Direct Simulation Scheme Derived from the Boltzmann Equation. IV. Correlation of Velocity

1981 ◽  
Vol 50 (9) ◽  
pp. 2829-2836 ◽  
Author(s):  
Kenichi Nanbu
Keyword(s):  
Boltzmann Equation ◽  
Direct Simulation ◽  
The Boltzmann Equation ◽  
Simulation Scheme

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.

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