A KINETIC-THEORETIC DESCRIPTION OF THE FORMATION OF A SHOCK WAVE.
Rept. no. 11,
COLUMBIA UNIV NEW YORK PLASMA LAB
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The classical Riemann problem--the flow of a gas in a shock tube--is treated in the context of kinetic theory as an initial value problem for the one-dimensional Krook equation. The only simplifying assumption made is that the gas is one-dimensional its particles all move in one direction. A finite difference method is proposed, tilizing the fact that for sufficiently small time intervals, the gas experiences essentially free molecular flow, so that the collision effects can be treated as a first order correction. The conservation laws are not used. The computed results generalize the classical solution the computed solution agrees excellently with the classical solution, but in addition, has shock structure, diffusion of the contactct discontinuity, and dispersion of the expansion wave, all incorporated. The same procedure is used to calculate steady state shock structure, to which the shock developed in the shock tube is compared. Author