Local Time-Stepping Algorithm for Solving Probability Density Function Turbulence Model Equations

Abstract

A local time-stepping algorithm has been developed to improve the numerical efe ciency of Lagrangian particlebased Monte Carlo methods for obtaining the steady-state solutions of the modeled probability density function equations of turbulent reacting e ows. On each step in the pseudo-time-marching algorithm, the properties of each particle are advanced by a time step, the magnitude of which depends on the particle’ s spatial location. This algorithm has been incorporated into the consistent hybrid e nite volume/particle method. The performance of the localtime-steppingmethodisevaluated intermsofnumericalefe ciencyandaccuracy throughapplication toa nonreacting bluff-body e ow. Forthistest case,itisfound that localtime stepping can acceleratetheglobal convergence of the hybrid method by as much as an order of magnitude, depending on the grid stretching. Additionally, local time stepping is found to improve signie cantly the robustness of the hybrid method mainly due to the accelerated convection of error waves out of thecomputational domain. The method is very simpleto implement, and the small increase in CPU time per step (typically 3%) is a negligible penalty compared to the substantial reduction in the number of time steps required to reach convergence.