Micro-macro Kolmogorov–Fokker–Planck models for a hard-sphere gas

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• 作者：S. V. Bogomolov ; N. B. Esikova…
• 关键词：Boltzmann equation ; Kolmogorov–Fokker–Planck equation ; Navier–Stokes equation ; random processes ; stochastic differential equations with respect to Poisson and Wiener measures ; particle method
• 刊名：Mathematical Models and Computer Simulations
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：8
• 期：5
• 页码：533-547
• 全文大小：492 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Modeling and IndustrialMathematics
  Simulation and Modeling
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：2070-0490
• 卷排序：8

文摘

Using a stochastic microscopic model of a rigid-sphere gas in a phase space, which is diffusive in the velocity space and valid at moderate Knudsen numbers, macroscopic equations of gas dynamics are derived, which are different from the system of Navier–Stokes equations or quasi-gasdynamic systems. The main pecularity of our derivation is more accurate velocity averaging due to the analytical solution of stochastic differential equations with respect to the Wiener measure, which describes our original meso model. The problem of a shock-wave front is used as an example showing that such an approach yields a greater and thus more realistic diffusion of the front than the one based on the Navier–Stokes equation. The numerical solution is based on a “discontinuous” particle method well suited for supercomputer applications.