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Abstract. Progress in computer hardware and improvement of numerical methods made solution of the Boltzmann equation for rather complex gas dynamic problems real. The method developed by the author is based on a projection technique for evaluation of the collision operator. The computed collision integral is conservative by density, impulse, and energy, and became equal to zero when the solution has a form of the Maxwellian distribution. The later feature sharply increases its efficiency, especially for the near equilibrium flows. The method is extended on a mixture of gases and the gases with internal degrees of freedom, where it can incorporate real physical parameters of molecular potential and of internal energy spectrum. Examples of computations for a range of Mach and Knudsen numbers are presented.

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