Lie group analysis and propagation of weak discontinuity in one-dimensional ideal isentropic magnetogasdynamics

The aim of this paper is to carry out symmetry group analysis to obtain important classes of exact solutions from the given system of nonlinear partial differential equations (PDEs). Lie group analysis is employed to derive some exact solutions of one dimensional unsteady flow of an ideal isentropic, inviscid and perfectly conducting compressible fluid, subject to a transverse magnetic field for the magnetogasdynamics system. By using Lie group theory, the full one-parameter infinitesimal transformations group leaving the equations of motion invariant is derived. The symmetry generators are used for constructing similarity variables which leads the system of PDEs to a reduced system of ordinary differential equations; in some cases, it is possible to solve these equations exactly. Further, using the exact solution, we discuss the evolutionary behavior of weak discontinuity.     

The Riemann problem for an isentropic ideal dusty gas flow with a magnetic field

This paper deals with Riemann problem for one-dimensional inviscid, isentropic, and perfectly conducting ideal dusty gas flow with a transverse magnetic field. The explicit expressions of elementary waves are derived in terms of the density, velocity, and transverse magnetic induction of an ideal dusty gas flow. The analytical properties of elementary wave curves and the influence of parameter on the elementary waves are discussed. A new approach is proposed to resolve the Riemann problem. By applying this approach, we obtain 10 kinds of exact solutions and their corresponding criteria.     

Computational Modeling of the Structure of a High-Current Discharge in a Magnetogasdynamic Channel

A two-dimensional computational model is proposed to calculate radiative-convective heat transfer in gas flows with large gradients of physical properties. The model is based on the numerical solution of the unsteady dynamic equations for a compressible inviscid gas and the radiative transfer equations. Flow calculations for the magnetogasdynamic channel of a rail accelerator show that the dynamics of the process is substantially affected by the flow in the discharge region and hydrodynamic instability, resulting in the nonstationarity and nonuniformity of the flow and discharge structure. During the process, the discharge can exist both in the form of several current-carrying channels and in the form of a unified plasma formation. Results of the numerical calculations agree qualitative with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 5–13, November–December, 2005.     

磁气体动力学守恒律方程组的基本波

本文研究了磁气体动力学守恒律方程组的基本波,给出了基本波曲线的表达式,并利用所得到的表达式证明了基本波曲线的一些性质．