The Formulation of Finite Difference RBFWENO Schemes for Hyperbolic Conservation Laws: An Alternative Technique
Year: 2023
Author: Rooholah Abedian, Mehdi Dehghan
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 4 : pp. 1023–1055
Abstract
To solve conservation laws, efficient schemes such as essentially non-oscillatory (ENO) and weighted ENO (WENO) have been introduced to control the Gibbs oscillations. Based on radial basis functions (RBFs) with the classical WENO-JS weights, a new type of WENO schemes has been proposed to solve conservation laws [J. Guo et al., J. Sci. Comput., 70 (2017), pp. 551–575]. The purpose of this paper is to introduce a new formulation of conservative finite difference RBFWENO schemes to solve conservation laws. Unlike the usual method for reconstructing the flux functions, the flux function is generated directly with the conservative variables. Comparing with Guo and Jung (2017), the main advantage of this framework is that arbitrary monotone fluxes can be employed, while in Guo and Jung (2017) only smooth flux splitting can be used to reconstruct flux functions. Several 1D and 2D benchmark problems are prepared to demonstrate the good performance of the new scheme.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0241
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 4 : pp. 1023–1055
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Weighted essentially non-oscillatory scheme radial basis functions interpolation finite difference method hyperbolic conservation laws.