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.
Numerical Solution of two dimensional coupled viscous Burgers Equation using the Modified Cubic B Spline Differential Quadrature Method
DDU Gorakhpur University（德杜戈拉克普尔大学）；ISRO Telemetry, Tracking and Command Network (ISTRAC)（印度空间研究组织遥测、跟踪和指挥网络）；ISRO Satellite Center (ISAC)（印度空间研究组织卫星中心）
Global Stabilization of 2D Forced Viscous Burgers' Equation Around Nonconstant Steady State Solution by Nonlinear Neumann Boundary Feedback Control:Theory and Finite Element Analysis
An Efficient Space-Time Two-Grid Compact Difference Scheme for the Two-Dimensional Viscous Burgers' Equation
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University（湘潭大学数学与计算科学学院）；School of Mathematics, Shandong University（山东大学数学学院）
A splitting method for the augmented Burgers equation
Institute of Mathematics “Simion Stoilow” of the Romanian Academy（罗马尼亚科学院西米翁·斯托伊洛数学研究所）；CBT - Innovalia（CBT-Innovalia）；BCAM - Basque Center for Applied Mathematics（巴斯克应用数学中心）
Multi-Grade Deep Learning for Partial Differential Equations with Applications to the Burgers Equation
Department of Mathematics and Statistics, Old Dominion University（数学与统计学系，老 Dominion 大学）；School of Mathematical Science, South China Normal University（数学科学学院，华南师范大学）
Large-time asymptotics, vanishing viscosity and numerics for 1-D scalar conservation laws
Institute of Mathematics “Simion Stoilow” of the Romanian Academy（罗马尼亚科学院西缪恩·斯托伊洛瓦数学研究所）；Faculty of Mathematics and Computer Science, University of Bucharest（布加勒斯特大学数学与计算机科学学院）；BCAM - Basque Center for Applied Mathematics（巴斯克应用数学中心）；Ikerbasque, Basque Foundation for Science（伊克尔巴斯科，巴斯克科学基金会）
