A high resolution scheme for flows in open channels with arbitrary cross-section.

The aim of this paper is to present a numerical scheme to simulate unsteady, one-dimensional flows in open channels with arbitrary cross-section. This scheme is fully conservative of volume and momentum and preserves the non-negativity of the water depth. The finite difference method derived is semi-implicit in time and based on a space staggered grid. A high-resolution technique, the flux limiter method, is implemented to control the accuracy of the proposed scheme. Our purpose is to achieve the precision and the stability of the method with respect to the regularity of the data. A few computational examples on classical test cases are given to illustrate the properties of the present method in terms of stability, accuracy and efficiency.