Three-Dimensional Adaptive Central Schemes on Unstructured Staggered Grids

We present a new formulation of three-dimensional central finite volume methods on unstructured staggered grids for solving systems of hyperbolic equations. Based on the Lax-Friedrichs and Nessyahu-Tadmor one-dimensional central finite difference schemes, the numerical methods we propose involve a staggered grids in order to avoid solving Riemann problems at cell interfaces. The cells are barycentric, while those of the staggered grid are diamond-shaped. In order to reduce artificial viscosity, we start with an adaptively refined primal grid in 3D, where the theoretical a posteriori result of the first-order scheme is used to derive appropriate refinement indicators. We apply those methods and solve Euler equations. Our numerical results are in good agreement with corresponding results appearing in the literature.