Orthogonal Polynomial Solution of the Boltzmann Equation for a Strong Shock Wave

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Abstract
The structure of a strong shock wave in a neutral, monatomic gas is studied here using the generalized orthogonal polynomial method of solution of the Boltzmann equation suggested by Mintzer. Mott‐Smith's bimodal distribution function, with the shock thickness X(M) left arbitrary, is used as the weight function to generate the orthogonal polynomials of the expansion. This automatically makes Mott‐Smith's distribution function the zeroth‐ and first‐approximation distribution functions without specification of X(M). In the second approximation a particular choice of X(M) must be made in order that the equations have a unique solution which represents a shock wave and, with that choice of X(M), predictions are made only for Mach numbers above 2.14. The X(M) thus determined is the same as obtained by Mott‐Smith by transporting cx2, but with the restriction to Mach numbers above 2.14.

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