中国物理B ›› 2005, Vol. 14 ›› Issue (7): 1398-1406.doi: 10.1088/1009-1963/14/7/023

• CLASSICAL AREAS OF PHENOMENOLOGY • 上一篇    下一篇

A new lattice Boltzmann model for incompressible magnetohydrodynamics

陈兴旺, 施保昌   

  1. Department of Mathematics, Huazhong University of Science and Technology,Wuhan 430074, China
  • 收稿日期:2004-09-13 修回日期:2004-12-28 出版日期:2005-06-20 发布日期:2005-06-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 70271069 and 60073044).

A new lattice Boltzmann model for incompressible magnetohydrodynamics

Chen Xing-Wang (陈兴旺), Shi Bao-Chang (施保昌)   

  1. Department of Mathematics, Huazhong University of Science and Technology,Wuhan 430074, China
  • Received:2004-09-13 Revised:2004-12-28 Online:2005-06-20 Published:2005-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 70271069 and 60073044).

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摘要： Most of the existing lattice Boltzmann magnetohydrodynamics (MHD) models can be viewed as compressible schemes to simulate incompressible MHD flows. The compressible effect might lead to some undesired errors in numerical simulations. In this paper a new incompressible lattice Boltzmann MHD model without compressible effect is presented for simulating incompressible MHD flows. Numerical simulations of the Hartmann flow are performed. We do numerous tests and make comparison with Dellar's model in detail. The numerical results are in good agreement with the analytical solutions. The scheme preserved a consistent approximation of the divergence-free condition $\nabla \cdot {{ B}}=0$ to round-off error.

Abstract: Most of the existing lattice Boltzmann magnetohydrodynamics (MHD) models can be viewed as compressible schemes to simulate incompressible MHD flows. The compressible effect might lead to some undesired errors in numerical simulations. In this paper a new incompressible lattice Boltzmann MHD model without compressible effect is presented for simulating incompressible MHD flows. Numerical simulations of the Hartmann flow are performed. We do numerous tests and make comparison with Dellar's model in detail. The numerical results are in good agreement with the analytical solutions. The scheme preserved a consistent approximation of the divergence-free condition $\nabla \cdot {{ B}}=0$ to round-off error.

Key words: lattice Boltzmann method, MHD, incompressible

中图分类号:  (Magnetohydrodynamics and electrohydrodynamics)

  • 47.65.-d
47.10.-g (General theory in fluid dynamics)