A robust iterative scheme for finite volume discretization of diffusive flux on highly skewed meshes

A new approach for diffusive flux discretization on a nonorthogonal mesh for finite volume method is proposed. This approach is based on an iterative method, Deferred correction introduced by M. Peric [J.H. Fergizer, M. Peric, Computational Methods for Fluid Dynamics, Springer, 2002]. It converges on highly skewed meshes where the former approach diverges. A convergence proof of our method is given on arbitrary quadrilateral control volumes. This proof is founded on the analysis of the spectral radius of the iteration matrix. This new approach is applied successfully to the solution of a Poisson equation in quadrangular domains, meshed with highly skewed control volumes. The precision order of used schemes is not affected by increasing skewness of the grid. Some numerical tests are performed to show the accuracy of the new approach.