Upwind WENO scheme for Shallow Water Equations in contravariant formulation

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• 作者：F. Gallerano ; ^{francesco.gallerano@uniroma1.it} ; G. Cannata ^{giovanni.cannata@uniroma1.it} ; M. Tamburrino ^{marco.tamburrino@uniroma1.it}
• 关键词：2D Shallow Water Equations ; Upwind WENO scheme ; Contravariant formulation ; Christoffel symbols ; Freestream preservation
• 刊名：Computers and Fluids
• 出版年：2012
• 出版时间：15 June, 2012
• 年：2012
• 卷：62
• 期：Complete
• 页码：1-12
• 全文大小：1603 K

文摘

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 proposed scheme ensures the satisfaction of the C-property. The model is verified against several benchmark tests, and the results are compared with theoretical and alternative numerical solutions.