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The paper presents a solution to the Boltzmann kinetic equation based on theconstruction of its discrete conservative model. Discrete analogue of thecollision integral is presented as a contraction of a tensor, which isindependent from the initial distribution function, colliding with a tensorcomposed of medium densities in the cells. Numerical implementation of thediscrete model is demonstrated on the example of the isotropic gas relaxationproblem applied to the hard spheres model. The key feature of the method isindependence of the collision tensor components from the distribution function.Consequently the components of the collision tensor are calculated once forvarious initial distribution functions, which substantially increasesperformance of the suggested method.

Solution to the relaxation problem for a gas with a distribution function dependent on the velocity modulus