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.