Author(s): S. Joyce; Q. Zhang; Mohamed S. Ghidaoui
Keywords: Shallow water equation; Dam-break; Boltzmann; Riemann
Abstract: A Kinetic Flux Vector Splitting (KFVS) scheme and a Flux Difference Splitting (FDS) scheme for 1-D shallow water equations are investigated. The KFVS scheme is based on the collisionless form of the Boltzmann equation. The FDS scheme is based on the exact Riemann solution of the gravity wave problem. In both schemes, the gravitational and frictional forces are included through operator splitting. In addition, both schemes are explicit and their numerical stability is governed by Courant-Frederich-Lewy (CFL) condition (i. e., Courant number≤1.0). The comparison of both schemes are performed for the following cases: (i) a single dam break with horizontal and frictionless channel; (ii) a double break with horizontal and frictionless channel; (iii) a single dam break in the presence of gravitational and frictional force for which there is experimental data. The results show that both methods are of similar accuracy and efficiency. The shock and expansion waves are well resolved by both schemes. It is noted that the scalar nature of the Boltzmann equation means that the KFVS does not require characteristic decomposition and that its extension to multi-dimensional problems is relatively straightforward.