A Godunov-type method based on an exact solution to the Riemann problem for the shallow-water equations (Q1975110)

In this paper the authors develop and analyze a Godunov-tipe front-capturing method designed to compute fluid flows described by the one- and two-dimensional shallow-water equations. The method is particulary suitable for computing flows characterized by moderate and high values of the Froude number, which can involve gradients or even jumps in the values of flow variables. The algorithm developed can adecuately predict the propagation dynamics of strong hydraulic jumps and simulate the monotonic profiles of grid variables in the vicinity of a hydraulic jump. Examples of one- and two-dimensional computations are given to illustrate the effectiveness of the method.