Limited Advection Schemes for Solving the Advection Dispersion Equation

摘要

The accurate numerical solution of advection equation is of great interest for modeling the advection-dominated contaminant transport problems. This paper presents the comparative study of two numerical schemes, Lax-Wendroff scheme and QUICKEST scheme, in which the flux limiter algorithm is incorporated for solving the advection equation. The von Neumann stability analysis is employed to demonstrate the stability property of the numerical scheme for solving the linear partial differential equation. The numerical tests are carried out and the comparison between the numerical results with the analytical solutions has been carried out. Moreover, the experimental data have been used to test the developed model. It is found both the QUICKEST and Lax-Wendroff (LW) schemes with the flux limiter algorithm could achieve accurate results without numerical oscillations near the sharp gradient of the variables. However, the limited LW algorithm is much simpler than the limited QUICKEST and can be extended to the fully 2D flow and mass simulation.