A consistent and conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part III: On a staggered mesh
A consistent and conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part III: On a staggered mesh
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低磁雷诺数下不可压缩 MHD 流动的一致且保守的方案。
DOI：
10.1016/j.jcp.2011.08.013
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发表时间：
2012
影响因子：
4.1
通讯作者：
Li Jun-Feng
中科院分区：
文献类型：
--
作者：
Ni Ming-Jiu;Li Jun-Feng
本文在矩形同位网格上发展了一种相容的守恒格式[M. J. Ni，R. Munipalli，N.B.莫利，黄鹏，硕士。Abdou，低磁雷诺数下不可压缩MHD流的电流密度守恒格式。Part I：on a rectangular collocated grid system，Journal of Computational Physics 227（2007）174-204] and on an arbitrary collocated mesh [M.- J. Ni，R. Munipalli，P. Huang，N.B.莫利，文学硕士Abdou，低磁雷诺数下不可压缩MHD流的电流密度守恒格式。第二部分：在任意配置的网格上，Journal of Computational Physics 227（2007）205-228]已被扩展并专门设计用于通过求解磁流体力学（MHD）的电势方程来计算交错网格系统上的洛伦兹力（第三部分）低磁雷诺数。在交错网格中，压力（p）和电势（φ）位于单元中心，而速度和电流通量位于主控制体积的单元面上。该格式在数值上满足物理守恒定律、电荷守恒定律和动量守恒定律。物理上，当磁场恒定或与空间坐标无关时，洛伦兹力保持动量。电池表面上的电流密度通量的计算使用与电位泊松方程的离散化一致的方案进行，这可以确保计算的电流密度保持电荷。利用洛仑兹力的发散公式计算了主控制体胞心处的洛仑兹力，该力在恒定磁场或空间坐标无关磁场下均能保持动量守恒。然后将计算出的单元中心洛伦兹力插值到单元表面，通过求解动量方程来获得相应的速度通量。该格式的“保守性”是一个重要的性质，它可以保证高Hartmann数下MHD流动的计算精度，并采用强非均匀网格来处理Hartmann层和边层。在交错网格下进行了二维完全发展的MHD流场的数值模拟，并给出了解析解。利用已有的实验数据，在交错网格上计算了矩形管道内恒定磁场和变化磁场下的三维MHD流动，以验证该格式的计算精度。预计洛伦兹力的方案可以与对流项和压力项的完全保守方案一起使用[Y。Morinishi，T.S.隆德，O. V. Vasilyev，P. Moin，不可压缩流的完全守恒高阶有限差分格式，计算物理杂志143（1998）90-124]用于交错网格下具有良好精度的MHD湍流和MHD不稳定性的直接模拟。
The consistent and conservative scheme developed on a rectangular collocated mesh [M.-J. Ni, R. Munipalli, N.B. Morley, P. Huang, M.A. Abdou, A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part I: on a rectangular collocated grid system, Journal of Computational Physics 227 (2007) 174–204] and on an arbitrary collocated mesh [M.-J. Ni, R. Munipalli, P. Huang, N.B. Morley, M.A. Abdou, A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part II: on an arbitrary collocated mesh, Journal of Computational Physics 227 (2007) 205–228] has been extended and specially designed for calculation of the Lorentz force on a staggered grid system (Part III) by solving the electrical potential equation for magnetohydrodynamics (MHD) at a low magnetic Reynolds number. In a staggered mesh, pressure (p) and electrical potential (φ) are located in the cell center, while velocities and current fluxes are located on the cell faces of a main control volume. The scheme numerically meets the physical conservation laws, charge conservation law and momentum conservation law. Physically, the Lorentz force conserves the momentum when the magnetic field is constant or spatial coordinate independent. The calculation of current density fluxes on cell faces is conducted using a scheme consistent with the discretization for solution of the electrical potential Poisson equation, which can ensure the calculated current density conserves the charge. A divergence formula of the Lorentz force is used to calculate the Lorentz force at the cell center of a main control volume, which can numerically conserve the momentum at constant or spatial coordinate independent magnetic field. The calculated cell-center Lorentz forces are then interpolated to the cell faces, which are used to obtain the corresponding velocity fluxes by solving the momentum equations. The “conservative” is an important property of the scheme, which can guarantee computational accuracy of MHD flows at high Hartmann number with a strongly non-uniform mesh employed to resolve the Hartmann layers and side layers. 2D fully developed MHD flows with analytical solutions available have been conducted to validate the scheme at a staggered mesh. 3D MHD flows, with the experimental data available, at a constant magnetic field in a rectangular duct with sudden expansion and at a varying magnetic field in a rectangular duct are conducted on a staggered mesh to verify the computational accuracy of the scheme. It is expected that the scheme for the Lorentz force can be employed together with a fully conservative scheme for the convective term and the pressure term [Y. Morinishi, T.S. Lund, O.V. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, Journal of Computational Physics 143 (1998) 90–124] for direct simulation of MHD turbulence and MHD instability with good accuracy at a staggered mesh.
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DOI：
10.13182/fst95-a30346
发表时间：
1995
期刊：
Fusion Technology
影响因子：
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作者：
L. Bühler
通讯作者：
L. Bühler
影响因子：
4.6
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Y. Shimomura
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Y. Shimomura
影响因子：
0.9
作者：
A. Kulikovskii
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A. Kulikovskii
DOI：
10.1115/1.1445331
发表时间：
2001-03
期刊：
--
影响因子：
--
作者：
U. Muller;L. Buhler;G. Dulikravich
通讯作者：
U. Muller;L. Buhler;G. Dulikravich
DOI：
10.1016/j.jcp.2009.06.004
发表时间：
2009-10
期刊：
J. Comput. Phys.
影响因子：
--
作者：
M. Ni
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