Cell-centered finite volume methods with flexible stencils for diffusion equations on general nonconforming meshes

A cell-centered finite volume method is presented for discretizing diffusion operator on general nonconforming meshes. The node values are accurately approximated using a new weighted interpolation formula, in which the calculation of the weight is adaptive to both geometric parameters and diffusion coefficients. It follows that an explicit expression, composed of cell-centered unknowns only, is obtained for the discretization of normal flux. Numerical results demonstrate that linear solutions are reproduced exactly on the nonconforming random grids, and that the convergence rate is close to second order for non-linear or discontinuous problems.