Timestep Buffering to Preserve the Well-Mixed Condition in Lagrangian Stochastic Simulations

Abstract

Using one or more physical time scales as a basis for timestep ($\Delta t$) selection is common in Lagrangian stochastic simulations of particle dispersion. This approach generally works well when the velocity statistics (and thus $\Delta t$) vary slowly but problems such as the $\Delta t$ bias and imbalanced particle fluxes at interfaces can occur when the velocity statistics vary rapidly. These problems can result in violations of the well-mixed condition (WMC) and inaccurate predictions. An additional problem is that unrealistically high (or rogue) particle velocities can occur if $\Delta t$ is too large. A small constant timestep can be used to reduce or eliminate these problems but incurs the penalty of considerable computational cost. A timestep-buffering technique that eliminates abrupt changes in a variable timestep through linear interpolation is demonstrated to be effective at satisfying the WMC and minimizing rogue velocities for particle dispersion in an idealized one-dimensional turbulence regime with a steep gradient. The technique is also shown to be effective when applied to a more realistic three-dimensional system.