Author(s)

J.Q. Deng & M.S. Ghidaoui

Abstract

Although most of numerical schemes based on shallow water equations work well for continuous surface flows, they are not suitable for flows containing vertical motions, such as the dam break problem, expansion and shock waves problems because they are based on the governing equations which have no effective mechanism to account for the vertical motion. To overcome this shortcoming, the authors of this paper apply the Boltzmann equation of gas kinetic theory to the surface water flow modeling and develop a set of equations governing surface water flows which incorporate the energy losses at the vertical motion. The test examples show that the Boltzmann equation based scheme has high resolution and high accuracy in modeling the discontinuities flows. In addition, Boltzmann based scheme is highly accurate in mode

Keywords