Godunov-Type Solution of Curvilinear Shallow-Water Equations

Abstract

This paper presents details of a second-order accurate Godunov-type numerical model of the two-dimensional conservative hyperbolic shallow-water equations written in a nonorthogonal curvilinear matrix form and discretized using finite volumes. Roe's flux function is used for the convection terms, and a nonlinear limiter is applied to prevent spurious oscillations. Validation tests include frictionless rectangular and circular dam-breaks, an oblique hydraulic jump, jet-forced flow in a circular basin, and vortex shedding from a vertical surface-piercing cylinder. The results indicate that the model accurately simulates sharp fronts, a flow discontinuity between subcritical and supercritical conditions, recirculation in a basin, and unsteady wake flows.