A dynamic mass transport method for Poisson-Nernst-Planck equations
A dynamic mass transport method for Poisson-Nernst-Planck equations
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DOI：
10.1016/j.jcp.2022.111699
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发表时间：
2022-05
期刊：
影响因子：
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通讯作者：
H. Liu;W. Maimaitiyiming
中科院分区：
文献类型：
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作者：
H. Liu;W. Maimaitiyiming
提出了一种近似求解Poisson-Nernst-Planck（PNP）方程的动态质量输运方法。基于JKO型变分公式的半离散格式自然地强制执行解的正性和能量定律，对于连续PNP系统。完全离散的计划被进一步制定为一个约束最小化问题，证明是可解的，并满足所有三个解决方案的性质（质量守恒，积极性和能量耗散）独立的时间步长或空间网格大小。数值实验验证了计算结果的收敛性和格式的结构保持性。
A dynamic mass-transport method is proposed for approximately solving the Poisson–Nernst–Planck (PNP) equations. The semi-discrete scheme based on the JKO type variational formulation naturally enforces solution positivity and the energy law as for the continuous PNP system. The fully discrete scheme is further formulated as a constrained minimization problem, shown to be solvable, and satisfy all three solution properties (mass conservation, positivity and energy dissipation) independent of time step size or the spatial mesh size. Numerical experiments are conducted to validate convergence of the computed solutions and verify the structure preserving property of the proposed scheme.