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Volume 26, Issue 2
An Adaptive Conservative Finite Volume Method for Poisson-Nernst-Planck Equations on a Moving Mesh

Xiulei Cao & Huaxiong Huang

DOI: 10.4208/cicp.OA-2018-0134

Commun. Comput. Phys., 26 (2019), pp. 389-412.

Published online: 2019-04

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  • Abstract

In this paper, we present a finite volume method for solving Poisson-Nernst-Planck (PNP) equations in one spatial dimension. To reduce computational cost, an adaptive moving mesh strategy is employed in order to resolve thin Debye layers near the boundary. In addition to the standard monitor functions, we propose two new ones for the moving mesh partial differential equations to improve the accuracy of the numerical solution. The method guarantees the strict mass conservation. We have proved that the scheme maintains positivity on the adaptive moving mesh which has not been done for PNP.

  • Keywords

Poisson-Nernst-Planck, finite volume method, adaptive moving mesh, mass conservation.

  • AMS Subject Headings

65N08, 68U20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-26-389, author = {Xiulei Cao and Huaxiong Huang}, title = {An Adaptive Conservative Finite Volume Method for Poisson-Nernst-Planck Equations on a Moving Mesh}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {2}, pages = {389--412}, abstract = {

In this paper, we present a finite volume method for solving Poisson-Nernst-Planck (PNP) equations in one spatial dimension. To reduce computational cost, an adaptive moving mesh strategy is employed in order to resolve thin Debye layers near the boundary. In addition to the standard monitor functions, we propose two new ones for the moving mesh partial differential equations to improve the accuracy of the numerical solution. The method guarantees the strict mass conservation. We have proved that the scheme maintains positivity on the adaptive moving mesh which has not been done for PNP.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0134}, url = {http://global-sci.org/intro/article_detail/cicp/13096.html} }
TY - JOUR T1 - An Adaptive Conservative Finite Volume Method for Poisson-Nernst-Planck Equations on a Moving Mesh AU - Xiulei Cao & Huaxiong Huang JO - Communications in Computational Physics VL - 2 SP - 389 EP - 412 PY - 2019 DA - 2019/04 SN - 26 DO - http://doi.org/10.4208/cicp.OA-2018-0134 UR - https://global-sci.org/intro/article_detail/cicp/13096.html KW - Poisson-Nernst-Planck, finite volume method, adaptive moving mesh, mass conservation. AB -

In this paper, we present a finite volume method for solving Poisson-Nernst-Planck (PNP) equations in one spatial dimension. To reduce computational cost, an adaptive moving mesh strategy is employed in order to resolve thin Debye layers near the boundary. In addition to the standard monitor functions, we propose two new ones for the moving mesh partial differential equations to improve the accuracy of the numerical solution. The method guarantees the strict mass conservation. We have proved that the scheme maintains positivity on the adaptive moving mesh which has not been done for PNP.

Xiulei Cao and Huaxiong Huang. (2019). An Adaptive Conservative Finite Volume Method for Poisson-Nernst-Planck Equations on a Moving Mesh. Communications in Computational Physics. 26 (2). 389-412. doi:10.4208/cicp.OA-2018-0134
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