Central WENO scheme for the integral form of contravariant shallow‐water equations

Abstract

A new Central Weighted Essentially Non-Oscillatory scheme for the solution of the shallow-water equations expressed in contravariant formulation is presented. One of the most efficient methodologies belonging to Central WENO family involves: reconstructions of cell-averaged values of flow variables, reconstruction of point-values of flow variables, advancing from time level t(n) to time level t(n+1) of the cell-averaged values. The extension of the above-mentioned methodology into the contravariant environment implies that the contravariant shallow-water equations must be expressed in an integral form. An element of novelty presented in this paper regards the definition of a formal integral expression of the shallow-water equations in a contravariant formulation, in which the Christoffel symbols are avoided. The WENO reconstructions are performed by a two-dimensional interpolating procedure taking into account the curved coordinate lines. The proposed scheme ensures the satisfaction of the exact C-property. Several two-dimensional test cases are used to verify the good resolution for smooth and discontinuous solutions. Copyright (C) 2010 John Wiley & Sons, Ltd

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