Finite volume monotone scheme for highly anisotropic diffusion operators on unstructured triangular meshes. (Schéma volumes finis monotone pour des opérateurs de diffusion fortement anisotropes sur des maillages de triangles non structurés).(French)Zbl 1081.65086
Summary: We introduce a new finite volume method for highly anisotropic diffusion operators on unstructured meshes. The main idea is to calculate the gradient using a nonlinear scheme. For parabolic problems, if the time step is small enough, the resulting global matrix is monotone without geometrical constraints on the mesh and restrictive conditions on the anisotropy ratio. We check the precision of the method in comparison with analytical solutions. The efficiency of the algorithm is demonstrated by comparing it with numerical schemes which do not satisfy a discrete maximum principle on the studied case.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35K15 | Initial value problems for second-order parabolic equations |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
Keywords:
finite volume method;highly anisotropic diffusion operators;unstructured meshes;gradient;parabolic problems;algorithm;discrete maximum principleCite
References:
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