An efficient three‐level explicit time‐split scheme for solving two‐dimensional unsteady nonlinear coupled Burgers' equations

Summary This work deals with the numerical solutions of two‐dimensional viscous coupled Burgers' equations with appropriate initial and boundary conditions using a three‐level explicit time‐split MacCormack approach. In this technique, the differential operators split the two‐dimensional problem into two pieces so that the two‐step explicit MacCormack scheme can be easily applied to each subproblem. This reduces the computational cost of the algorithm. For low Reynolds numbers, the proposed method is second‐order accurate in time and fourth‐order convergent in space, whereas it is second‐order convergent in both time and space for high Reynolds numbers problems. This observation shows the utility and efficiency of the considered method compared with a broad range of numerical schemes widely studied in the literature for solving the two‐dimensional time‐dependent nonlinear coupled Burgers' equations. A large set of numerical examples that confirm the theoretical results are presented and critically discussed. Both figures and tables provide the stability analysis and convergence rate of the method. The approach is more efficient and effective (stable, second‐order convergent in time, and fourth‐order accurate in space) than a broad range of methods widely studied in the literature for solving 2D unsteady coupled Burgers' equations. It can be considered as robust tools for integration of multidimensional problems.