77 citations · 211 across the 9 of their papers we have counts for
9 papers
A positivity-preserving hybrid DDG method for Poisson--Nernst--Planck systems
Hailiang Liu, Zhongming Wang, Peimeng Yin
In earlier work [H. Liu and Z. Wang, J. Comput. Phys., 328(2017)], an arbitrary high-order conservative and energy-dissipative direct discontinuous Galerkin (DDG) scheme was develo…
Positivity-preserving third order DG schemes for Poisson--Nernst--Planck equations
Hailiang Liu, Zhongming Wang, Peimeng Yin +1
In this paper, we design and analyze third order positivity-preserving discontinuous Galerkin (DG) schemes for solving the time-dependent system of Poisson--Nernst--Planck (PNP) eq…
Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study
Svetlana Roudenko, Zhongming Wang, Kai Yang
We consider the generalized Benjamin-Ono (gBO) equation on the real line, , and perform nu…
Structure-Preserving and Efficient Numerical Methods for Ion Transport
Jie Ding, Zhongming Wang, Shenggao Zhou
Ion transport, often described by the Poisson--Nernst--Planck (PNP) equations, is ubiquitous in electrochemical devices and many biological processes of significance. In this work,…
A Modified Poisson--Nernst--Planck Model with Excluded Volume Effect: Theory and Numerical Implementation
Farjana Siddiqua, Zhongming Wang, Shenggao Zhou
The Poisson--Nernst--Planck (PNP) equations have been widely applied to describe ionic transport in ion channels, nanofluidic devices, and many electrochemical systems. Despite the…
Computational Study on Hysteresis of Ion Channels: Multiple Solutions to Steady-State Poisson--Nernst--Planck Equations
Jie Ding, Hui Sun, Zhongming Wang +1
The steady-state Poisson-Nernst-Planck (ssPNP) equations are an effective model for the description of ionic transport in ion channels. It is observed that an ion channel exhibits…
A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson--Nernst--Planck systems
Hailiang Liu, Zhongming Wang
We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for solving time-dependent Poisson-Nernst-Planck systems. Both the semi-discrete and fully di…
An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations
Hailiang Liu, Zhongming Wang
We propose a high order discontinuous Galerkin (DG) method for solving nonlinear Fokker-Planck equations with a gradient flow structure. For some of these models it is known that t…
A free energy satisfying finite difference method for Poisson--Nernst--Planck equations
Hailiang Liu, Zhongming Wang
In this work we design and analyze a free energy satisfying finite difference method for solving Poisson-Nernst-Planck equations in a bounded domain. The algorithm is of second ord…