A Robust Three-Level Time-Split MacCormack Scheme for Solving ‎Two-Dimensional Unsteady Convection-Diffusion Equation

A three-level time-split MacCormack method has been developed for solving the two-dimensional time-dependent convection-diffusion equation. The differential operator "splits" the two-dimensional problem into two pieces so that each subproblem is easy to solve using the original MacCormack procedure. The obtained scheme is temporal second-order convergent and spatial fourth-order accurate. This considerably reduces the computational cost of the algorithm. Under a suitable time-step restriction, both stability and convergence of the proposed technique are analyzed in the L∞(0, T; L2)-norm. A large set of numerical examples which provide the convergence rate of the new algorithm are presented. Overall, the considered approach is found to lie in the class of robust numerical schemes for solving general systems of partial differential equations.