To the Problem of Closure of the Systems of Moment Equations

Aim: to formulate the principle of selecting correct physical and mathematical models based on systems of partial differential equations.

Methodology. The procedure for selecting correct models consists of a comparative analysis of the relationships between the total differentials from the convective part of the system equations and the eigenvalues of their Jacobian matrix. There total differential method and finite differences method are used in this paper.

Results. With increasing number of moment equations in finite closed systems as the Grad 10 moment or 13-moment systems, there may be several characteristics sound velocities, not equal acoustic sound velocity. This results in the appearance of a subshock within the shock wave profile. Solutions to the Grad equations lose stability already at M=1.65. Equations of the Navier – Stokes are acoustic compatibility.

Research implications. The principle proposed in this paper allows for the elimination of mathematically incorrect models at the initial stages of their development.

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