Numerical study of a stochastic weighted particle method for a model kinetic equation
The paper continues the study of a new partial method for nonlinear kinetic equations introduced by the authors [J. Comput. Phys. 124, No. 2, 243-253, Art. No. 0057 (1996)]. The method is based on a generalized procedure of modelling collisions between particles providing some freedom in the random choice of the collision partners. Earlier the existence of the solution of the kinetic model equation, the stability of the solution, and the convergence of a class of difference schemes was studied. The solution can be expressed as sum of a complex Fourier series and belongs to the space \(L^2(0,1)\). The stochastic weighted particle method presented in this paper consists in modelling trajectories of a stochastic particle system. The main feature of the method is the presence of certain control parameters giving the opportunity to adapt the behavior of the particle system to specific numerical purposes. It is shown that the numbers of particles with prescribed velocities may be artificially increased by the new method. The computations were performed for a model kinetic equation, for which the exact solution is known. The results obtained give us recommendations for mode complicated kinetic equations like the Boltzmann equation.
scientific article; zbMATH DE number 947687