Stochastic Weighted Particle Method Research Articles

Efficient particle control in systems with large density gradients

Simulations of large density gradients present a number of challenges for direct Monte Carlo methods, since they lead to too few particles in dilute regions and prohibitively many in the dense regions. We propose a particle control methodology that gives the user more control of the number of particles per cell by introducing a variable weight for each particle. The proposed scheme is based on the stochastic weighted particle method, requires only small modifications to DSMC, and exactly conserves mass, momentum, and energy. In validation tests of systems with density ratios of order 102-104, we observe 101-102 times less variance in the dilute region compared to a DSMC solution with the same number of system particles, while introducing a moderate additional computational cost.

Interspecies fractional collisions

Relaxing the direct simulation Monte Carlo (DSMC) method to be compatible with variable particle weights has significant advantages when applied to simulations with a large density variation, as the statistical noise in the low density region can be controlled. The stochastic weighted particle method [S. Rjasanow and W. Wagner, J. Comput. Phys. 124, 243–253 (1996)] enables the control of particle weight but has never been applied to a multicomponent gas mixture or plasma. This paper focuses on charge-exchange collisions, but the method is applicable to any interspecies collision reactions including ionization and excitation collisions, providing the correct collision rate between different species with different weights in the context of no-time-counter scheme, which can easily be extended to other DSMC schemes. The method is first verified through two test cases observing the depletion of high-energy ions as impacting background neutral particles and looking at the spatial variation and temporal evolution of different species. Then, the method is applied to a simple electric propulsion plume simulation, demonstrating the controllability of species ratio and capability in reducing statistical noise for the charge-exchange ions.

A Higher Order Moment Preserving Reduction Scheme for the Stochastic Weighted Particle Method

The Stochastic Weighted Particle Method (SWPM) is a Monte Carlo technique developed by Rjasanow and Wagner that generalizes Bird's Direct Simulation Monte Carlo (DSMC) method for solving the Boltzmann equation. To reduce computational cost due to the gradual increase in the number of stochastic particles in the SWPM, Rjasanow and Wagner proposed several particle reduction schemes designed to preserve specified moments of the velocity distribution. Here, we introduce an improved particle reduction scheme that preserves all moments of the velocity distribution up to the second order, as well as the raw and central heat flux both within each group of particles to be reduced and for the entire system. Furthermore, we demonstrate that with the new reduction scheme the scalar fourth-order moment can be computed more accurately at a reduced computational cost.

A stochastically weighted operator splitting Monte Carlo (SWOSMC) method for the numerical simulation of complex aerosol dynamic processes

PurposeThe purpose of this paper is to study the complex aerosol dynamic processes by using this newly developed stochastically weighted operator splitting Monte Carlo (SWOSMC) method.Design/methodology/approachStochastically weighted particle method and operator splitting method are coupled to formulate the SWOSMC method for the numerical simulation of particle-fluid systems undergoing the complex simultaneous processes.FindingsThis SWOSMC method is first validated by comparing its numerical simulation results of constant rate coagulation and linear rate condensation with the corresponding analytical solutions. Coagulation and nucleation cases are further studied whose results are compared with the sectional method in excellent agreement. This SWOSMC method has also demonstrated its high numerical simulation capability when used to deal with simultaneous aerosol dynamic processes including coagulation, nucleation and condensation.Originality/valueThere always exists conflict and tradeoffs between computational cost and accuracy for Monte Carlo-based methods for the numerical simulation of aerosol dynamics. The operator splitting method has been widely used in solving complex partial differential equations, while the stochastic-weighted particle method has been commonly used in numerical simulation of aerosol dynamics. However, the integration of these two methods has not been well investigated.

A Stochastic Weighted Particle Method for Coagulation--Advection Problems

A spatially resolved stochastic weighted particle method for inception--coagulation--advection problems is presented. Convergence to a deterministic limit is briefly studied. Numerical experiments are carried out for two problems with very different coagulation kernels. These tests show the method to be robust and confirm the convergence properties. The robustness of the weighted particle method is shown to contrast with two direct simulation algorithms which develop instabilities.

SOLUSI NUMERIK PERSAMAAN BOLTZMANN

Particle methods are well known tools to solve the kinetic Boltzmann equation numerically. The usual procedure of such method is the direct simulation Monte-Carlo, which directly simulate the collision between particles. The second method of interest is the stochastic weighted particle method, which is developed to improve the previous method. The main idea of the second method is to use random weight transfer between particles during collisions. In order to reduce the stochastic fluctuations, this method provides a way to increase the number of particles. But if the additional particles cannot be compensated in some natural way, then this number should be reduced. Several reduction procedures have been proposed. Some numerical results using both methods are presented. It is shown that the second method gives some better results in some ways.

Convergence of the Stochastic Weighted Particle Method for the Boltzmann Equation

This paper studies convergence of the stochastic weighted particle method for the Boltzmann equation. First the method is extended by introducing new stochastic reduction procedures in order to control the number of simulation particles. Then, under rather general conditions, convergence to the solution of the Boltzmann equation is proved. Finally, numerical experiments are performed illustrating both convergence and considerable variance reduction for the specific problem of calculating tails of the velocity distribution.

Simulation of rare events by the stochastic weighted particle method for the Boltzmann equation

An extension of the stochastic weighted particle method for the numerical treatment of the Boltzmann equation is presented. A new procedure for modelling the inflow boundary conditions is introduced and its performance is tested in two-dimensional example with strong density gradients. A gain factor in computing time of several orders of magnitude is achieved in specific situations.

Reduction of the Number of Particles in the Stochastic Weighted Particle Method for the Boltzmann Equation

Different ideas for reducing the number of particles in the stochastic weighted particle method for the Boltzmann equation are described and discussed. The corresponding error bounds are obtained and numerical tests for the spatially homogeneous Boltzmann equation presented. It is shown that if an appropriate reduction procedure is used then any effect on the accuracy of the numerical scheme is negligible.

Numerical Study of a Stochastic Weighted Particle Method for a Model Kinetic Equation

A stochastic weighted particle method is applied to a model nonlinear kinetic equation. A detailed study of various numerical approximations is presented. The main effect achieved by the new method is an artificial increase of the relative number of simulation particles with prescribed velocities.