A Two-Dimensional Artificial Viscosity Technique for Modelling Discontinuity in Shallow Water Flows

Abstract

In this study, a two-dimensional cell-centred finite volume scheme is used to simulate dis- continuity in shallow water flows. Instead of using a Riemann solver, an artificial viscos- ity technique is developed to minimise unphysical oscillations. This is constructed from a combination of a Laplacian and a biharmonic operator using a maximum eigenvalue of the Jacobian matrix. In order to achieve high-order accuracy in time, we use the fourth-order Runge–Kutta method. A hybrid formulation is then proposed to reduce computational time, in which the artificial viscosity technique is only performed once per time step. The con- vective flux of the shallow water equations is still re-evaluated four times, but only by averaging left and right states, thus making the computation much cheaper. A comparison of analytical and laboratory results shows that this method is highly accurate for deal- ing with discontinuous flows. As such, this artificial viscosity technique could become a promising method for solving the shallow water equations.