Quiet direct simulation Monte-Carlo with random timesteps

Use of a high-order deterministic sampling technique in direct simulation Monte-Carlo (DSMC) simulations eliminates statistical noise and improves computational performance by orders of magnitude. In this paper it is also shown that if a random timestep is used in place of a fixed timestep, there is an additional improvement in performance. This performance can be increased by using a timestep that samples a random variable with a high-kurtosis probability density function. As a simple example of the method, the one-dimensional diffusion equation with an exponentially-distributed timestep is simulated, and a performance gain of approximately two is obtained. Applications to numerical simulations of fluids and plasmas are indicated.