Analysis on general meshes of a discrete duality finite volume method for subsurface flow problems

作者：Njifenjou A^*; Donfack H; Moukouop Nguena I

来源：Computational Geosciences, 2013, 17(2): 391-415.

DOI：10.1007/s10596-012-9339-6

• Flow problems
• Nonhomogeneous anisotropic media
• Discrete duality finite volumes
• Stability and error estimates
• Numerical tests

This work presents and analyzes, on unstructured grids, a discrete duality finite volume method (DDFV method for short) for 2D-flow problems in nonhomogeneous anisotropic porous media. The derivation of a symmetric discrete problem is established. The existence and uniqueness of a solution to this discrete problem are shown via the positive definiteness of its associated matrix. Properties of this matrix combined with adequate assumptions on data allow to define a discrete energy norm. Stability and error estimate results are proven with respect to this norm. L (2)-error estimates follow from a discrete Poincar, inequality and an L (aaEuro parts per thousand)-error estimate is given for a P (1)-DDFV solution. Numerical tests and comparison with other schemes (especially those from FVCA5 benchmark) are provided.

• 出版日期2013-4