Local time-stepping algorithm for solving probability density function turbulence model equations

A local time-stepping algorithm has been developed to improve the numerical efficiency of Lagrangian particle-based Monte Carlo methods for obtaining the steady-state solutions of the modeled probability density function equations of turbulent reacting flows. 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 finite volume/particle method. The performance of the local time-stepping method is evaluated in terms of numerical efficiency and accuracy through application to a non-reacting bluff-body flow. For this test case, it is found that local time stepping can accelerate the global 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 significantly the robustness of the hybrid method mainly due to the accelerated convection of error waves out of the computational domain. The method is very simple to 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.