Unconditionally energy stable numerical schemes for the three-dimensional magneto-micropolar equations
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929280126025728 |
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| author | Qiu, Hailong |
| author_facet | Qiu, Hailong |
| contents | In this paper we consider unconditionally energy stable numerical schemes for the nonstationary 3D magneto-micropolar equations that describes the microstructure of rigid microelements in electrically conducting fluid flow under some magnetic field. The first scheme is comprised of the Euler semi-implicit discretization in time and conforming finite element/stabilizedfinite element in space. The second one is based on Crank-Nicolson discretization in time and extrapolated treatment of the nonlinear terms such that skew-symmetry properties are retained. We prove that the proposed schemes are unconditionally energy stable. Some error estimates for the velocity field, the magnetic field, the micro-rotation field and the fluid pressure are obtained. Furthermore, we establish some first-order decoupled numerical schemes. Numerical tests are provided to check the theoretical rates and unconditionally energy stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06000 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Unconditionally energy stable numerical schemes for the three-dimensional magneto-micropolar equations Qiu, Hailong Numerical Analysis In this paper we consider unconditionally energy stable numerical schemes for the nonstationary 3D magneto-micropolar equations that describes the microstructure of rigid microelements in electrically conducting fluid flow under some magnetic field. The first scheme is comprised of the Euler semi-implicit discretization in time and conforming finite element/stabilizedfinite element in space. The second one is based on Crank-Nicolson discretization in time and extrapolated treatment of the nonlinear terms such that skew-symmetry properties are retained. We prove that the proposed schemes are unconditionally energy stable. Some error estimates for the velocity field, the magnetic field, the micro-rotation field and the fluid pressure are obtained. Furthermore, we establish some first-order decoupled numerical schemes. Numerical tests are provided to check the theoretical rates and unconditionally energy stable. |
| title | Unconditionally energy stable numerical schemes for the three-dimensional magneto-micropolar equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2303.06000 |