An adaptive discrete-velocity model for the shallow water equations

✍ Scribed by B.T. Nadiga

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 652 KB
• Volume: 121
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/s0021-9991(95)90102-7

✦ Synopsis

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.