A sixth-order finite difference WENO scheme for non-linear degenerate parabolic equations: an alternative technique
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 7 April 2023
Issue publication date: 19 May 2023
Abstract
Purpose
This paper aims to construct a sixth-order weighted essentially nonoscillatory scheme for simulating the nonlinear degenerate parabolic equations in a finite difference framework.
Design/methodology/approach
To design this scheme, we approximate the second derivative in these equations in a different way, which of course is still in a conservative form. In this way, unlike the common practice of reconstruction, the approximation of the derivatives of odd order is needed to develop the numerical flux.
Findings
The results obtained by the new scheme produce less error compared to the results of other schemes in the literature that are recently developed for the nonlinear degenerate parabolic equations while requiring less computational times.
Originality/value
This research develops a new weighted essentially nonoscillatory scheme for solving the nonlinear degenerate parabolic equations in multidimensional space. Besides, any selection of the constants (sum equals one is the only requirement for them), named the linear weights, will obtain the desired accuracy.
Keywords
Acknowledgements
The author is very thankful to the reviewers for carefully reading the paper; their comments and suggestions have improved the quality of the paper.
Funding: No funding was received for conducting this study.
Statements and Declarations
Ethical approval: Not Applicable.
Availability of supporting data: Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
Competing interests: The author has no relevant financial or non-financial interests to disclose.
Authors’ contributions: The author has accepted responsibility for the entire content of this submitted manuscript and approved submission. The figures/tables in this research work are our own work, and the publisher has permission to publish them.
Citation
Abedian, R. (2023), "A sixth-order finite difference WENO scheme for non-linear degenerate parabolic equations: an alternative technique", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 7, pp. 2544-2565. https://doi.org/10.1108/HFF-11-2022-0641
Publisher
:Emerald Publishing Limited
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