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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.05941 |
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| _version_ | 1866915220321992704 |
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| author | Xie, Jialin Zhang, Xiaodi |
| author_facet | Xie, Jialin Zhang, Xiaodi |
| contents | In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear, and multiphysics system efficiently, we develop a decoupled, linear, second-order in time, and unconditionally energy stable finite element scheme. We incorporate several distinct numerical techniques, including reformulations of the equations and a scalar auxiliary variable to handle the coupled nonlinear terms,a symmetric implicit-explicit treatment for the symmetric positive definite nonlinearity, and stable finite element approximations. We also prove that the numerical scheme is provably uniquely solvable and unconditionally energy stable rigorously. A series of numerical examples are presented to illustrate the accuracy and performance of our scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05941 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reformulated formulation and efficient fully discrete finite element method for a conductive ferrofluid model Xie, Jialin Zhang, Xiaodi Numerical Analysis In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear, and multiphysics system efficiently, we develop a decoupled, linear, second-order in time, and unconditionally energy stable finite element scheme. We incorporate several distinct numerical techniques, including reformulations of the equations and a scalar auxiliary variable to handle the coupled nonlinear terms,a symmetric implicit-explicit treatment for the symmetric positive definite nonlinearity, and stable finite element approximations. We also prove that the numerical scheme is provably uniquely solvable and unconditionally energy stable rigorously. A series of numerical examples are presented to illustrate the accuracy and performance of our scheme. |
| title | Reformulated formulation and efficient fully discrete finite element method for a conductive ferrofluid model |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.05941 |