Invariant Transformation of Equations of Motion of Ideal Monatomic Gas and New Classes of Their Accurate Solutions

摘要

The transformation is considered of equations of motion of ideal monatomic gases to coordinates of uniform expanded space. With the corresponding transformation of time, fields of speeds, pressures, density, and temperature in new variables the same equation of motion is obtained as in fixed coordinates. All usual gasdynamics may be extended to the dynamics of expanded gas and available accurate solutions of equations of gasdynamics compared to the new accurate solutions. During the considered new motions of gas for an infinite interval of time t processes are realized similar to those for the initial usual motions of gas in a finite interval of time. The motion of gas is investigated with surfaces of discontinuity (strong discontinuity, tangential discontinuity). Fundamental theorems for such flows are proven. Examples of new accurate solutions are considered. The problem pointwise explosion in a uniformly expanded and uniformly compressed gas is investigated. (Author)