An Adaptive Conservative Finite Volume Method for Poisson-Nernst-Planck Equations on a Moving Mesh (Communications in Computational Physics, 2019)
In this paper, we present a finite volume method for solving Poisson-Nernst-Planck (PNP) equations in one spatial dimension. To reduce computational cost, anadaptive moving mesh strategy is employed in order to resolve thin Debye layers nearthe boundary. In addition to the standard monitor functions, we propose two newones for the moving mesh partial differential equations to improve the accuracy of thenumerical solution. The method guarantees the strict mass conservation. We haveproved that the scheme maintains positivity on the adaptive moving mesh which hasnot been done for PNP.