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Maximum-Principle-Preserving High-Order Conservative Difference Schemes for Convection-Dominated Diffusion Equations

Maximum-Principle-Preserving High-Order Conservative Difference Schemes for Convection-Dominated Diffusion Equations

Year:    2024

Author:    Lele Liu, Hong Zhang, Xu Qian, Songhe Song

Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 4 : pp. 855–881

Abstract

This paper proposes a high-order maximum-principle-preserving (MPP) conservative scheme for convection-dominated diffusion equations. For high-order spatial discretization, we first use the fifth-order weighted compact nonlinear scheme (WCNS5) for the convection term and the sixth-order central difference scheme for the diffusion term. Owing to the nonphysical oscillations caused by the high-order scheme, we further adopt a parameterized MPP flux limiter by modifying a high-order numerical flux toward a lower-order monotone numerical flux to achieve the maximum principle. Subsequently, the resulting spatial scheme is combined with third-order strong-stability-preserving Runge-Kutta (SSPRK) temporal discretization to solve convection-dominated diffusion problems. Several one-dimension (1D) and two-dimension (2D) numerical experiments show that the proposed scheme maintains up to fifth-order accuracy and strictly preserves the maximum principle. The results indicate the proposed scheme’s strong potential for solving convection-dominated diffusion and incompressible flow problems.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2023-0165

Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 4 : pp. 855–881

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Maximum-principle-preserving weighted compact nonlinear schemes parameterized MPP flux limiter convection-dominated diffusion equations.

Author Details

Lele Liu

Hong Zhang

Xu Qian

Songhe Song