Sergey Litvinov

Multiscale modeling of particle in suspension with smoothed dissipative particle dynamics

We apply smoothed dissipative particle dynamics (SDPD) [Espanol and Revenga, Phys. Rev. E 67, 026705 (2003)] to model solid particles in suspension. SDPD is a thermodynamically consistent version of smoothed particle hydrodynamics (SPH) and can be interpreted as a multiscale particle framework linking the macroscopic SPH to the mesoscopic dissipative particle dynamics (DPD) method. Rigid structures of arbitrary shape embedded in the fluid are modeled by frozen particles on which artificial velocities are assigned in order to satisfy exactly the no-slip boundary condition on the solid-liquid interface. The dynamics of the rigid structures is decoupled from the solvent by solving extra equations for the rigid body translational/angular velocities derived from the total drag/torque exerted by the surrounding liquid. The correct scaling of the SDPD thermal fluctuations with the fluid-particle size allows us to describe the behavior of the particle suspension on spatial scales ranging continuously from the dif...

Self-diffusion coefficient in smoothed dissipative particle dynamics

Smoothed dissipative particle dynamics (SDPD) is a novel coarse grained method for the numerical simulation of complex fluids. It has considerable advantages over more traditional particle-based methods. In this paper we analyze the self-diffusion coefficient D of a SDPD solvent by using the strategy proposed by Groot and Warren [J. Chem. Phys. 107, 4423 (1997)]. An analytical expression for D in terms of the model parameters is developed and verified by numerical simulations.

Towards consistence and convergence of conservative SPH approximations

Typical conservative smoothed particle hydrodynamics (SPH) approximations of the gradient of a scalar field introduce two errors: one (smoothing error) is due to smoothing of the gradient by an integration associated with a kernel function; the other (integration error) is due to approximating the integration by summation over all particles within the kernel support. When particles are not on a uniform grid, the integration error leads to violation of zero-order consistency, i.e. the inability to reproduce a constant field. In this paper we confirm that partition of unity is the condition under which the conservative SPH approximation achieves both consistence and convergence. We show that this condition can be achieved by relaxing a particle distribution under a constant pressure field and invariant particle volume. The resulting particle distribution is very similar to that is typical for liquid molecules. We further show that with two different typical kernel functions the SPH approximation, upon satisfying the partition of unity property, is able to achieve very high-order of the integration error, which previously could be shown only with particles on a uniform grid. The background pressure used in a weakly compressible SPH simulation implies a self-relaxation mechanism, which explains that convergence with respect to increasing particle numbers could be obtained in SPH simulations, although not predicted by previous numerical analysis. Furthermore, by relating the integration error to the background pressure, we explain why the previously proposed transport-velocity formulation of SPH (S. Adami et al. (2013) 1) is able to achieve unprecedented accuracy and stability.

Numerical simulation of tethered DNA in shear flow

The behavior of tethered DNA in shear flow is investigated numerically by the smoothed dissipative particle dynamics (SDPD) method. Unlike numerical methods used in previous studies, SDPD models the solvent explicitly, takes into account the fully coupled hydrodynamic interactions and is free of the numerical artifact of wall sticking. Based on numerical simulations the static and dynamic properties of a tethered DNA is studied both qualitatively and quantitatively. The observed properties are in general agreement with previous experimental, numerical and theoretical work. Furthermore, the cyclic-motion phenomenon is studied by power spectrum density and cross-correlation function analysis, which suggest that there is only a very weak coherent motion of tethered DNA for a characteristic timescale larger than the relaxation time. Cyclic motion is more likely relevant as an isolated event than a typical mode of DNA motion.

Determination of macroscopic transport coefficients of a dissipative particle dynamics solvent.

We present an approach to determine macroscopic transport coefficients of a dissipative particle dynamics (DPD) solvent. Shear viscosity, isothermal speed of sound, and bulk viscosity result from DPD-model input parameters and can be determined only a posteriori. For this reason approximate predictions of these quantities are desirable in order to set appropriate DPD input parameters. For the purpose of deriving an improved approximate prediction we analyze the autocorrelation of shear and longitudinal modes in Fourier space of a DPD solvent for Kolmogorov flow. We propose a fitting function with nonexponential properties which gives a good approximation to these autocorrelation functions. Given this fitting function we improve significantly the capability of a priori determination of macroscopic solvent transport coefficients in comparison to previously used exponential fitting functions.

Numerical methods for the weakly compressible Generalized Langevin Model in Eulerian reference frame

A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker-Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) 1). The natural representation of GLM is a system of stochastic differential equations in a Lagrangian reference frame, typically solved by particle methods. A representation in a Eulerian reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a Eulerian-frame numerical flow solver. GLM in a Eulerian frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) 12. Unlike the more common Landau-Lifshitz Navier-Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered finite-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge-Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.

Numerical Investigation of the Micromechanical Behavior of DNA Immersed in a Hydrodynamic Flow

The topic of the project is relevant to the development of novel single-molecule manipulation techniques in biophysics and bionanotechnology where complex DNA-liquid interactions occur. The goals of the project are to verify the proposed numerical method by comparing the results for simple flow conditions with available numerical and analytical results, to analyze the dynamics of the DNA macromolecular exposed to an uniform and shear flow, perform simulations corresponding to the more complex experimental conditions.