An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence

Abstract

Lagrangian statistical quantities are of fundamental physical importance in our understanding of turbulence, but are very difficult to measure and hence infrequently reported in the literature. A particle-tracking algorithm is developed to extract accurate Lagrangian statistics from numerically calculated velocity fields. Lagrangian time-series are obtained from the method of direct numerical simulation, which supplies the Eulerian' velocity field on a three-dimensional grid network. The accuracy of the Lagrangian time series depends; primarily; on the accuracy of the interpolation scheme used to calculate fluid-particle velocities. Interpolation schemes based on Taylor series and on cubic splines have been implemented and tested. Errors in computed particle displacements are quantified for simple, frozen velocity fields. The algorithm is applied to stationary homogeneous isotropic turbulence with the energy maintained by artificial forcing. It is demonstrated that with adequate spatial resolution, accurate estimates of Lagrangian statistics such as velocity autocorrelations, structure functions, and frequency spectra can be obtained either with a third-order Taylor series interpolation scheme or with a cubic spline scheme. Cubic splines give higher interpolation accuracy, but they are more difficult to implement in codes that rely on secondary storage.