High-resolution and non-oscillatory solution of the St. Venant equations in non-rectangular and non-prismatic channels

Abstract

A scheme to model open channel flow over wet and dry beds in non-rectangular and non-prismatic channels is presented. The scheme is second-order accurate, stable for Courant numbers up to unity, and monotonicity preserving. The scheme solves the St. Venant equations using a Godunov-type finite volume method. Mass and momentum fluxes are computed using a Roe-type Riemann solver, the MUSCL (Monotone Upwind Scheme for Conservation Laws) approach is applied for second-order spatial accuracy, and a treatment is introduced to model the hydrostatic pressure force exerted by the channel walls in the stream wise direction. The treatment permits momentum fluxes and the channel wall force to be balanced to numerical precision, preventing the artificial acceleration of the flow. Comparisons between model results, exact solutions, and experimental data show that the scheme is robust. Accurate and monotone results are obtained in the presence of discontinuities, supercritical flow, subcritical flow, transcritical flow, and dry-bed flow problems without the need for special front-tracking approaches or deforming grids. In addition, the scheme will conserve mass to numerical precision in all applications.