An Effective Particle Tracing Scheme on Structured/Unstructured Grids in Hybrid Finite Volume/PDF Monte Carlo Methods

To date, PDF/Monte Carlo simulations, either in stand-alone codes or in hybrid finite volume/PDF Monte Carlo programs, appear to have been mostly carried out with cells of similar size. In many situations, such as capturing sharp gradients in a flow field, fine grids or unstructured solution-adaptive grids must be used in the finite volume code, resulting in a cell system with large variations in cell size. Such grids present a challenge for a combined PDF/Monte Carlo code. In this paper, a new particle tracing scheme is proposed, in which we introduce the concept of variable time steps. Using locally adaptive time steps in the integration of particle equations, the particlesʹ parameters are updated more frequently in regions of strong gradients than in those of flat gradients, which greatly improves the time efficiency of particle tracing. To reduce statistical errors, a particle splitting and combination procedure is also used. The new scheme allows the hybrid finite volume/PDF Monte Carlo code to use any grid that is constructed in the finite volume code. This relaxation of restrictions on the grid makes it possible to couple PDF/Monte Carlo methods to all popular commercial CFD codes and, consequently, extend existing CFD codesʹ capability to simulate turbulent reactive flow in a more accurate way. The numerical performance of the new particle tracing scheme and the solution procedure are illustrated by considering a turbulent heat transfer problem in a parallel channel and a turbulent diffusion combustion problem in a cylindrical combustor.