Solving a system of 2D Burgers' equations using Semi-Lagrangian finite difference schemes

In this paper, we aim to generalize semi-Lagrangian finite difference schemes for a system of two-dimensional (2D) Burgers' equations. Our scheme is not limited by the Courant-Friedrichs-Lewy (CFL) condition and therefore we can apply larger step size for the time variable. Proposed schemes can be implemented in parallel very well and in fact, it is a local one-dimensional (LOD) scheme which obtained on the basis of the modified equation approach and applied to solve a system of 2D Burgers' equations. A valuable advantage of the proposed schemes is that in any iteration just two tridiagonal linear systems must be solved and therefore its computational cost is low.