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A Version of Closing the System of Moment Equations of an Arbitrary Order


A method for closing the system of moment equations of order greater than two that does not use the approximation function of speed distribution of molecules is proposed. The moments closing this system are built as combinations of moments of lower orders. Systems of moment equations up to the sixth order, inclusive, are constructed. Using the shock wave profile problem as an example, it is shown that an increase in the order of the system of moment equations does not result in improving the solution. This is explained by the fact that the terms of the closing moment equations that cannot be expressed in terms of lower moments introduce an error comparable in magnitude with the magnitude of the closing moment. The solutions are verified using the model kinetic equation of polyatomic gases.

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I am grateful to A.V. Tikhonovets for her help in writing this paper.


This work was supported by the Ministry for Science and Education of Russian Federation, project no. FSFF-2020-0013.

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Correspondence to Yu. A. Nikitchenko.

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Translated by A. Klimontovich

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Nikitchenko, Y.A. A Version of Closing the System of Moment Equations of an Arbitrary Order. Comput. Math. and Math. Phys. 62, 487–507 (2022).

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  • system of moment equations
  • closing moments
  • shock wave profile
  • model kinetic equation