Numerical simulation of flows of a heavy nonviscous fluid with a free surface in the gravity field over a bed surface with an arbitrary profile

摘要

A numerical method is proposed in this paper for studying hydrodynamic flows of heavy nonviscous fluid with a free surface over an arbitrary bed profile. This arbitrary bed profile is approximated by a piecewise-linear function splitting it into a finite number of domains with a step boundary. In order to implement this method, a quasi-two-layer model of fluid flow over a step boundary is used taking into account physical processes near the step. In this paper we implement numerical modelling of various physical phenomena, such as fluid flow over a sloping bed surface, shock wave creeping on a sloping bank, a fluid column fall over a bed surface given in various ways, fluid flow over a bed surface of a complex profile.