On boundary approximation for simulation of granular flow

We introduce a Cartesian cut-cell method to numerically solve a system of granular equations in complicated domains. A non-Newtonian Navier-Stokes model is used, which covers both the dense and dilute regime of granular flow. In a Cartesian cut-cell method, one starts from a Cartesian grid and modifies cells that intersect the boundary. In contrast to adaptive or boundary fitting grids, the cutting process yields only local modifications. Thus, the simple Cartesian finite volume structure can be sustained on the interior. To ensure stability in the presence of arbitrarily small cut cells, a merging process will be used, which will result in a combination of the discretization equations on the algebraic level. An interpolation is used to ensure first order convergence near the boundary. We restrict the presentation of numerical examples to two dimensions, while the method derivation includes the three dimensional case.