Comparison of higher-order accurate schemes for solving the two-dimensional unsteady Burgers' equation

Authors:
Samir F. Radwan
Affiliations:
Department of Engineering Mathematics, Faculty of Engineering, Alexandria University, Alexandria, Egypt
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

This paper is devoted to the testing and comparison of numerical solutions obtained from higher-order accurate finite difference schemes for the two-dimensional Burgers' equation having moderate to severe internal gradients. The fourth-order accurate two-point compact scheme, and the fourth-order accurate Du Fort Frankel scheme are derived. The numerical stability and convergence are presented. The cases of shock waves of severe gradient are solved and checked with the fourth-order accurate Du Fort Frankel scheme solutions. The present study shows that the fourth-order two-point compact scheme is highly stable and efficient in comparison with the fourth-order accurate Du Fort Frankel scheme.