A new theoretical model for electromagnetic gas dynamics solved by the space-time conservation element and solution element method.

摘要

A new theoretical model for the electromagnetic gas dynamics (EMGD) has been developed to model the flow motions of plasma. The ionized gas consists of characteristics of gas dynamics and electromagnetism. As a result, theoretical and numerical analyses of plasma dynamics are much more complex than that for gas dynamics and electromagnetism. In the present dissertation, the governing equations are systematically re-derived and presented in a conservative form ready for implementing modern numerical schemes for time accurate solutions. Following the presentation of the comprehensive EMGD equations, we studied two extreme conditions, i.e., the magneto-hydro-dynamic (MHD) model where the electric effect is negligible, and electro-hydro-dynamic (EHD) model where the magnetic effect is neglected. For the employment of the modern computational fluid dynamics (CFD) methods, eigensystems of the MHD and EHD model equations were derived. Contrast to the conventional approaches, the present model equations were derived based on relations of reversible thermodynamics, many difficulties encountered in traditional derivation have been avoided. In the deriving the above model equations, we clearly stated the assumptions and the associated justifications, which greatly clarify the conditions for suitable applications of the EMGD, MHD, and EHD model equations.; The space-time conservation element and solution element (CESE) method is used to solve the above model equations. Numerical solutions of the ideal MHD equations are reported. The results compare favorably with the previous data reported in the literature. In particular, no special treatment was employed to maintain the divergence free condition for the magnetic flux density. These results show that the CESE method is an accurate and robust numerical framework for complex EMGD model equations.