Abstract
The method and results previously obtained [C. K. Chu, Phys. Fluids 8, 12 (1965)] for a one-dimensional gas (γ = 3) is extended to a monatomic three-dimensional gas (γ = 5/3). The classical Riemann problem—the flow of a gas in a shock tube—is treated as an initial value problem for the Krook equation, after the Krook equation is first reduced to two simultaneous Krook equations each for a one-dimensional gas. The numerical scheme used is the same as that previously proposed. Results are obtained on the formation of shocks corresponding to Mach numbers of 1.27, 1.5, and 1.75. It is seen that the stronger the shock, the shorter the formation time. The short-time behavior of the flow agrees with free flow, while the long-time behavior agrees with fluid dynamics. The shocks formed agree very closely with the results of Liepmann, Narasimha, and Chahine.
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