Non-Linear Shallow Water Equations numerical integration on curvilinear boundary-conforming grids

An Upwind Weighted Essentially Non-Oscillatory scheme for the solution of the Shallow Water Equations on generalized curvilinear coordinate systems is proposed. The Shallow Water Equations are expressed in a contravariant formulation in which Christoffel symbols are avoided. The equations are solved by using a high-resolution finite-volume method incorporated with an exact Riemann Solver. A procedure developed in order to correct errors related to the difficulties of numerically satisfying the metric identities on generalized boundary-conforming grids is presented; this procedure allows the numerical scheme to satisfy the freestream preservation property on highly-distorted grids. The capacity of the proposed model is verified against test cases present in literature. The results obtained are compared with analytical solutions and alternative numerical solutions.