NUMERICAL TREATMENT OF NON-IDEAL MGD BASIC EQUATIONS,
INNSBRUCK UNIV (AUSTRIA) INST FOR THEORETICAL PHYSICS
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The mathematical treatment of the MGD basic equations is rendered extremely difficult by dissipation terms, as, e.g., caused by thermal conductivity, internal friction of finite electrical conductivity of the medium. Such terms give rise to a parabolic degeneration of the otherwise hyperbolic equations and, consequently, exclude the application of the method of characteristics which is usually used in the non-dissipative case. Summarizing the treatment of a previous report, and generalizing some of its results, a numerical method of solution for the parabolically degenerated one-dimensional MGD basic equations is given it has been developed in analogy to the theory of characteristics. This method is advantageous insofar as it has - particularly for weak dissipation - similar stability properties as the method of characteristics in the case of vanishing dissipation. Using this numerical method, the unsteady development of the structure of a magnetically driven shock under the influence of finite electrical conductivity is investigated in MGD--B1-approximation. The B1-approximation was chosen since it leads to a particularly simple and perspicuous form of the basic equations.
- Numerical Mathematics
- Plasma Physics and Magnetohydrodynamics