Simple invariant solutions of the dynamic equation for a monatomic gas. (English. Russian original) Zbl 1522.76072
Proc. Steklov Inst. Math. 321, Suppl. 1, S186-S203 (2023); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 29, No. 2, 115-132 (2023).
Summary: We consider a system of gas dynamics equations with the state equation of a monatomic gas. The equations admit a group of transformations with a 14-dimensional Lie algebra. We consider 4-dimensional subalgebras containing the projective operator from the optimal system of subalgebras. The invariants of the basis operators are computed. Eight simple invariant solutions of rank 0 are obtained. Of these, four physical solutions specify a gas motion with a linear velocity field and one physical solution specifies a motion with a linear dependence of components of the velocity vector on two space coordinates. All these solutions except one have variable entropy. The motion of gas particles as a whole is constructed for the isentropic solution. The solutions obtained have a density singularity on a constant or moving plane, which is a boundary with vacuum or a wall.
MSC:
| 76N15 | Gas dynamics (general theory) |
| 76M60 | Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics |
Keywords:
projective operator; transformation group; 14-dimensional Lie algebra; optimal subalgebra system; linear velocity field; isentropic solutionSoftware:
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