On generalized simple waves of the equations of gas dynamics

Abstract: The presentation is devoted to the analysis of generalized simple waves of the gas dynamics and magnetogas dynamics equations. In contrast to simple waves, generalized simple waves for a polytropic gas (with the polytropic exponent not equal to 5/3) are non-isentropic. The study considers one-dimensional plane and two-dimensional steady solutions. Using the method of differential constraints, a class of nontrivial exact solutions of the Cauchy problem for one-dimensional unsteady gas dynamics equations is obtained. For nonsmooth and non-constant initial data, a solution to the Riemann problem is presented, which is reduced to integrating systems of ordinary differential equations. The solutions of these ordinary differential equations are given in explicit form. Generalized simple waves are also obtained for the equations of magnetogas dynamics.

REFERENCES

1. Meleshko S.V. Methods for constructing exact solutions of partial differential equations. Springer, New York, 2005. 352 p.

2. Meleshko S.V., Shapeev V.P. Nonisentropic solutions of simple wave type of the gas dynamics equations // Journal of Nonlinear Mathematical Physics. 2011. Vol. 18, No. 1, P. 195–212.

3. Meleshko S.V., Moyo S., Webb G.M. Solutions of generalized simple wave type of magnetic fluid // Commun Nonlinear Sci Numer Simulat. 2021. Vol. 103. 105991.

Russianmathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic

Mathematical models and integration methods