ADAPTIVE COMPUTATIONS OF RESERVOIR FLOWS VIA A GODUNOV-TYPE MODEL OF THE SHALLOW WATER EQUATIONS BASED ON UNSTRUCTURED GRIDS

摘要

A versatile adaptive, second-order accurate both in time and space, solver for the depth integrated Shallow Water Equations has been developed and results are presented herein. The solver is based upon a Godunov-type second order upwind hyperbolic finite volume formulation as applied on unstructured triangular meshes, where the inviscid fluxes at the interface between two cells of the system of equations under consideration are computed using Roe's approximate Riemann solver. The viscous terms of the Shallow Water Equations are computed via second-order accurate finite volume formulations. The robustness of the present algorithm stems from the fact that the adopted mathematical formulation is capable of handling a wide range of flow regimes such as steady and unsteady flows, gradually varying or discontinuous flows and flows over uniform or non-uniform bed topography. Moreover, a non-linear slope limiter is used to remove unwanted numerical oscillations. In addition grid adaptivity, based on h- and reverse h-refinement, enhances the versatility of the present solver. Refinement is achieved based on criteria applicable to individual cell properties. Results presented herein prove that grid adaptivity is an efficient and accurate approach for flows locally demonstrating steep gradients.