Author(s)

P. J. Montgomery

Abstract

A finite difference method, known as the relaxation method, is generalized from a class of relaxation schemes with the ultimate aim of numerically modelling hydraulic jumps at a phase interface. This method has been applied previously to model gravity currents arising from the instantaneous release of a dense volume of fluid. The relaxation scheme is an iterative, second order accurate, time- marching method which is able to capture shocks and interfaces without front tracking or calculation of the eigenvalues of the Jacobian matrix for the flux vector. In this paper, the relaxation scheme will be described, with specific attention paid to the new generalizations included to account for boundary conditions, spatially dependent flux terms, and simple forcing terms. Numerical resu

Keywords