Strategies for Efficient Particle Resolution in the Direct Simulation Monte Carlo Method

Parallel three-dimensional DSMC method using mesh refinement and variable time-step scheme

“…This results the reduction of number of simulation particles. Thus, the variable time-step method may represent one of the simplest and most efficient ways of particle weighting that avoids the problem of particle cloning, if careful grid manipulation is done [18]. Not only does it satisfy the fluxes conservation (mass, momentum and energy) exactly when a simulated particle moves across cell interface during simulation, but also it reduces tremendously the number of iterations required for transient period towards steady state.…”

“…It can be shown that careless use of cell or particle weighting often introduces some detrimental effects to the statistical accuracy, which is caused by repeatedly cloning the particles in the flow field [18]. Ivanov et al [19] proposed a variable time-step method that divides the computational domain into four subdomains having single time-step in each sub-domain.…”

“…In addition to the parallel implementation of the DSMC method [13][14][15][16][17], the other strategy to increase the computational speed is to reduce the number of simulated particles by varying particle or cell weighting in the computational domain, while maintaining relatively uniform particle distribution per cell, e.g., radial weighting for axisymmetric flow [1,2], particle weighting [18] and variation of time-steps [18,19]. It can be shown that careless use of cell or particle weighting often introduces some detrimental effects to the statistical accuracy, which is caused by repeatedly cloning the particles in the flow field [18].…”

An asymptotic-preserving Monte Carlo method for the Boltzmann equation

“…This line of research is of significance not only in rarefied gas and reentry problems [22,26,27,30,38] governed by the Boltzmann equation, but also in some more complicated transport phenomena, whose master equations are the quantum Boltzmann equation [15] and the Landau equation [25] in plasma physics. For the space homogeneous Boltzmann equation, it was realized in [39] that the successive penalization step can be written as a convex combination of the density distribution of the previous time step, a positive collision operator and the local Maxwellian.…”

An Effective Particle Tracing Scheme on Structured/Unstructured Grids in Hybrid Finite Volume/PDF Monte Carlo Methods

“…In many such flows, sharp gradients of the flow field occur near the axis, requiring cells to be smaller still, making things even worse. The imbalance of particle counts has been recognized as a problem in other types of Monte Carlo simulations as well [15,16]. The need to control particle number density has been realized for a while [1], but this issue has been given little attention in the literature.…”