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Volume 14, Issue 5
Positive and Conservative Characteristic Block-Centered Finite Difference Methods for Convection Dominated Diffusion Equations

Xinshu Li & Kai Fu

Adv. Appl. Math. Mech., 14 (2022), pp. 1087-1110.

Published online: 2022-06

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  • 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.

  • Keywords

Positivity preserving, conservative, characteristic method.

  • AMS Subject Headings

65M06, 76R99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-14-1087, author = {Xinshu and Li and and 23519 and and Xinshu Li and Kai and Fu and and 23520 and and Kai Fu}, title = {Positive and Conservative Characteristic Block-Centered Finite Difference Methods for Convection Dominated Diffusion Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {5}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0051}, url = {http://global-sci.org/intro/article_detail/aamm/20553.html} }
TY - JOUR T1 - Positive and Conservative Characteristic Block-Centered Finite Difference Methods for Convection Dominated Diffusion Equations AU - Li , Xinshu AU - Fu , Kai JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1087 EP - 1110 PY - 2022 DA - 2022/06 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2021-0051 UR - https://global-sci.org/intro/article_detail/aamm/20553.html KW - Positivity preserving, conservative, characteristic method. AB -

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.

Xinshu Li & Kai Fu. (2022). Positive and Conservative Characteristic Block-Centered Finite Difference Methods for Convection Dominated Diffusion Equations. Advances in Applied Mathematics and Mechanics. 14 (5). 1087-1110. doi:10.4208/aamm.OA-2021-0051
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