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 - <p style="text-align: justify;">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.</p>