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.

中文翻译：

---

在混合有限体积/概率密度函数蒙特卡罗方法中采用基于重心坐标的高效粒子跟踪算法

这项工作的一个主要关注点是在基于混合压力的有限体积/概率密度函数 (FV/PDF) 蒙特卡罗 (MC) 求解算法的框架内开发一种有效的粒子跟踪管理算法，以扩展将FV/PDF MC方法应用于绝对不可压缩流，加快湍流模拟中脉动速度-湍流频率联合PDF方程求解的收敛速度。与基于密度的算法相反，基于压力的算法即使在零马赫数流中也具有稳定的收敛速度。作为另一个贡献，文献表明，过去开发的方法主要使用网格搜索技术在每个跟踪时间步开始时将粒子归因于细胞。此外，他们必须在每个时间步计算线性基函数，以估计粒子平均场并对数据进行插值。在具有任意形状的 3D 网格的计算域中，这些计算的计算成本非常昂贵、耗时且效率低下。众所周知，重心跟踪是一种连续粒子跟踪方法，在处理具有一般网格形状的 3D 域时提供更高的效率。重心跟踪消除了任何网格搜索技术，并且很容易提供方便的线性基函数。因此，这项工作受益于这些优点，并根据粒子的重心坐标来跟踪粒子。它导致本方法的计算工作更少并且效率更高。通过检查钝体湍流情况来验证当前的 FV/PDF MC 方法。从精度的角度来看，表明该算法的结果与实验数据和可用的数值解非常吻合。本研究表明，达到统计稳态条件所需的粒子时间步数比以前开发的算法至少少六分之一。这也证实了当前基于混合压力的算法具有更快的收敛速度。