Positive and Conservative Characteristic Block-Centered Finite Difference Methods for Convection Dominated Diffusion Equations
Year: 2022
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 5 : pp. 1087–1110
Abstract
In this work, spatial second order positivity preserving characteristic block-centered finite difference methods are proposed for solving convection dominated diffusion problems. By using a conservative piecewise parabolic interpolation with positive constraint, the temporal first order scheme is shown to conserve mass exactly and preserve the positivity property of solution. Taking advantage of characteristics, there is no strict restriction on time steps. The scheme is extended to temporal second order by using a particular extrapolation along the characteristics. To restore solution positivity, a mass conservative local limiter is introduced and verified to keep second order accuracy. Numerical examples are carried out to demonstrate the performance of proposed methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0051
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 5 : pp. 1087–1110
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Positivity preserving conservative characteristic method.
Author Details
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L1-robust analysis of a fourth-order block-centered finite difference method for two-dimensional variable-coefficient time-fractional reaction-diffusion equations
Ma, Li
Fu, Hongfei
Zhang, Bingyin
Xie, Shusen
Computers & Mathematics with Applications, Vol. 148 (2023), Iss. P.211
https://doi.org/10.1016/j.camwa.2023.08.020 [Citations: 1]