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Volume 13, Issue 2
Upwind Strategy for Localized Method of Approximate Particular Solutions with Applications to Convection Dominated Diffusion Problems

Xueying Zhang & Luyu Ran

DOI: 10.4208/aamm.OA-2019-0103

Adv. Appl. Math. Mech., 13 (2021), pp. 455-466.

Published online: 2020-12

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  • Abstract

A novel upwind technique for the localized method of approximate particular solutions (LMAPS) is proposed to solve the convection-diffusion equations. An upwind approximation to the convective terms is implemented by choosing upwind interpolation stencils while the central interpolation stencils are used for the diffusive terms. The proposed upwind LMAPS scheme is also been compared with conventional LMAPS without upwind technique, to demonstrate its superiority in generating high accurate solutions than the latter. Numerical results show that the proposed upwind LMAPS has high accuracy and efficiency for a variety of convection-diffusion equations.

  • Keywords

LMAPS, convection dominated problems, upwind scheme, radial basis functions.

  • AMS Subject Headings

65M10, 65M70, 35L03

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-13-455, author = {Zhang , Xueying and Ran , Luyu}, title = {Upwind Strategy for Localized Method of Approximate Particular Solutions with Applications to Convection Dominated Diffusion Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {13}, number = {2}, pages = {455--466}, abstract = {

A novel upwind technique for the localized method of approximate particular solutions (LMAPS) is proposed to solve the convection-diffusion equations. An upwind approximation to the convective terms is implemented by choosing upwind interpolation stencils while the central interpolation stencils are used for the diffusive terms. The proposed upwind LMAPS scheme is also been compared with conventional LMAPS without upwind technique, to demonstrate its superiority in generating high accurate solutions than the latter. Numerical results show that the proposed upwind LMAPS has high accuracy and efficiency for a variety of convection-diffusion equations.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0103}, url = {http://global-sci.org/intro/article_detail/aamm/18492.html} }
TY - JOUR T1 - Upwind Strategy for Localized Method of Approximate Particular Solutions with Applications to Convection Dominated Diffusion Problems AU - Zhang , Xueying AU - Ran , Luyu JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 455 EP - 466 PY - 2020 DA - 2020/12 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2019-0103 UR - https://global-sci.org/intro/article_detail/aamm/18492.html KW - LMAPS, convection dominated problems, upwind scheme, radial basis functions. AB -

A novel upwind technique for the localized method of approximate particular solutions (LMAPS) is proposed to solve the convection-diffusion equations. An upwind approximation to the convective terms is implemented by choosing upwind interpolation stencils while the central interpolation stencils are used for the diffusive terms. The proposed upwind LMAPS scheme is also been compared with conventional LMAPS without upwind technique, to demonstrate its superiority in generating high accurate solutions than the latter. Numerical results show that the proposed upwind LMAPS has high accuracy and efficiency for a variety of convection-diffusion equations.

Zhang , Xueying and Ran , Luyu. (2020). Upwind Strategy for Localized Method of Approximate Particular Solutions with Applications to Convection Dominated Diffusion Problems. Advances in Applied Mathematics and Mechanics. 13 (2). 455-466. doi:10.4208/aamm.OA-2019-0103
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