AN ADAPTIVE DISCRETE-VELOCITY MODEL FOR THE SHALLOW-WATER EQUATIONS

A new approach to solving the shallow water equations is presented. This involves using discrete velocities of an adaptive nature in a finite volume context. The origin of the discrete-velocity space and the magnitudes of the discrete-velocities are both spatially and temporally variable. The near-equilibrium flow method of Nadiga and Pullin is used to arrive at a robust second-order (in both space and time) scheme-the adaptive discrete velocity (ADV) scheme-which captures hydraulic jumps with no oscillations. The flow over a two-dimensional ridge, over a wide range of undisturbed upstream Froude numbers prove the robustness and accuracy of the scheme. A comparison of the interaction of two circular vortex patches in the presence of bottom topography as obtained by the ADV scheme and a semi-Lagrangian scheme more than validates the new scheme in two dimensions. (C) 1995 Academic Press. Inc.