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In this paper, we analyze the three-level explicit time-split MacCormackprocedure in the numerical solutions of two-dimensional viscous coupledBurgers' equations subject to initial and boundary conditions. The differentialoperators split the two-dimensional problem into two pieces so that thetwo-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 convergent inspace, while it is second order convergent in both time and space for highReynolds numbers problems. This shows the efficiency and effectiveness of theconsidered method compared to a large set of numerical schemes widely studiedin the literature for solving the two-dimensional time dependent nonlinearcoupled Burgers' equations. Numerical examples which confirm the theoreticalresults are presented and discussed.

A Novel Three-Level Time-Split MacCormack Method for Solving Two-Dimensional Viscous Coupled Burgers Equations