The moving mesh method is one of the important adaptive mesh methods which is practically useful when the mesh size and overall resolution are provided and fixed as seen in many engineering computations. We employ a moving mesh technique combined with a finite element method (FEM) to solve a widely -used charged carrier transport model, the Poisson-Nernst-Planck (PNP) equations, the solutions of which often have boundary or internal layers and sharp interfaces when the convection is dominated. Considering that flux is a significant physical quantity in designing stable and accurate numerical algorithm for transport problems such as the PNP system, we start from a relatively general functional and propose a flux -based monitor function and an adaptive step size -controlling algorithm for guiding the mesh movement in the FEM solution of the PNP equations. The numerical results illustrate that the moving mesh method is effectively addressing challenges arising from solution singularities and the convectiondominated effects. It also shows that the moving mesh finite element method we propose exhibits superior performance compared to both the traditional moving mesh finite element method and fixed mesh finite element method in some scenarios. Furthermore, it demonstrates better adherence to the physical properties of energy dissipation inherent in the PNP equation.

Publication:

Journal of Computational Physics Volume 513, 15 September 2024

https://doi.org/10.1016/j.jcp.2024.113169

Author:

Minrui Lv

LSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Benzhuo Lu

LSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Email: bzlu@lsec.cc.ac.cn