An implicit finite difference scheme for the numerical solutions of two-dimensional Burgers equations

In this study, the system of two-dimensional Burgers equations is solved by a new approximation that approaches the solution at two time legs: approximation is explicit in x-direction and implicit in y-direction at the first leg while approximation is implicit in x-direction and explicit in y-direction at the second leg. Two test problems are used to illustrate the accuracy of the present approximation. Comparisons are made with the existing methods in the literature. The approximation is analyzed by von-Neumann stability analysis method and it is displayed that the approximation is unconditionally stable. The method is shown to be consistent and second order accurate in time and space. The obtained results show that the present approximation is successful to solve the system of two-dimensional Burgers equations.