Numerical Calculation of Flows with Dominant Nonlinear Advection

Abstract

In the recent years, some accurate methods for calculation of linear advection term have been developed and performance of some of them on nonlinear cases have also been attempted. In this paper, the split operator approach and the characteristic method were adopted for the calculation of nonlinear advection term. The computational method was proposed from a combination of the upwind difference and the 6-point scheme resulting into a scheme which has proved to give accurate solution for 1-D Burger's equation. Its application to practical cases such as hydraulic bore etc. is also straightforward and accurate.