Direct 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 lim...Direct 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.展开更多
基金This research is supported in part by the Air Force Office of Scientific Research,Project Number PEDRS001The views expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air Force,Department of Defense,or the US Government。
文摘Direct 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.
