Particle Methods in Computational Fluid Dynamics

Abstract

Particle methods in computational fluid dynamics (CFD) are numerical tools for the solution of the equations of fluid dynamics, obtained by replacing the fluid continuum with a finite set of particles. One of the key attributes of particle methods is that pure advection is treated exactly. The convection of properties eases the solution of multi‐material problems, simplifying the detection of interfaces. The use of particles also allows to bridge the gap between the continuum and fragmentation in a natural way, for example, in fracture or droplets problems. Particle methods can be roughly classified into two types: (i) those based on probabilistic models, which represent macroscopic properties as statistical behaviors of microscopic particles, and (ii) those based on deterministic models, implying that the state in every point at a given time is perfectly defined. This chapter covers the most common deterministic particle methods. The layout of this chapter is as follows. First we present the governing equations for the motion of fluids. Then, we describe the basic concepts of two methods that rely only on the particles to obtain the field of variables and their derivatives: smoothed particle hydrodynamics (SPH) and the moving particle semi‐implicit method (MPS). The next sections describe three methods that use the particles in combination with a finite element method (FEM) mesh to improve the accuracy. First the material point method (MPM) is described, followed by a more detailed evaluation of the particle finite element method (PFEM) and the finite element method second generation (PFEM‐2). For each of the particle methods, the advantages and disadvantages of the strategies are evaluated. The chapter concludes with an overview of the DEM and the coupling of the DEM with the FEM for the analysis of particulate flows and their interaction with structures.

Involving Particle Technology in Computational Fluid Dynamics Research: A Bibliometric Analysis

“…These findings can help better understand the system of interest. CFD results can be used to demonstrate how a piece of equipment works, how to troubleshoot problems, optimize performance, and design new equipment [1][2][3]. CFD simulations have been proposed for filtration applications such as filtration in fibrous media [4][5][6] and particulate filters [7], reactor modeling [8][9][10], colloids deposition in bidimensional [11], and three-dimensional porous media [12], to name a few.…”