CONSERVATIVE MULTIDIMENSIONAL UPWINDING FOR THE STEADY 2-DIMENSIONAL SHALLOW-WATER EQUATIONS

In recent years upwind differencing has gained acceptance as a robust and accurate technique for the numerical approximation of the one-dime nsional shallow water equations. In two dimensions the benefits have b een less marked due to the reliance of the methods on standard operato r splitting techniques. Two conservative genuinely multidimensional up wind schemes are presented which have been adapted from flux balance d istribution methods recently proposed for the approximation of steady state solutions of the Euler equations on unstructured triangular grid s. A method for dealing with source terms, such as those introduced by modelling bed slope and friction, is also suggested and results are p resented for two-dimensional steady state channel flows to illustrate the accuracy and robustness of the new algorithms. (C) 1997 Academic P ress.