Two-dimensional shallow water flows simulation using TVD-MacCormack Scheme

Abstract

This paper reports a finite volume TVD-MacCormack scheme for the computation of two-dimensional open channel flows with abrupt changes. The algorithm modified the widely-used MacCormack scheme by implementing a conservative dissipation step to avoid the unphysical oscillation in the vicinity of strong gradients in the numerical solution. Compared with other numerical models, this scheme does not bring in any additional difficulty in dealing with the source terms. Furthermore, this algorithm remains second-order accuracy in both space and time. A series of simulation, such as oblique hydraulic jump, circular dambreak and two-dimensional dambreak are carried out to demonstrate its robustness and stability in capturing strong gradients and discontinuities in open channel flows, The accuracy of numerical scheme is also verified with two laboratory dambreak experiments.