Group analysis of the two‐dimensional two‐temperature gas dynamics equations

Abstract

The two‐dimensional two‐temperature nonstationary gas dynamics equations with the relaxation Landau–Teller equation are considered in the paper. The group analysis method is applied to the study these equations. The admitted Lie groups are found for two modifications of relaxation time. Optimal systems of one‐ and two‐dimensional subalgebras are constructed for the group corresponding to the case of varying relaxation time which is closer to the case of ideal gas dynamics. Solutions with two and one independent invariant variables are derived using the optimal systems of admitted Lie algebras. The corresponding reduced systems were numerically calculated and compared with numerical solutions of analogous problems for classical gas dynamics equations. The differential conservation laws which present the fundamental properties of two‐temperature gas dynamics equations are also obtained.