A Method of Tracing Particles in Irregular Unstructured Grid System

Abstract

Particle localization is commonly encountered in many areas of numerical computations. A method of tracing particles in irregular unstructured grid system is presented. The method introduced an additional set of indexical grid system to overlap the original irregular unstructured computational grid system. The particle tracing was first conducted in the indexical grid system to obtain which indexical grid cell the particle lies in, and then was carried out among the original irregular computation grid cells which were included in this localized indexical grid cell. The new method is easy to realize in numerical calculations and can apparently improve the efficiency of particle localization. INTRODUCTIONThe particle localization in the grid system is commonly encountered in many areas of numerical computations, such as in multiphase flow with Lagrangian method and PDF method in reactive turbulence.In numerical simulations of multiphase flows, one of two main methods is to solve the ordinary differential equations for the position, mass, momentum, and energy of the particles (liquid droplets or solid particles) with Lagrangian method. The solution of these equations requires the assessment of the fluid properties at the particle's locations. If the fluid properties are developed by an Eulerian method, assessing fluid properties at the particle's position requires locating the cell which contains the particle. For those structured grid systems, the particle localization can be easily conducted in the sequence of coordinate direction. But for irregular unstructured grid systems, new methods are necessarily to be developed to improve the localization efficiency.Many researchers have made studies on particle-localization algorithms over last years. Westermann [1] described two basic criteria on determining whether a particle lies in a specific grid cell. Seldner and Westermann [2] introduced a technique for interpolation as well as for localization in irregular four-point meshes and then particles were located in boundary-fitted grids with a Cartesian background grid. For particle tracing, there are generally three algorithms termed as brute-force, modified brute-force and known-vicinity algorithm, respectively. The brute-force algorithm simply loops over all the cells of the grid and utilized the localization criteria mentioned above to judge whether the particle is inside the cell or not. This method has a very low efficiency, especially when the number of particles is very huge. Brackbill and Ruppel [3] developed a particle-localization algorithm for utilizing with the particle-in-cell approach in two dimensions. They evolved a relatively efficient algorithm based on the computational coordinates which limits searching to nearby cells. The method has several properties that an almost total absence of numerical dissipation and the ability to represent large variations in the data. The modified brute-force algorithm is able to estimate the position of node which is nearest to the particle, then only considers...

A Fast Particle-Locating Method for the Arbitrary Polyhedral Mesh

“…Several methods have been proposed for the particle locating on irregular meshes. Existing methods can be categorized into two types, i.e., the known vicinity face-to-face searching methods, such as Chen and Pereira [3], Vaidya et al [4], Haselbacher et al [5], Macpherson et al [6], Ke et al [7], Capodaglio [8], and Stuart et al [9], among others, and the auxiliary grid methods, such as Seldner and Westermann [10], Muradoglu and Kayaalp [11], Martin et al [12], and Jin et al [13], among others.…”