Unconditional positivity-preserving and energy stable schemes for a reduced Poisson-Nernst-Planck system

2019/09/28 by Hailiang Liu, Liu, Hailiang, Wumaier Maimaitiyiming +1 · 2 citations
Physics and Astronomy · #Quantum, superfluid, helium dynamics #Cold Atom Physics and Bose-Einstein Condensates #Spectroscopy and Quantum Chemical Studies

paper · pdf · doi:10.48550/arxiv.1909.13161

Abstract

The Poisson-Nernst-Planck (PNP) system is a widely accepted model for simulation of ionic channels. In this paper, we design, analyze, and numerically validate a second order unconditional positivity-preserving scheme for solving a reduced PNP system, which can well approximate the three dimensional ion channel problem. Positivity of numerical solutions is proven to hold true independent of the size of time steps and the choice of the Poisson solver. The scheme is easy to implement without resorting to any iteration method. Several numerical examples further confirm the positivity-preserving property, and demonstrate the accuracy, efficiency, and robustness of the proposed scheme, as well as the fast approach to steady states.

Cited by

• A unified structure preserving scheme for a multi-species model with a gradient flow structure and nonlocal interactions via singular kernels
• A positivity-preserving hybrid DDG method for Poisson--Nernst--Planck systems

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