A new algorithm for the simulation of the boltzmann equation using the direct simulation monte-carlo method

2009 ◽  
Vol 23 (10) ◽  
pp. 2861-2870 ◽  
Author(s):  
A. A. Ganjaei ◽  
S. S. Nourazar
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Monte Carlo Method ◽  
Direct Simulation Monte Carlo ◽  
Direct Simulation ◽  
The Boltzmann Equation ◽  
Simulation Monte Carlo

DSMC: Fast direct simulation Monte Carlo solver for the Boltzmann equation by Multi-Chain Markov Chain and multicore programming

2016 ◽  
Vol 07 (02) ◽  
pp. 1650009
Author(s):  
Di Zhao ◽  
Haiwu He
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Boltzmann Equation ◽  
Direct Simulation Monte Carlo ◽  
Collision Term ◽  
Direct Simulation ◽  
Multicore Programming ◽  
The Boltzmann Equation ◽  
Simulation Monte Carlo

Direct Simulation Monte Carlo (DSMC) solves the Boltzmann equation with large Knudsen number. The Boltzmann equation generally consists of three terms: the force term, the diffusion term and the collision term. While the first two terms of the Boltzmann equation can be discretized by numerical methods such as the finite volume method, the third term can be approximated by DSMC, and DSMC simulates the physical behaviors of gas molecules. However, because of the low sampling efficiency of Monte Carlo Simulation in DSMC, this part usually occupies large portion of computational costs to solve the Boltzmann equation. In this paper, by Markov Chain Monte Carlo (MCMC) and multicore programming, we develop Direct Simulation Multi-Chain Markov Chain Monte Carlo (DSMC3): a fast solver to calculate the numerical solution for the Boltzmann equation. Computational results show that DSMC3 is significantly faster than the conventional method DSMC.

Convergence of A Distributional Monte Carlo Method for the Boltzmann Equation

2012 ◽  
Vol 4 (1) ◽  
pp. 102-121 ◽  
Author(s):  
Christopher R. Schrock ◽  
Aihua W. Wood
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Substantial Reduction ◽  
Direct Simulation Monte Carlo ◽  
Collision Operator ◽  
Direct Simulation ◽  
The Boltzmann Equation ◽  
Distributional Method ◽  
Point Measure ◽  
Simulation Monte Carlo

AbstractDirect Simulation Monte Carlo (DSMC) methods for the Boltzmann equation employ a point measure approximation to the distribution function, as simulated particles may possess only a single velocity. This representation limits the method to converge only weakly to the solution of the Boltzmann equation. Utilizing kernel density estimation we have developed a stochastic Boltzmann solver which possesses strong convergence for bounded and L∞ solutions of the Boltzmann equation. This is facilitated by distributing the velocity of each simulated particle instead of using the point measure approximation inherent to DSMC. We propose that the development of a distributional method which incorporates distributed velocities in collision selection and modeling should improve convergence and potentially result in a substantial reduction of the variance in comparison to DSMC methods. Toward this end, we also report initial findings of modeling collisions distributionally using the Bhatnagar-Gross-Krook collision operator.

Study on the Deposition Profile Characteristics in the Micron-Scale Trench Using Direct Simulation Monte Carlo Method

1998 ◽  
Vol 120 (2) ◽  
pp. 296-302 ◽  
Author(s):  
Masato Ikegawa ◽  
Jun’ichi Kobayashi ◽  
Morihisa Maruko
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Boundary Conditions ◽  
Gas Flow ◽  
Direct Simulation Monte Carlo ◽  
Low Pressure ◽  
Sputter Deposition ◽  
Direct Simulation ◽  
Simulation Monte Carlo ◽  
Profile Characteristics

As integrated circuits are advancing toward smaller device features, step-coverage in submicron trenches and holes in thin film deposition are becoming of concern. Deposition consists of gas flow in the vapor phase and film growth in the solid phase. A deposition profile simulator using the direct simulation Monte Carlo method has been developed to investigate deposition profile characteristics on small trenches which have nearly the same dimension as the mean free path of molecules. This simulator can be applied to several deposition processes such as sputter deposition, and atmospheric- or low-pressure chemical vapor deposition. In the case of low-pressure processes such as sputter deposition, upstream boundary conditions of the trenches can be calculated by means of rarefied gas flow analysis in the reactor. The effects of upstream boundary conditions, molecular collisions, sticking coefficients, and surface migration on deposition profiles in the trenches were clarified.

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