A non-stationary method of direct statistical modelling of rarefied gas flows

The Direct Simulation Monte Carlo Method: Current Status and Perspectives

“…For example, the null-collision technique of Koura (1986) addresses itself to a hypothetical problem associated with chemically reacting flows that had not, in fact, been present in the previous applications (Bird, 1977a;Moss and Bird, 1985) of the DSMC method to these flows. Similarly, the critical study of the now obsolete time counter method by Belotserkovskii et al (1980) is based on an oversimplified mathematical model of its operation. The cell time does not have to be synchronised with the flow time at the end of each time step and an averaged number density can be used for one of the components in the product the number of molecules and the number density in each cell.…”

Monte Carlo fictitious collision algorithms for nonlinear Boltzmann equation

“…The structure of such methods correspond to the Monte Carlo methods for evaluating the iterations of a linear operators. The density /(i, x) tends to the solution of the Boltzmann equation as There exists a connection between the methods (Po^Qo) and the well known Direct Simulation Methods (DSM) [4,5]. The DSM can be deduced from ('Po, θο) by discretizing the time variable t (using a time step Δί) and splitting the operator of the governing equations of the process PQ.…”

“…and ad.j. from [8,10], and with the costs of DSM: the A spcm (statistical particle-in-cell method) from [5] and A tc (time counter methods) from [4]. For the latter we have These estimations are given in [8,10].…”

“…= N t (N t -l)/2 from[12]; Algorithm 2 of the type Pfi from[10]; Algorithm 3 of the type (Aoo, N™)· Algorithm 4 of the type A 3pcm , Δί = 0.05 from[5]. Algorithm 5 of the type A tc , Δ< = 0.05 from[4].…”

Analysis of numerical techniques of the direct simulation Monte Carlo method in the rarefied gas dynamics

“…A detailed investigation of the relation between the numerical algorithm and the kinetic equation is given in [3] where a probabilistic model of a system of N particles is constructed such that a Markov property holds. Next, a difference scheme for the master kinetic equation written for the N-particle distribution function is derived from the evolution of the model described.…”