Discretisation and multigrid solution of elliptic equations with mixed derivative terms and strongly discontinuous coefficients
A new conservative cell centered finite volume method is considered for the accurate solution of elliptic diffusion equations with strongly varying coefficients. Such problems arise in oil reservoir simulation when renormalisation techniques are used to model the reservoir geology. A multigrid scheme based on that of \textit{P. Wesseling} [J. Comput. Phys. 79, No. 1, 85-91 (1988; Zbl 0658.65095)] is applied to the resulting algebraic system, showing that a rapid mesh independent convergence rate may be obtained for problems of this type. A series of test problems demonstrates the efficiency of the multigrid procedure in comparison to single grid methods.
conservative cell centered finite volume method
scientific article; zbMATH DE number 740635