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We consider a compact approximation of the kinetic velocity distribution function by a sum of isotropic Gaussian densities in the problem of spatially homogeneous relaxation. Derivatives of the macroscopic parameters of the approximating Gaussians are obtained as solutions to a linear least squares problem derived from the Boltzmann equation with full collision integral. Our model performs well for flows obtained by mixing upstream and downstream conditions of normal shock wave with Mach number 3. The model was applied to explore the process of approaching equilibrium in a spatially homogeneous flow of gas. Convergence of solutions with respect to the model parameters is studied. © 2019 The Authors


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Results in Applied Mathematics