Hydrodynamic correlations in multiparticle collision dynamics fluids

Abstract

The emergent fluctuating hydrodynamics of the multiparticle collision dynamics (MPC) approach, a particlebased mesoscale simulation technique for fluid dynamics, is analyzed theoretically and numerically. We focus on the stochastic rotation dynamics implementation of the MPC method. The fluid is characterized by its longitudinal and transverse velocity correlation functions in Fourier space and velocity autocorrelation functions in real space. Particular attention is paid to the role of sound, which leads to piecewise negative correlation functions. Moreover, finite system-size effects are addressed with an emphasis on the role of sound. Analytical expressions are provided for the transverse and longitudinal velocity correlations, which are derived from the linearized Landau-Lifshitz Navier-Stokes equation adopted for an isothermal MPC fluid. The comparison of the analytical results with simulations shows excellent agreement above a minimal length scale. The simulations indicate a breakdown in hydrodynamics on length scales smaller than this minimal length. This demonstrates that we have an excellent analytical description and understanding of the MPC method and its limitations in terms of time and length scales.

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

“…[24] and references therein). In particular, the hydrodynamic correlations of the MPC fluid have been determined and it has been shown that they agree with the solutions of the fluctuating Landau-Lifshitz NavierStokes equations [25]. Moreover, the hydrodynamic correlations of embedded colloids [26][27][28][29][30][31] and polymers [32] have been calculated.…”

“…(20)- (23) are in order. In the limitγ → 0, we get φ(k, t) → kt and χ(k, t) → k 2 t, and therefore the correlation functions are reduced to the corresponding equilibrium relations [25,33] to O(k 2 ). In the absence of shear, the correlation functions for an isothermal MPC fluid can be obtained for all orders in k; the exact expressions for the velocity autocorrelations are provided in Ref.…”

“…In the absence of shear, the correlation functions for an isothermal MPC fluid can be obtained for all orders in k; the exact expressions for the velocity autocorrelations are provided in Ref. [25]. We also note that the expression for C 33 (k, t) remains exact for all shear rates within the order we are working at, even if the neglected equal-time correlations of the form z i (k, 0)z j (−k, 0) for i = j are taken into account.…”

Toward Hydrodynamics with Solvent Free Lipid Models: STRD Martini

“…With an appropriate choice of parameters, SRD dynamics capture this hydrodynamic regime (27). Following the approach of Huang et al (36), analysis of the velocity correlations (Fig. S1 in the Supporting Material) demonstrates that SRD parameters appropriate for lipid simulation achieve the low-Re, incompressible regime.…”

Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

“…MPC simulations, previously used to study hydrodynamic correlations [44][45][46] and the fluctuation-dissipation theorem [47] in fluid dynamics, have the advantage of being carried out in a gaslike model, where the typical excitations yielding large density fluctuations typical of lattice models can be neglected.…”