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We study correlations of hydrodynamic fluctuations in shear flow analyticallyand also by dissipative particle dynamics~(DPD) simulations. The hydrodynamicequations are linearized around the macroscopic velocity field and then solvedby a perturbation method in Fourier-transformed space. The autocorrelationfunctions~(ACFs) from the analytical method are compared with results obtainedfrom DPD simulations under the same shear-flow conditions. Upto a moderateshear rate, various ACFs from the two approaches agree with each other well. Atlarge shear rates, discrepancies between the two methods are observed, hencerevealing strong additional coupling between different fluctuating variables,which is not considered in the analytical approach. In addition, the results atlow and moderate shear rates can serve as benchmarks for developing multiscalealgorithms for coupling of heterogeneous solvers, such as a hybrid simulationof molecular dynamics and fluctuating hydrodynamics solver, where thermalfluctuations are indispensable.

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