Fundamentals of numerical magnetohydrodynamics

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Magnetohydrodynamics is a fluid model for the motion of an ionized gas in a magnetic field. In its ideal, non-dissipative form, the Lundquist equations, it has the same mathematical character as the model for gas dynamics. It gives, in the same way, a self-consistent description of the fluid dynamics, including the exchange of momentum and energy between the field and the fluid. However, because of the greater complexity of the physics which they describe, some aspects of the solutions are quite different. The magnetic field introduces a strong anisotropic character to the medium which causes wave propagation to depend on ... continued below

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Pages: 17

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Brackbill, J.U. January 1, 1987.

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Description

Magnetohydrodynamics is a fluid model for the motion of an ionized gas in a magnetic field. In its ideal, non-dissipative form, the Lundquist equations, it has the same mathematical character as the model for gas dynamics. It gives, in the same way, a self-consistent description of the fluid dynamics, including the exchange of momentum and energy between the field and the fluid. However, because of the greater complexity of the physics which they describe, some aspects of the solutions are quite different. The magnetic field introduces a strong anisotropic character to the medium which causes wave propagation to depend on the direction of propagation with respect of the magnetic field. In addition, there are several distinct speeds so that, in general, the responses to disturbances are quite complex. To capture the principal features of the solutions in numerical calculations, several problems must be addressed. Some of these problems are unique to MHD: for example, preserving the solenoidality of the magnetic field. Others are similar to ordinary gas dynamics, such as energy conservation, numerical stability, and computational diffusion, but are more complex or have different consequences for MHD than for ordinary fluid flow. These fundamental problems in the numerical solution of the MHD equations are discussed as four topics: the dispersion of the Lundquist equations and the dispersion and stability of finite difference approximations; the conservation laws of MHD and the achievement of conservation in the numerical solutions; a discussion of convective transport and its role in computational diffusion; and finally, a method for preserving the solenoidality of the magnetic field.

Physical Description

Pages: 17

Notes

NTIS, PC A02/MF A01.

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  • International school for space simulations, La Londe les Maures, France, 15 Jun 1987

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  • Other: DE87011769
  • Report No.: LA-UR-87-2052
  • Report No.: CONF-8706150-1
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 6063630
  • Archival Resource Key: ark:/67531/metadc1113670

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Office of Scientific & Technical Information Technical Reports

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  • January 1, 1987

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  • Feb. 22, 2018, 7:45 p.m.

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  • May 22, 2018, 4:30 p.m.

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Brackbill, J.U. Fundamentals of numerical magnetohydrodynamics, article, January 1, 1987; New Mexico. (digital.library.unt.edu/ark:/67531/metadc1113670/: accessed September 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.