Algorithms and Numerical Implementation of Imitation Monte Carlo Methods with Splitting for Problems of the Boltzmann Equation

ABSTRACT

This article presents constructing optimal algorithms used for statistical modeling of a rarefied gas. The algorithms implement Imitation Monte Carlo methods with splitting by groups of particles focused on the flows with small Knudsen numbers. The above algorithms reduce the computational cost (complexity) of computations and the corresponding methods contain only two sources of systematic error with respect to the smoothed Boltzmann equation. In the paper, firstly, the criterion of splitting time step Δt selection is defined differently; secondly, one of the algorithms is adapted for solving spatially multidimensional stationary problems. As an example, spatially two-dimensional problem of longitudinal hypersonic flow over flat plate is considered.

Keywords:

• Boltzmann Equation
• flow over flat plate
• Monte Carlo methods
• stationary multidimensional flows