A Stable Backward Monte Carlo Method for the Solution of the Boltzmann Equation

摘要

Backward Monte Carlo methods for solving the Boltzmann equation are investigated. A stable estimator is proposed since a previously published estimator was found to be numerically unstable. The principle of detailed balance, which is obeyed by state transitions of a physical system and ensures existence of a stable equilibrium solution, is violated by the transition probability of the unstable method, and is satisfied by construction with the proposed backward transition probability.