Reduced-order hybrid multiscale method combining the molecular dynamics and the discontinuous-galerkin method

We present a new reduced-order hybrid multiscale method to simulate com- plex fluids. continuum and molecular descriptions. We follow the framework of the heterogeneous multi-scale method (HMM) that makes use of the scale separation into macro- and micro-levels. On the macro-level, the governing equations of the incompressible flow are the continuity and momentum equations. The equations are solved using a high-order accurate discontinuous Galerkin Finite Element Method (dG) and implemented in the BoSSS code. The missing information on the macro-level is represented by the unknown stress tensor evaluated by means of the molecular dynam- ics (MD) simulations on the micro-level. We shear the microscopic system by applying Lees-Edwards boundary conditions and either an isokinetic or Lowe-Andersen thermostat. The data obtained from the MD simulations underlie large stochastic errors that can be controlled by means of the least-square approximation. In order to reduce a large number of computationally expensive MD runs, we apply the reduced order approach. Nume al experiments confirm the robustness of our newly developed hybrid MD-dG method

Coarse-grained models for fluids and their mixtures: Comparison of Monte Carlo studies of their phase behavior with perturbation theory and experiment

The prediction of the equation of state and the phase behavior of simple fluids (noble gases, carbon dioxide, benzene, methane, short alkane chains) and their mixtures by Monte Carlo computer simulation and analytic approximations based on thermodynamic perturbation theory is discussed. Molecules are described by coarse grained (CG) models, where either the whole molecule (carbon dioxide, benzene, methane) or a group of a few successive CH_2 groups (in the case of alkanes) are lumped into an effective point particle. Interactions among these point particles are fitted by Lennard-Jones (LJ) potentials such that the vapor-liquid critical point of the fluid is reproduced in agreement with experiment; in the case of quadrupolar molecules a quadrupole-quadrupole interaction is included. These models are shown to provide a satisfactory description of the liquid-vapour phase diagram of these pure fluids. Investigations of mixtures, using the Lorentz-Berthelot (LB) combining rule, also produce satisfactory results if compared with experiment, while in some previous attempts (in which polar solvents were modelled without explicitly taking into account quadrupolar interaction), strong violations of the LB rules were required. For this reason, the present investigation is a step towards predictive modelling of polar mixtures at low computational cost. These very simple coarse-grained models of small molecules developed here should be useful e.g. for simulations of polymer solutions with such molecules as solvent.Comment: J. Chem. Phys., accepte

Effective Soft-Core Potentials and Mesoscopic Simulations of Binary Polymer Mixtures

Mesoscopic molecular dynamics simulations are used to determine the large scale structure of several binary polymer mixtures of various chemical architecture, concentration, and thermodynamic conditions. By implementing an analytical formalism, which is based on the solution to the Ornstein-Zernike equation, each polymer chain is mapped onto the level of a single soft colloid. From the appropriate closure relation, the effective, soft-core potential between coarse-grained units is obtained and used as input to our mesoscale simulations. The potential derived in this manner is analytical and explicitly parameter dependent, making it general and transferable to numerous systems of interest. From computer simulations performed under various thermodynamic conditions the structure of the polymer mixture, through pair correlation functions, is determined over the entire miscible region of the phase diagram. In the athermal regime mesoscale simulations exhibit quantitative agreement with united atom simulations. Furthermore, they also provide information at larger scales than can be attained by united atom simulations and in the thermal regime approaching the phase transition.Comment: 19 pages, 11 figures, 3 table

Simulation study of the link between molecular association and reentrant miscibility for a mixture of molecules with directional interactions

The reentrant liquid-liquid miscibility of a symmetrical mixture with highly directional bonding interactions is studied by Gibbs ensemble Monte Carlo simulation. The resulting closed loop of immiscibility and the corresponding lower critical solution temperature are shown to be a direct consequence of the dramatic increase in association between unlike components as the temperature is lowered. Our exact calculations for an off-lattice system with a well-defined anisotropic potential confirm the findings of previous theoretical studies.Dirección General de Investigación Científica y Técnica PB94-144

A multi-scale method for complex flows of non-Newtonian fluids

We introduce a new heterogeneous multi-scale method for the simulation of flows of non-Newtonian fluids in general geometries and present its application to paradigmatic two-dimensional flows of polymeric fluids. Our method combines micro-scale data from non-equilibrium molecular dynamics (NEMD) with macro-scale continuum equations to achieve a data-driven prediction of complex flows. At the continuum level, the method is model-free, since the Cauchy stress tensor is determined locally in space and time from NEMD data. The modelling effort is thus limited to the identification of suitable interaction potentials at the micro-scale. Compared to previous proposals, our approach takes into account the fact that the material response can depend strongly on the local flow type and we show that this is a necessary feature to correctly capture the macroscopic dynamics. In particular, we highlight the importance of extensional rheology in simulating generic flows of polymeric fluids

Three-step decay of time correlations at polymer-solid interfaces

Two-step decay of relaxation functions, i.e., time scale separation between microscopic dynamics and structural relaxation, is the defining signature of the structural glass transition. We show that for glass-forming polymer melts at an attractive surface slow desorption kinetics introduces an additional time scale separation among the relaxational degrees of freedom leading to a three-step decay. The inherent length scale of this process is the radius of gyration in contrast to the segmental scale governing the glass transition. We show how the three-step decay can be observed in incoherent scattering experiments and discuss its relevance for the glass transition of confined polymers by analogy to surface critical phenomena

Accelerated GPU simulation of compressible flow by the discontinuous evolution Galerkin method

The aim of the present paper is to report on our recent results for GPU accelerated simulations of compressible flows. For numerical simulation the adaptive discontinuous Galerkin method with the multidimensional bicharacteristic based evolution Galerkin operator has been used. For time discretization we have applied the explicit third order Runge-Kutta method. Evaluation of the genuinely multidimensional evolution operator has been accelerated using the GPU implementation. We have obtained a speedup up to 30 (in comparison to a single CPU core) for the calculation of the evolution Galerkin operator on a typical discretization mesh consisting of 16384 mesh cells