# Analytical and Computational Studies of Correlations of Hydrodynamic Fluctuations in Shear Flow

## TL;DR

This study compares analytical and DPD simulation methods to analyze hydrodynamic fluctuation correlations in shear flow, revealing good agreement at moderate shear rates and discrepancies at high shear rates, highlighting complex variable coupling.

## Contribution

It introduces a combined analytical and simulation approach to study hydrodynamic fluctuations in shear flow, identifying limitations of analytical methods at high shear rates.

## Key findings

- Analytical and DPD results agree well at moderate shear rates.
- Discrepancies emerge at high shear rates due to complex variable coupling.
- Results can serve as benchmarks for multiscale simulation algorithms.

## Abstract

We study correlations of hydrodynamic fluctuations in shear flow analytically and also by dissipative particle dynamics~(DPD) simulations. The hydrodynamic equations are linearized around the macroscopic velocity field and then solved by a perturbation method in Fourier-transformed space. The autocorrelation functions~(ACFs) from the analytical method are compared with results obtained from DPD simulations under the same shear-flow conditions. Upto a moderate shear rate, various ACFs from the two approaches agree with each other well. At large shear rates, discrepancies between the two methods are observed, hence revealing strong additional coupling between different fluctuating variables, which is not considered in the analytical approach. In addition, the results at low and moderate shear rates can serve as benchmarks for developing multiscale algorithms for coupling of heterogeneous solvers, such as a hybrid simulation of molecular dynamics and fluctuating hydrodynamics solver, where thermal fluctuations are indispensable.