A Seventh-order Perturbational Weighted Essentially Non-oscillatory Scheme for Hyperbolic Conservation Laws | ||
| Alfarama Journal of Basic & Applied Sciences | ||
| Article 11, Volume 4, Issue 3, July 2023, Pages 506-528 PDF (1.23 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/ajbas.2023.201613.1150 | ||
| Authors | ||
| Amr H. Abdalla1; Martina W. Azer* 2; Moutaz Ramadan3 | ||
| 1Department of Physics and Engineering Mathematics, Faculty of Engineering, Port Said University, Egypt. | ||
| 2Department of physics and Engineering Mathematics, Faculty of Engineering, Port Said university, Port Said City. | ||
| 3Department of mathematics and computer science, faculty of science, port said university, port said, Egypt. | ||
| Abstract | ||
| This study presents a modified seventh-order weighted essentially non-oscillatory (WENO) finite difference scheme based on the numerical perturbation method established in [1]. The perturbed candidate polynomials of the seventh-order WENO scheme are evolved using a perturbational polynomial of the grid spacing, which modifies the polynomial approximation used for the classical WENO7-Z reconstruction on each candidate stencil. Furthermore, it is found that the new weighted scheme constructed with the new perturbed polynomials candidate has necessary and sufficient conditions for seventh-order convergence that are one order lower than those used by Henrick for the classic WENO scheme with seventh-order convergence, as presented in [2]. As a result, even at critical locations, the new seventh-order WENO scheme, which uses the perturbed polynomials and the same weights as the WENO7-Z scheme as demonstrated in [3], is able to satisfy the necessary and sufficient condition for seventh-order convergence. The new WENO7-P scheme reduces numerical dissipation in WENO schemes. Numerical examples verify the new scheme's accuracy, low dissipation, and robustness. | ||
| Keywords | ||
| Hyperbolic Conservation Laws; WENO Scheme; Perturbational Approach; Seventh-Order WENO Scheme; Runge-Kutta Method | ||
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