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

Abstract

The paper presents a solution to the Boltzmann kinetic equation based on the construction of its discrete conservative model. Discrete analogue of the collision integral is presented as a contraction of a tensor, which is independent from the initial distribution function, colliding with a tensor composed of medium densities in the cells. Numerical implementation of the discrete model is demonstrated on the example of the isotropic gas relaxation problem applied to the hard spheres model. The key feature of the method is independence of the collision tensor components from the distribution function. Consequently the components of the collision tensor are calculated once for various initial distribution functions, which substantially increases performance of the suggested method.