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simulation propagation of a shock wave in a polytropic gas

This example models the one-dimensional propagation of a shock wave in a polytropic gas

 the model consists of a compartmentalized shock tube filled with a polytropic gas. A diaphragm separates the tube into two equal compartments

Both compartments are filled with the same gas, but the ratio of the density of the gas in compartment A to the density of the gas in compartment B is 2:1

The diaphragm separating the compartments is instantaneously removed, causing a shock wave to advance into compartment B and a rarefaction wave to propagate back into compartment A

A schematic of the model is shown in Figure

an initial density of 0.2 for compartment A, and an initial density of 0.1 for compartment B

for simulation the gas , we use ideal gas equation

the gas moves from high-pressure to low-pressure

Comparison of the density along the length of the shock tube

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