Abstract
The first part of this chapter contains a summary of the main properties of the Boltzmann equation: some popular models of the collision kernel, moments and physical quantities, weak formulation of the Boltzmann equation, the H-theorem, the moment equations, boundary conditions and scaling transformation. The second part contains a short description of the Stochastic Weighted Particle Method (SWPM) and its variants, discretisation of the time and space variables and modelling of the initial and boundary conditions. In the final, third part of the paper two numerical examples are presented. The first example illustrates the advantages of the SWPM in computing the tail of the distribution function while the second example deals with the spatially two-dimensional flow and shows the possibility to resolve extremely low density using SWPM.
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Rjasanow, S. (2004). Monte-Carlo methods for the Boltzmann equation. In: Degond, P., Pareschi, L., Russo, G. (eds) Modeling and Computational Methods for Kinetic Equations. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8200-2_3
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DOI: https://doi.org/10.1007/978-0-8176-8200-2_3
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