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**Statistical modeling of rarefied gas flow based on the majorant frequency principle.**
*(English.
Russian original)*
Zbl 0707.76073

Sov. Phys., Dokl. 35, No. 5, 387-390 (1990); translation from Dokl. Akad. Nauk SSSR 312, No. 2, 315-320 (1990).

Summary: To solve problems of rarefied gas aerodynamics on the basis of nonlinear the Boltzmann equation, or of modeling equations, various numerical methods are used, among which the direct statistical modeling method holds a leading position. The principal feature of this method is the modeling of the collisional relaxation stage. An algorithm has been formulated for the realization of this stage on the basis of an N- particle gas model, described by the fundamental Katz kinetic equations. The calculation of the particular features of such gas model in the homogeneous case makes it possible to formulate the majorant frequency principle. Based on this principle, an efficient scheme has been constructed for the modeling of collisional relaxation. The modeling time linearly depends on the number of particles.

In the present work, this principle, which combines the ideas from the methods of maximum cross section and of complementary randomizing, has been extended to the spatially nonuniform case, which allowed to develop new efficient schemes for the modeling of spatially nonuniform rarefied gas flows. It must be noted that a direct application of the maximum cross section method to an N-particle gas model leads to a quadratic dependence of the algorithm labor consumption on the number of particles.

In the present work, this principle, which combines the ideas from the methods of maximum cross section and of complementary randomizing, has been extended to the spatially nonuniform case, which allowed to develop new efficient schemes for the modeling of spatially nonuniform rarefied gas flows. It must be noted that a direct application of the maximum cross section method to an N-particle gas model leads to a quadratic dependence of the algorithm labor consumption on the number of particles.