A spectral projection method for the analysis of autocorrelation functions and projection errors in discrete particle simulation
Discrete particle simulation is a well-established tool for the simulation of particles and droplets suspended in turbulent flows of academic and industrial applications. The study of some properties such as the preferential concentration of inertial particles in regions of high shear and low vorticity requires the computation of autocorrelation functions. This can be a tedious task as the discrete point particles need to be projected in some manner to obtain the continuous autocorrelation functions. Projection of particle properties on to a computational grid, for instance, the grid of the carrier phase, is furthermore an issue when quantities such as particle concentrations are to be computed or Source terms between the carrier phase and the particles are exchanged. The errors committed by commonly used projection methods are often unknown and are difficult to analyse. Grid and sampling size limit the possibilities in terms of precision per computational cost. Here, we present a spectral projection method that is not affected by sampling issues and addresses all of the above issues. The technique is only limited by computational resources and is easy to parallelize. The only visible drawback is the limitation to simple geometries and therefore limited to academic applications. The spectral projection method consists of a discrete Fourier-transform of the particle locations. The Fourier-transformed particle number density and momentum fields can then be used to Compute the autocorrelation functions and the continuous physical space fields for the evaluation of the projection methods error. The number of Fourier components used to discretize the projector kernel can be chosen such that the corresponding characteristic length scale is as small as needed. This allows to study the phenomena of particle motion, for example, in a region of preferential concentration that may be smaller than the cell size of the carrier phase grid. The precision of the spectral projection method depends, therefore, only on the number of Fourier modes considered. Copyright (c) 2008 John Wiley & Sons, Ltd.
projection method autocorrelation discrete particle simulation error analysis fourier analysis interpolation