Nonisentropic solutions of simple wave type of the gas dynamics equations. (English) Zbl 1362.76047
Summary: The manuscript is devoted to nonisentropic solutions of simple wave type of the gas dynamics equations. For an isentropic flow these equations (in one-dimensional and steady two-dimensional cases) are reduced to the equations written in the Riemann invariants. The system written in the Riemann invariants is hyperbolic and homogeneous. It allows obtaining simple waves, which are also called Riemann waves. For nonisentropic flows there are no Riemann invariants. The question is: what solutions could substitute the Riemann waves? By the method of differential constraints such types of solutions are found here. For these classes of solutions one can integrate the gas dynamics equations: finite formulas with one parameter are obtained. These solutions have some properties similar to simple Riemann waves. For example, they describe a nonisentropic rarefaction wave. The rarefaction waves play the main role in many applications such as the problem of pulling a piston, decay of arbitrary discontinuity and others.
MSC:
| 76M60 | Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics |
| 76N15 | Gas dynamics (general theory) |
| 70H33 | Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics |
Keywords:
differential constraints; compatibility conditions; Riemann (simple) waves; gas dynamics equationsSoftware:
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