A monotone finite volume method for advectiondiffusion equations on unstructured polygonal meshes
We present a new second-order accurate monotone finite volume (FV) method for the steady-state advectiondiffusion equation. The method uses a nonlinear approximation for both diffusive and advective fluxes and guarantees solution non-negativity. The interpolation-free approximation of the diffusive flux uses the nonlinear two-point stencil proposed in Lipnikov [23]. Approximation of the advective flux is based on the second-order upwind method with a specially designed minimal nonlinear correction. The second-order convergence rate and monotonicity are verified with numerical experiments.
finite volume method advectiondiffusion equation polygonal mesh discrete maximum principle monotone method unstructured mesh