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A Finite Volume Simple WENO Scheme for Convection-Diffusion Equations

A Finite Volume Simple WENO Scheme for Convection-Diffusion Equations

Year:    2024

Author:    Pufan Deng, Gang Peng, Xinlong Feng, Dongmi Luo, Yibing Chen

Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 4 : pp. 882–903

Abstract

A simple weighted essentially non-oscillatory (SWENO) scheme for solving the convection-diffusion equation is proposed in this paper, where a seventh-order SWENO method and the third-order strong stability preserving (SSP) Runge-Kutta method are adopted for discretizing the space and time, respectively. Then the hyperbolic and diffusive part can achieve the seventh- and sixth-order accuracy, respectively. The proposed method has the following advantages. Firstly, negative linear weights are avoided. Secondly, one reconstruction with one stencil is required for the computation of convective and diffusive fluxes. Finally, the new method does not require the transformation while the diffusion coefficients are degenerate. Numerical examples demonstrate that the new method can achieve sixth-order accuracy in the smooth region and guarantee non-oscillatory properties for the discontinuous problems for one- and two-dimensional cases.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2024-0003

Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 4 : pp. 882–903

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Convection-diffusion equations finite volume simple WENO scheme high accuracy SSP Runge-Kutta method.

Author Details

Pufan Deng

Gang Peng

Xinlong Feng

Dongmi Luo

Yibing Chen