The Formulation of Finite Difference RBFWENO Schemes for Hyperbolic Conservation Laws: An Alternative Technique

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.

Author Details

Rooholah Abedian

Mehdi Dehghan