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首页> 外文期刊>International Journal of Heat and Mass Transfer >A multigrid method for the Poisson-Nernst-Planck equations
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A multigrid method for the Poisson-Nernst-Planck equations

机译：Poisson-Nernst-Planck方程的多重网格方法

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摘要

A computational technique for solving the Poisson-Nernst-Planck (PNP) equations is developed which overcomes the poor convergence rates of commonly used algorithms. The coupled Poisson and charge continuity equations are discretized using an unstructured cell-centered finite volume method. A New-ton-Raphson linearization accounting for the coupling between the equations through boundary conditions, and the space charge and drift terms, is developed. The resulting linear system of equations is solved using an algebraic multigrid method, with coarse level systems being created by agglomerating finer-level equations based on the largest coefficients of the Poisson equation. A block Gauss-Seidel update is used as the relaxation method. The method is shown to perform well for the transport of K~+ and Cl~- in a synthetic ion channel for driving voltages, surface charges, ion concentrations and channel aspect ratios ranging over several orders of magnitude.
机译：开发了一种用于解决泊松－能斯特－普朗克（PNP）方程的计算技术，该技术克服了常用算法的收敛速度慢的问题。泊松耦合和电荷连续性方程使用非结构化的以电池为中心的有限体积方法离散化。牛顿拉夫森线性化解决了通过边界条件，空间电荷和漂移项方程之间的耦合。使用代数多重网格法求解所得的线性方程组，并通过基于泊松方程的最大系数通过聚集更精细的方程来创建粗略系统。块高斯-塞德尔更新被用作松弛方法。结果表明，该方法在合成离子通道中的K〜+和Cl〜-的传输性能良好，驱动电压，表面电荷，离子浓度和通道长宽比都在几个数量级上。

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