A Seventh-order Perturbational Weighted Essentially Non-oscillatory Scheme for Hyperbolic Conservation Laws
Abdalla, A., Azer, M., Ramadan, M. (2023). A Seventh-order Perturbational Weighted Essentially Non-oscillatory Scheme for Hyperbolic Conservation Laws. EKB Journal Management System, 4(3), 506-528. doi: 10.21608/ajbas.2023.201613.1150
Amr H. Abdalla; Martina W. Azer; Moutaz Ramadan. "A Seventh-order Perturbational Weighted Essentially Non-oscillatory Scheme for Hyperbolic Conservation Laws". EKB Journal Management System, 4, 3, 2023, 506-528. doi: 10.21608/ajbas.2023.201613.1150
Abdalla, A., Azer, M., Ramadan, M. (2023). 'A Seventh-order Perturbational Weighted Essentially Non-oscillatory Scheme for Hyperbolic Conservation Laws', EKB Journal Management System, 4(3), pp. 506-528. doi: 10.21608/ajbas.2023.201613.1150
Abdalla, A., Azer, M., Ramadan, M. A Seventh-order Perturbational Weighted Essentially Non-oscillatory Scheme for Hyperbolic Conservation Laws. EKB Journal Management System, 2023; 4(3): 506-528. doi: 10.21608/ajbas.2023.201613.1150

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, Page 506-528  XML PDF (1.23 MB)
Document Type: Original Article
DOI: 10.21608/ajbas.2023.201613.1150
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Authors
Amr H. Abdallaorcid 1; Martina W. Azer email orcid 2; Moutaz Ramadanorcid 3
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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