A Self-Similar Flow behind a Magnetogasdynamic Shock Wave Generated by a Moving Piston in a Gravitating Gas with Variable Density: Isothermal Flow

Table 1

Variation of the density ratio 𝛽(=𝜌₁/𝜌₂) across the shock front and the position of the piston surface 𝜂_𝑝 for different values of 𝑀^𝐴−2, 𝑛, and 𝐺₀ with 𝛾=5/3, 𝑖=2.

𝑀^𝐴−2	𝑛	𝑤=−1/(𝑛+1)	Gravitating case			Nongravitating case
			𝛽(𝑀=10)	Position of the piston 𝜂𝑝
0.0	−1/4	−4/3	0.2575	𝐺0=10	𝐺0=100	𝛽(𝑀=∞)	𝜂𝑝
				0.792961	0.858979	0.2500	0.786644
	−1/6	−6/5	0.2575	0.828341	0.871949	0.2500	0.826576
𝑀^𝐴−2	𝑛	α    𝑤	𝛽	Position of the piston 𝜂𝑝
				Gravitating case		Nongravitating case
				𝐺0=10	𝐺0=100
0.01	−1/4	1/3 −4/3	0.273323	0.762936	0.850165	0.74148
	−1/6	1/5 −6/5	0.285626	0.810785	0.888747	0.78455
0.02	−1/4	1/3 −4/3	0.295947	0.753016	0.8622504	0.705453
	−1/6	1/5 −6/5	0.320305	0.799756	0.898664	0.747313
0.05	−1/4	1/3 −4/3	0.36106	0.726403	0.870199	0.606753
	−1/6	1/5 −6/5	0.421092	0.777162	0.904818	0.63214