Quasi-two-layer finite-volume scheme for modelling shallow water flows over an arbitrary bed in the presence of external force. II. Algorithm applications and numerical results

Abstract

A nite-volume numerical method for studying shallow water ows over an arbitrary bed pro le in the presence of external force has been proposed in [33]. This method uses the quasi-two-layer model of hydrodynamic ows over a stepwise boundary with advanced consideration of the ow features near the step. A distinctive feature of the suggested model is a separation of the studied ow into two layers in calculating the ow quantities near each step, and improving by this means the approximation of depth-averaged solutions of the initial three-dimensional Euler equations. We are solving the shallow-water equations for one layer, introducing the ctitious lower layer only as an auxiliary structure in setting up the appropriate Riemann problems for the upper layer. Besides, the quasi-two-layer approach leads to the appearance of additional terms in the one-layer nite-di erence representation of balance equations. Numerical simulations are performed based on the proposed in [33] algorithm of various physical phenomena, such as breakdown of the rectangular uid column over an inclined plane, large-scale motion of uid in the gravity eld in the presence of Coriolis force over a mounted obstacle on the underlying surface. Computations are made for the two-dimensional dam-break problem on a slope precisely conform to laboratory experiments. The interaction of the Tsunami wave with the shore line including an obstacle has been simulated to demonstrate the e ciency of the developed algorithm in domains, including partly ooded and dry regions.