WSEAS Transactions on Fluid Mechanics
Print ISSN: 1790-5087, E-ISSN: 2224-347X
Volume 10, 2015
Non-Linear Shallow Water Equations Numerical Integration on Curvilinear Boundary-Conforming Grids
Authors: , ,
Abstract: 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.
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Keywords: 2D Shallow Water Equations, Upwind WENO scheme, Contravariant formulation, Christoffel Symbols, Freestream preservation
Pages: 13-25
WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 10, 2015, Art. #2