MONTE CARLO EVALUATION OF THE BOLTZMANN COLLISION INTEGRAL
ILLINOIS UNIV AT URBANA COORDINATED SCIENCE LAB
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A Monte Carlo method of solving the fundamental equation of the kinetic theory of dilute gases has been developed and successfully applied to two problems, one involving translational relaxation of a spatially homogeneous gas and the other a plane steady shock of arbitrary strength shock strength limited only by the fineness of the velocity space mesh. This is the first and only method capable of computing the molecular velocity distribution under conditions far from equilibrium. The essence of the problem is evaluation of the non-linear five-dimensional collision integral. Straight forward numerical quadrature would require about a year on the fastest present day computers. The computation time is reduced to a practical value, of the order of an hour, by a statistical sampling technique closely resembling the real statistical collision phenomena in the gas. Computations to date have been restricted to elastic sphere scattering of molecules without internal degrees of freedom. Differential scattering cross-sections other than elastic sphere can be accommodated in the computer program without complications or computing time penalty. Introduction of one or two internal molecular degrees of freedom will increase the complexity and computing time, but not to an impractical degree.
- Physical Chemistry
- Fluid Mechanics