@Article{CiCP-21-1408,
author = {Xiaoling Liu and Chuanju Xu},
title = {Efficient Time-Stepping/Spectral Methods for the Navier-Stokes-Nernst-Planck-Poisson Equations},
journal = {Communications in Computational Physics},
year = {2018},
volume = {21},
number = {5},
pages = {1408--1428},
abstract = {<p style="text-align: justify;">This paper is concerned with numerical methods for the Navier-Stokes-Nernst-Planck-Poisson
equation system. The main goal is to construct and analyze
some stable time stepping schemes for the time discretization and use a spectral method
for the spatial discretization. The main contribution of the paper includes: 1) an useful
stability inequality for the weak solution is derived; 2) a first order time stepping
scheme is constructed, and the non-negativity of the concentration components of the
discrete solution is proved. This is an important property since the exact solution
shares the same property. Moreover, the stability of the scheme is established, together
with a stability condition on the time step size; 3) a modified first order scheme is proposed
in order to decouple the calculation of the velocity and pressure in the fluid field.
This new scheme equally preserves the non-negativity of the discrete concentration solution,
and is stable under a similar stability condition; 4) a stabilization technique is
introduced to make the above mentioned schemes stable without restriction condition
on the time step size; 5) finally, we construct a second order finite difference scheme in
time and spectral discretization in space. The numerical tests carried out in the paper
show that all the proposed schemes possess some desirable properties, such as conditionally/unconditionally
stability, first/second order convergence, non-negativity of
the discrete concentrations, and so on.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.191015.260816a},
url = {http://global-sci.org/intro/article_detail/cicp/11284.html}
}