Comparison of higher-order accurate schemes for solving the two-dimensional unsteady Burgers' equation |
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Affiliation: | Department of Engineering Mathematics, Faculty of Engineering, Alexandria University, Alexandria, Egypt |
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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. |
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Keywords: | Rational functions Müntz polynomials Orthogonality Inner product |
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