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

TL;DR

This paper introduces a three-level explicit time-split MacCormack method for efficiently solving two-dimensional viscous coupled Burgers' equations, demonstrating high accuracy and reduced computational cost.

Contribution

The paper presents a novel three-level time-split MacCormack scheme that improves efficiency and accuracy for 2D viscous coupled Burgers' equations, especially at different Reynolds numbers.

Findings

Second order accuracy in time for low Reynolds numbers

Fourth order convergence in space for low Reynolds numbers

Effective reduction in computational cost

Abstract

In this paper, we analyze the three-level explicit time-split MacCormack procedure in the numerical solutions of two-dimensional viscous coupled Burgers' equations subject to initial and boundary conditions. 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 convergent in space, while it is second order convergent in both time and space for high Reynolds numbers problems. This shows the efficiency and effectiveness of the considered method compared to a large set of numerical schemes widely studied in the literature for solving the two-dimensional time dependent nonlinear coupled Burgers' equations. Numerical examples which confirm the theoretical results are presented and discussed.