| Issue |
ESAIM: M2AN
Volume 59, Number 3, May-June 2025
|
|
|---|---|---|
| Page(s) | 1471 - 1504 | |
| DOI | https://doi.org/10.1051/m2an/2025020 | |
| Published online | 04 June 2025 | |
Stability and error analysis of pressure-correction scheme for the Navier–Stokes–Planck–Nernst–Poisson equations
1
School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, P.R. China
2
Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, Fujian 361005, P.R. China
* Corresponding author: chenht@xmu.edu.cn
Received:
14
May
2024
Accepted:
23
March
2025
In this paper, we propose and analyze first-order time-stepping pressure-correction projection scheme for the Navier–Stokes–Planck–Nernst–Poisson (NSPNP) equations. By introducing a governing equation for the auxiliary variable through the convective PNP parts, we reconstruct the original equations into an equivalent system and develop a first-order decoupled and linearized scheme. This scheme preserves non-negativity and mass conservation of the concentration components and is unconditionally energy stable. We derive the rigorous error estimates in the two dimensional case for the ionic concentrations, electric potential, velocity and pressure in the L2- and H1-norms. Numerical examples are presented to validate the proposed scheme.
Mathematics Subject Classification: 65M12 / 65M15 / 65N30 / 76M10
Key words: Navier–Stokes–Planck–Nernst–Poisson equations / SAV approach / pressure-correction scheme / unconditional energy stability / error analysis
© The authors. Published by EDP Sciences, SMAI 2025
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