**Analysis of hydrodynamic fluctuations in heterogeneous adjacent
multidomains in shear flow**

X Bian and MG Deng and YH Tang and GE Karniadakis, PHYSICAL REVIEW E, 93, 033312 (2016).

DOI: 10.1103/PhysRevE.93.033312

We analyze hydrodynamic fluctuations of a hybrid simulation under shear
flow. The hybrid simulation is based on the Navier-Stokes (NS) equations
on one domain and dissipative particle dynamics (DPD) on the other. The
two domains overlap, and there is an artificial boundary for each one
within the overlapping region. To impose the artificial boundary of the
NS solver, a simple spatial-temporal averaging is performed on the DPD
simulation. In the artificial boundary of the particle simulation, four
popular strategies of constraint dynamics are implemented, namely the
Maxwell buffer **Hadjiconstantinou and Patera, Int. J. Mod. Phys. C 08,
967 (1997)**, the relaxation dynamics **O'Connell and Thompson, Phys. Rev.
E 52, R5792 (1995)**, the least constraint dynamics **Nie et al., J. Fluid
Mech. 500, 55 (2004); Werder et al., J. Comput. Phys. 205, 373 (2005)**,
and the flux imposition **Flekkoy et al., Europhys. Lett. 52, 271
(2000)**, to achieve a target mean value given by the NS solver. Going
beyond the mean flow field of the hybrid simulations, we investigate the
hydrodynamic fluctuations in the DPD domain. Toward that end, we
calculate the transversal autocorrelation functions of the fluctuating
variables in k space to evaluate the generation, transport, and
dissipation of fluctuations in the presence of a hybrid interface. We
quantify the unavoidable errors in the fluctuations, due to both the
truncation of the domain and the constraint dynamics performed in the
artificial boundary. Furthermore, we compare the four methods of
constraint dynamics and demonstrate how to reduce the errors in
fluctuations. The analysis and findings of this work are directly
applicable to other hybrid simulations of fluid flow with thermal
fluctuations.

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