Brownian Approximation and Monte Carlo Simulation of the Non-Cutoff Kac Equation
Journal article, 2008

The non-cutoff Boltzmann equation can be simulated using the DSMC method, by a truncation of the collision term. However, even for computing stationary solutions this may be very time consuming, in particular in situations far from equilibrium. By adding an appropriate diffusion, to the DSMC-method, the rate of convergence when the truncation is removed, may be greatly improved. We illustrate the technique on a toy model, the Kac equation, as well as on the full Boltzmann equation in a special case.

Direct simulation Monte Carlo


Kac equation

Diffusion approximation

Markov jump process

Non-equilibrium stationary state


Mattias Sunden

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Bernt Wennberg

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Journal of Statistical Physics

0022-4715 (ISSN) 1572-9613 (eISSN)

Vol. 130 2 295-312

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