Benchmark on discretization schemes for anisotropic diffusion ...

Benchmark on discretization schemes
for anisotropic diffusion problems
on general grids (December 10th)
Raphaèle Herbin and Florence Hubert
Laboratoire d’Analyse, Topologie et Probabilités, UMR 6632
Université de Marseille
39 rue Joliot Curie 13453 Marseille
herbin@cmi.univ-mrs.fr, fhubert@cmi.univ-mrs.fr
ABSTRACT. We present here a number of test cases and meshes which were designed to form
a benchmark for finite volume schemes. We address a two-dimensional anisotropic diffusion
problem, which is discretized on general, possibly nonconforming meshes. In all cases, the
diffusion tensor is taken to be anisotropic, and at times heterogenous and/or discontinuous.
The meshes are either triangular or quadrangular. The results which are expected from the
participants to the benchmark range from the number of unknowns, the errors on the fluxes or
the minimum and maximum values, to the order of convergence (when available).
KEYWORDS: Anisotropic medium, diffusion process, finite volume schemes, benchmark
1. Introduction
The aim of this benchmark is to provide a number of test cases in order to com-
pare the properties (convergence, robustness...) of existing discretization schemes for
anisotropic diffusion problems using general grids.
In all test cases except test 8, the domainΩ is the unit square. The boundary of the
domain is divided into ∂Ω = Γ ∪ Γ where Dirichlet (resp. Neumann) boundaryD N
conditions are given on Γ (resp. on Γ ).D N
The considered diffusion problem is ...