Stability and error analysis of pressure-correction scheme for the Navier-Stokes-Planck-Nernst-Poisson equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914909885825024 |
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| author | He, Yuyu Chen, Hongtao |
| author_facet | He, Yuyu Chen, Hongtao |
| contents | In this paper, we propose and analyze first-order time-stepping pressure-correction projection scheme for the Navier-Stokes-Planck-Nernst-Poisson equations. By introducing a governing equation for the auxiliary variable through the ionic concentration equations, 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 $L^2$- and $H^1$-norms. Numerical examples are presented to validate the proposed scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability and error analysis of pressure-correction scheme for the Navier-Stokes-Planck-Nernst-Poisson equations He, Yuyu Chen, Hongtao Numerical Analysis 65M12, 65M15, 65N30, 76M10 In this paper, we propose and analyze first-order time-stepping pressure-correction projection scheme for the Navier-Stokes-Planck-Nernst-Poisson equations. By introducing a governing equation for the auxiliary variable through the ionic concentration equations, 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 $L^2$- and $H^1$-norms. Numerical examples are presented to validate the proposed scheme. |
| title | Stability and error analysis of pressure-correction scheme for the Navier-Stokes-Planck-Nernst-Poisson equations |
| topic | Numerical Analysis 65M12, 65M15, 65N30, 76M10 |
| url | https://arxiv.org/abs/2408.06085 |