polynomial reconstructions. Monotonicity is achieved by adapting themethod of Gao et al [A finite volume element scheme with a monotonicity correctionfor anisotropic diffusion problems on general quadrilateral meshes] to our schemes.Such a technique does not require the positiveness of the secondary unknowns. Weshow that the two new methods are second-order accurate and are indeed monotonicon some challenging benchmarks as a Fokker-Planck problem.