N.V.Saltanov The generalized potentials, Riemann invariants and simple waves in analog of the Chaplygin-Sedov hodograph method in magnetic gas dynamics |
Applied hydromechanics, Vol. 4 (76) ¹ 3, (2002) |
| In case when the equations of state and the integrals of symmetry involve not only specific volume dependence, but a stream function dependence, too, generalized potentials, that fulfill the linear equations, in which the coordinates x1 and x2 and a stream function y are expressed, are introduced to analog of Chaplygin-Sedov method of hodograph in magnetic gas dynamics. In case when basic linear equation of theory is hyperbolic the Riman invariants and equations for them are obtained. In case, when vectors of the magnetic field and velocity are collinear, the solutions of simple waves type, where velocity, magnetic field intensity and pressure are the functions of only specific volume, are obtained. On basis of the method, that is analogous to L. I. Sedov method of obtaining of the class of exact solutions with homogeneous relative deformations of single--parametric nonstationary gas dynamics, the very general occasion of integrability in quadratures of the equation for the variable "Ï" in hodograph plane, that is analogous to pressure in classical gas dynamics, is consideredi. Òhe case is considered, when the magnetic field vector is parallel to the particular axis. |
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| TEXT LANGUAGE: Russian |