Linear, decoupled, second-order and structure-preserving scheme for Carreau fluid equations coupled with steric Poisson-Nernst-Planck model
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| Format: | Preprint |
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2025
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| _version_ | 1866912563634110464 |
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| author | Zhu, Wenxing Pan, Mingyang He, Dongdong |
| author_facet | Zhu, Wenxing Pan, Mingyang He, Dongdong |
| contents | In this paper, to study ionic steric effects, we present a linear, decoupled, second-order accurate in time and structure-preserving scheme with finite element approximations for Carreau fluid equations coupled with steric Poisson-Nernst-Planck (SPNP) model. The logarithmic transformation for the ion concentration is used to preserve positivity property. To deal with the nonlinear coupling terms in fluid equation, a nonlocal auxiliary variable with respect to the free energy of SPNP equations and its associated ordinary differential equation are introduced. The obtained system is equivalent to the original system. The fully discrete scheme is proved to be mass conservative, positivity-preserving for ion concentration and energy dissipative at discrete level. Some numerical simulations are provided to demonstrate its stability and accuracy. Moreover, the ionic steric effects are numerically investigated. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_01270 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear, decoupled, second-order and structure-preserving scheme for Carreau fluid equations coupled with steric Poisson-Nernst-Planck model Zhu, Wenxing Pan, Mingyang He, Dongdong Numerical Analysis In this paper, to study ionic steric effects, we present a linear, decoupled, second-order accurate in time and structure-preserving scheme with finite element approximations for Carreau fluid equations coupled with steric Poisson-Nernst-Planck (SPNP) model. The logarithmic transformation for the ion concentration is used to preserve positivity property. To deal with the nonlinear coupling terms in fluid equation, a nonlocal auxiliary variable with respect to the free energy of SPNP equations and its associated ordinary differential equation are introduced. The obtained system is equivalent to the original system. The fully discrete scheme is proved to be mass conservative, positivity-preserving for ion concentration and energy dissipative at discrete level. Some numerical simulations are provided to demonstrate its stability and accuracy. Moreover, the ionic steric effects are numerically investigated. |
| title | Linear, decoupled, second-order and structure-preserving scheme for Carreau fluid equations coupled with steric Poisson-Nernst-Planck model |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2509.01270 |