Year: 2017
Communications in Computational Physics, Vol. 21 (2017), Iss. 5 : pp. 1408–1428
Abstract
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.191015.260816a
Communications in Computational Physics, Vol. 21 (2017), Iss. 5 : pp. 1408–1428
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
-
A linear, second-order accurate, positivity-preserving and unconditionally energy stable scheme for the Navier–Stokes–Poisson–Nernst–Planck system
Pan, Mingyang | Liu, Sifu | Zhu, Wenxing | Jiao, Fengyu | He, DongdongCommunications in Nonlinear Science and Numerical Simulation, Vol. 131 (2024), Iss. P.107873
https://doi.org/10.1016/j.cnsns.2024.107873 [Citations: 2] -
Stable and decoupled schemes for an electrohydrodynamics model
Yao, Hui | Xu, Chuanju | Azaiez, MejdiMathematics and Computers in Simulation, Vol. 206 (2023), Iss. P.689
https://doi.org/10.1016/j.matcom.2022.12.007 [Citations: 3] -
Efficiently high-order time-stepping R-GSAV schemes for the Navier–Stokes–Poisson–Nernst–Planck equations
He, Yuyu | Chen, HongtaoPhysica D: Nonlinear Phenomena, Vol. 466 (2024), Iss. P.134233
https://doi.org/10.1016/j.physd.2024.134233 [Citations: 3] -
Error estimates for the finite element method of the Navier-Stokes-Poisson-Nernst-Planck equations
Li, Minghao | Li, ZhenzhenApplied Numerical Mathematics, Vol. 197 (2024), Iss. P.186
https://doi.org/10.1016/j.apnum.2023.11.012 [Citations: 2] -
Convergence and superconvergence analysis for a mass conservative, energy stable and linearized BDF2 scheme of the Poisson–Nernst–Planck equations
Li, Minghao | Shi, Dongyang | Li, ZhenzhenCommunications in Nonlinear Science and Numerical Simulation, Vol. 140 (2025), Iss. P.108351
https://doi.org/10.1016/j.cnsns.2024.108351 [Citations: 0] -
Unconditional superconvergence analysis of a structure-preserving finite element method for the Poisson-Nernst-Planck equations
Yang, Huaijun | Li, MengAdvances in Computational Mathematics, Vol. 50 (2024), Iss. 3
https://doi.org/10.1007/s10444-024-10145-4 [Citations: 1] -
New mixed finite element methods for the coupled Stokes and Poisson–Nernst–Planck equations in Banach spaces
Correa, Claudio I. | Gatica, Gabriel N. | Ruiz-Baier, RicardoESAIM: Mathematical Modelling and Numerical Analysis, Vol. 57 (2023), Iss. 3 P.1511
https://doi.org/10.1051/m2an/2023024 [Citations: 10] -
Efficient time-stepping schemes for the Navier-Stokes-Nernst-Planck-Poisson equations
Zhou, Xiaolan | Xu, ChuanjuComputer Physics Communications, Vol. 289 (2023), Iss. P.108763
https://doi.org/10.1016/j.cpc.2023.108763 [Citations: 2] -
Second-order energy-stable scheme and superconvergence for the finite difference method on non-uniform grids for the viscous Cahn–Hilliard equation
Chen, Yanping | Yan, Yujing | Li, Xiaoli | Zhao, XuanCalcolo, Vol. 61 (2024), Iss. 2
https://doi.org/10.1007/s10092-024-00579-z [Citations: 0] -
Structure-preserving algorithms for the two-dimensional fractional Klein-Gordon-Schrödinger equation
Fu, Yayun | Cai, Wenjun | Wang, YushunApplied Numerical Mathematics, Vol. 156 (2020), Iss. P.77
https://doi.org/10.1016/j.apnum.2020.04.011 [Citations: 18]