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

TL;DR

This paper introduces a fast, novel discrete method for generating Gaussian Random Fields tailored for direct numerical simulations of stochastic transport, improving convergence and computational efficiency while accurately modeling particle trajectories.

Contribution

The paper presents a new spectral-based discrete method combining Fourier and Blob techniques for Gaussian Random Fields, enhancing simulation speed and accuracy.

Findings

Method is twice as fast as standard approaches.

Improved convergence rates in Eulerian simulations.

Accurately reproduces Lagrangian invariant laws.

Abstract

We propose a novel discrete method of constructing Gaussian Random Fields (GRF) 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 others a pertinent description of particle trajectories in turbulent velocity fields: the exact Lagrangian invariant laws are well reproduced. From a computational perspective, our method is twice as fast as standard numerical representations.