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We deal with multidimensional regularized systems of equations for the one-velocity and one-temperature inert gas mixture dynamics consisting of the balance equations for the mass of components and the momentum and total energy of the mixture, with diffusion fluxes between the components as well as the viscosity and heat conductivity terms. The regularizations are kinetically motivated and aimed at constructing conditionally stable symmetric in space discretizations without limiters. We consider a new combined form of regularizing velocities containing the total pressure of the mixture. To confirm the physical correctness of the regularized systems, we derive the balance equation for the mixture entropy with the non-negative entropy production, under generalized assumptions on the diffusion fluxes. To confirm nice regularizing properties, we derive the systems of equations linearized at constant solutions and provide the existence, uniqueness and L²-dissipativity of weak solutions to an initial-boundary problem for them. For the original systems, we also discuss the related Petrovskii parabolicity property and its important corollaries. In addition, in the one-dimensional case, we also present the special three-point and symmetric finite-difference discretization in space of the regularized systems and prove that it inherits the entropy correctness property. We also give results of numerical experiments confirming that the discretization is able to simulate well various dynamic problems of contact between two different gases. Full article

One-dimensional regularized systems of equations for the general (multi-velocity and multi-temperature) and one-velocity and one-temperature compressible multicomponent gas mixture dynamics are considered in the absence of chemical reactions. Two types of the regularization are taken. For the latter system, diffusion fluxes between the components of the mixture are taken into account. For both the systems, the important mixture entropy balance equations with non-negative entropy productions are valid. By generalizing a discretization constructed previously in the case of a single-component gas, we suggest new nonstandard symmetric three-point spatial discretizations for both the systems which are not only conservative in mass, momentum, and total energy but also satisfy semi-discrete counterparts of the mentioned entropy balance equations with non-negative entropy productions. Importantly, the basic discretization in the one-velocity and one-temperature case is not constructed directly but by aggregation of the discretization in the case of general mixture, and that is a new approach. In this case, the results of numerical experiments are also presented for contact problems between two different gases for initial pressure jumps up to 2500. Full article