Employment of an efficient particle tracking algorithm based on barycentric coordinates in hybrid finite‐volume/probability‐density‐function Monte Carlo methods

Abstract

One main concern of this work is to develop an efficient particle‐tracking‐managing algorithm in the framework of a hybrid pressure‐based finite‐volume/probability‐density‐function (FV/PDF) Monte‐Carlo (MC) solution algorithm to extend the application of FV/PDF MC methods to absolutely incompressible flows and speedup the convergence rate of solving the fluctuating velocity‐turbulent frequency joint PDF equation in turbulent flow simulations. Contrary to the density‐based algorithms, the pressure‐based algorithms have stable convergence rates even in zero‐Mach number flows. As another contribution, literature shows that the past developed methods mostly used mesh searching techniques to attribute particles to cells at the beginning of each tracking time‐step. Also, they had to calculate the linear basis functions at every time‐step to estimate the particle mean fields and interpolate the data. These calculations would be computationally very expensive, time‐consuming, and inefficient in computational domains with arbitrary‐shaped 3D meshes. As known, the barycentric tracking is a continuous particle tracking method, which provides more efficiency in case of handling 3D domains with general mesh shapes. The barycentric tracking eliminates any mesh searching technique and readily provides the convenient linear basis functions. So, this work benefits from these advantages and tracks the particles based on their barycentric coordinates.  It leads to less computational work and a better efficiency for the present method. A bluff‐body turbulent flow case is examined to validate the present FV/PDF MC method. From the accuracy perspective, it is shown that the results of the present algorithm are in great agreement with experimental data and available numerical solutions. The present study shows that the number of particle time‐steps required to reach the statistically steady‐state condition is at least one‐sixth less than the previously developed algorithms. This also approves a faster convergence rate for the present hybrid pressure‐based algorithm.