A monotone nonlinear finite volume method for advection – diffusion equations on unstructured polyhedral meshes in 3

@inproceedings{Nikitin2010AMN,
  title={A monotone nonlinear finite volume method for advection – diffusion equations on unstructured polyhedral meshes in 3},
  author={K. Nikitin and Yu. Vassilevski},
  year={2010}
}
We present a new monotone finite volume method for the advection–diffusion equation with a full anisotropic discontinuous diffusion tensor and a discontinuous advection field on 3D conformal polyhedral meshes. The proposed method is based on a nonlinear flux approximation both for diffusive and advective fluxes and guarantees solution non-negativity. The approximation of the diffusive flux uses the nonlinear two-point stencil described in [9]. Approximation of the advective flux is based on the… CONTINUE READING