Hydrodynamic correlations in shear flow: Multiparticle-collision-dynamics simulation study

Varghese, Anoop; Huang, Chien-Cheng; Winkler, Roland G.; Gompper, Gerhard

doi:10.1103/physreve.92.053002

Cited by 10 publications

(22 citation statements)

References 42 publications

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“…[8], using fluctuating hydrodynamics calculations, the correlations in hydrodynamic fluctuations in a sheared fluid were evaluated for small wave vectors and arbitrary shear rates. It was shown that the temporal decay of the velocity and density fluctuations in shear flow are anisotropic and shear-rate dependent, which we recently verified using mesoscopic hydrodynamic simulations [14]. More importantly, the equal-time correlations were predicted to be spatially long-ranged and follow an algebraic decay for unbounded systems.…”

Section: Introductionsupporting

confidence: 68%

“…In order to maintain an isothermal state under shear, we employ a cell-level Maxwell-Boltzmann rescaling of the relative velocities of the particles [29]. This rescaling method for MPC fluid has been shown to reproduce the isothermal states consistent with the fluctuating Navier-Stokes equations in equilibrium and under shear flow [14,25]. Length and time scales in our simulations are given in terms of the length a of a cubic cell and τ = ma 2 /k B T , where m is the mass of a MPC fluid particle.…”

Section: Simulation Approach a Mpc Simulationsmentioning

confidence: 99%

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Spatial correlations of hydrodynamic fluctuations in simple fluids under shear flow: A mesoscale simulation study

2017

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Hydrodynamic fluctuations in simple fluids under shear flow are demonstrated to be spatially correlated, in contrast to the fluctuations at equilibrium, using mesoscopic hydrodynamic simulations. The simulation results for the equal-time hydrodynamic correlations in a multiparticle collision dynamics (MPC) fluid in shear flow are compared with the explicit expressions obtained from fluctuating hydrodynamics calculations. For large wave vectors k, the nonequilibrium contributions to transverse and longitudinal velocity correlations decay as k −4 for wave vectors along the flow direction and as k −2 for the off-flow directions. For small wave vectors, a crossover to a slower decay occurs, indicating long-range correlations in real space. The coupling between the transverse velocity components, which vanishes at equilibrium, also exhibits a k −2 dependence on the wave vector. In addition, we observe a quadratic dependency on the shear rate of the nonequilibrium contribution to pressure.

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Section: Introductionsupporting

confidence: 68%

Section: Simulation Approach a Mpc Simulationsmentioning

confidence: 99%

Spatial correlations of hydrodynamic fluctuations in simple fluids under shear flow: A mesoscale simulation study

2017

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“…Since the random terms do not contribute in this shear rate regime [26,29], the correlations of the fluctuating variables are readily expressed as Given the values of λ µ , ξ µ and χ µ ,, we find that G ǫι = 0 for ǫ = ι and G ǫι = 0 for ǫ = ι.…”

Section: B Hydrodynamic Matrixmentioning

confidence: 97%

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

Bian¹,

Deng²,

Karniadakis³

2018

CICP

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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.

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“…By considering moderate shear rateγ < ∼ νk 2 0 , cross correlations may be neglected [25,35,36]. To account for the advection of the shear, let k(t) = (k x , k y −γtk x , k z ) denote the time dependent wave vector and k(t) = |k(t)|.…”

Section: Transversal Autocorrelation Functions Of Fluctuations Imentioning

confidence: 99%

“…(31), (32), and (33) are time-dependent as well. The evolutions of the fluctuating variables in k-space can be solved via the perturbation theory [25] and therefore, the normalized transversal autocorrelation functions (TACFs) read as [36]…”

Section: Transversal Autocorrelation Functions Of Fluctuations Imentioning

confidence: 99%

Analysis of hydrodynamic fluctuations in heterogeneous adjacent multidomains in shear flow

et al. 2016

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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 [Flekkøy 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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Hydrodynamic correlations in shear flow: Multiparticle-collision-dynamics simulation study

Cited by 10 publications

References 42 publications

Spatial correlations of hydrodynamic fluctuations in simple fluids under shear flow: A mesoscale simulation study

Spatial correlations of hydrodynamic fluctuations in simple fluids under shear flow: A mesoscale simulation study

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

Analysis of hydrodynamic fluctuations in heterogeneous adjacent multidomains in shear flow

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