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We investigate the coupling between the two components of a Large Eddy Simulation/Probability Density Function (LES/PDF) algorithm for the simulation of turbulent reacting flows. In such an algorithm, the Large Eddy Simulation (LES) component provides a solution to the hydrodynamic equations, whereas the Lagrangian Monte Carlo Probability Density Function (PDF) component solves for the PDF of chemical compositions. Special attention is paid to the transfer of specific volume information from the PDF to the LES code: the specific volume field contains probabilistic noise due to the nature of the Monte Carlo PDF solution, and thus the use of the specific volume field in the LES pressure solver needs careful treatment. Using a test flow based on the Sandia/Sydney Bluff Body Flame, we determine the optimal strategy for specific volume feedback. Then, the overall second-order convergence of the entire LES/PDF procedure is verified using a simple vortex ring test case, with special attention being given to bias errors due to the number of particles per LES Finite Volume (FV) cell. [ABSTRACT FROM AUTHOR]

Abstract: This work addresses the issue of particle mass consistency in Large Eddy Simulation/Probability Density Function (LES/PDF) methods for turbulent reactive flows. Numerical schemes for the implicit and explicit enforcement of particle mass consistency (PMC) are introduced, and their performance is examined in a representative LES/PDF application, namely the Sandia–Sydney Bluff-Body flame HM1. A new combination of interpolation schemes for velocity and scalar fields is found to better satisfy PMC than multilinear and fourth-order Lagrangian interpolation. A second-order accurate time-stepping scheme for stochastic differential equations (SDE) is found to improve PMC relative to Euler time stepping, which is the first time that a second-order scheme is found to be beneficial, when compared to a first-order scheme, in an LES/PDF application. An explicit corrective velocity scheme for PMC enforcement is introduced, and its parameters optimized to enforce a specified PMC criterion with minimal corrective velocity magnitudes. [Copyright &y& Elsevier]

We describe a new family of weak pth order accurate SDE time integration schemes, called the direct Richardson pth order accurate (DRp) schemes. The DRp schemes use the idea of Richardson extrapolation on Euler time steps, performed by way of an acceptance-rejection algorithm. Previous applications of Richardson extrapolation to the Euler scheme are applicable only when the objective is to estimate a functional of the final distribution of the process. In contrast, provided that the diffusion matrix is strictly positive definite, the DRp class of schemes can be used in all applications which require a weak SDE time integration scheme. Numerical results have been obtained, and a comparison is made between the second- and third-order accurate DRp schemes and other modern SDE time integration schemes, indicating that the DRp schemes incur less error than standard algorithms based on Ito-Taylor expansions, and have similar computational efficiency. Finally, we provide a proof of the convergence properties of the DRp schemes. [ABSTRACT FROM AUTHOR]

Abstract: We describe a particle position time advancement algorithm that is designed for use with several subgrid velocity reconstruction schemes used in LES/FDF methods, and potentially in other applications. These reconstruction schemes yield a subgrid velocity field with desirable divergence properties, but also with discontinuities across cell faces. Therefore, a conventional time advancement algorithm, such as second-order Runge–Kutta (RK2), does not perform as well as it does with a smooth velocity field. The algorithm that we describe, called Multi-Step RK2 (MRK2), builds upon RK2 by breaking up the time step into two or more substeps whenever a particle crosses one or more velocity discontinuities. When used in conjunction with the parabolic edge reconstruction method, MRK2 performs considerably better than RK2: both the final position of an advected particle, and the final area of a 2D infinitesimal area element are second-order accurate in time (as opposed to first-order accurate for RK2). Furthermore, MRK2 has the theoretical advantage that it better preserves the continuity of the mapping between initial and final particle positions. [Copyright &y& Elsevier]