Fast generation of Gaussian random fields for direct numerical simulations of stochastic transport

We propose a novel discrete method of constructing Gaussian Random Fields based on a combination of modified spectral representations, Fourier and Blob. The method is intended for Direct Numerical Simulations of the V-Langevin equations. The latter are stereotypical descriptions of anomalous stochastic transport in various physical systems. From an Eulerian perspective, our method is designed to exhibit improved convergence rates. From a Lagrangian perspective, our method offers a pertinent description of particle trajectories in turbulent velocity fields: the exact Lagrangian invariant laws are well reproduced. From a computational perspective, the computing time is reduced by a factor of two in comparison with Fourier-like or Blob-like methods and an order of magnitude in comparison with FFT algorithms.