A Cell-Centered Second-Order Accurate Finite Volume Method for Convection-Diffusion Problems on Unstructured Meshes

A MUSCL-like cell-centered finite volume method is proposed to approximate the solution of multi-dimensional steady advection–diffusion equations. The second-order accuracy is provided by an appropriate definition of the diffusive and advective numerical fluxes. The method is based on a least squares reconstruction of the vertex values from cell averages. The slope limiter, which is required to prevent the formation and growth of spurious numerical oscillations, is designed to guarantee that the discrete solution of the nonlinear scheme exists. Several theoretical issues regarding the solvability of the resulting discrete problems are thoroughly discussed. Finally, numerical experiments that validate the effectiveness of the approach are presented.