A consistent nonlocal scheme based on filters for the homogenization of heterogeneous linear materials with non-separated scales

In this work, the question of homogenizing linear elastic, heterogeneous materials with periodic microstructures in the case of non-separated scales is addressed. A framework if proposed, where the notion of mesoscopic strain and stress fields are defined by appropriate integral operators which act as low-pass filters on the fine scale fluctuations. The present theory extends the classical linear homogenization by substituting averaging operators by integral operators, and localization tensors by nonlocal operators involving appropriate Green functions. As a result, the obtained constitutive relationship at the mesoscale appears to be nonlocal. Compared to nonlocal elastic models introduced from a phenomenological point of view, the nonlocal behavior has been fully derived from the study of the microstructure. A discrete version of the theory is presented, where the mesoscopic strain field is approximated as a linear combination of basis functions. It allows computing the mesoscopic nonlocal operator by means of a finite number of transformation tensors, which can be computed numerically on the unit cell.     

On Coarse-Graining by the Inverse Monte Carlo Method: Dissipative Particle Dynamics Simulations Made to a Precise Tool in Soft Matter Modeling

We present a promising coarse-graining strategy for linking micro- and mesoscales of soft matter systems. The approach is based on effective pairwise interaction potentials obtained from detailed atomistic molecular dynamics (MD) simulations, which are then used in coarse-grained dissipative particle dynamics (DPD) simulations. Here, the effective potentials were obtained by applying the inverse Monte Carlo method [Lyubartsev and Laaksonen, Phys. Rev. E. 52, 3730 (1995)] on a chosen subset of degrees of freedom described in terms of radial distribution functions. In our first application of the method, the effective potentials were used in DPD simulations of aqueous NaCl solutions. With the same computational effort we were able to simulate systems of one order of magnitude larger than the MD simulations. The results from the MD and DPD simulations are in excellent agreement.     

Coarse-graining atomistic dynamics of brittle fracture by finite element method

In this work we present the finite element (FE) implementation of an atomistic formulation of balance equations and its application to coarse-grained (CG) simulation of dynamic fracture. First, we simulate a notched specimen that contains about 1.8 million atoms by the CG-FE method, and we compare the CG-FE results with that by all-atom molecular dynamics (MD) simulations. We find that CG-FE simulations with about 5% degrees of freedom of the MD simulation can capture the essential dynamic features, not in exact correspondence, but qualitatively and quantitatively similar to that obtained by MD simulations. We then proceed to simulate a series of micron-sized specimens by the CF-FE method. We find that it is the interaction of the forward propagating crack with the stress waves being reflected back by the boundaries of the specimen that triggers the dynamic instability and hence the branching of cracks in micron-sized specimens. The potential application of the method and future work for improvements are discussed.     

Evaluation of coarse-grained CFD-DEM models with the validation of PEPT measurements

Computational Fluid Dynamics coupled with Discrete Element Method (CFD-DEM) is a commonly used numerical method to model gas-solid flow in fluidised beds and other multiphase systems. A significant limitation of CFD-DEM is the feasibility of the realistic simulation of large numbers of particles. Coarse-graining (CG) approaches, through which groups of multiple individual particles are represented by single, larger particles, can substantially reduce the total number of particles while maintaining similar system dynamics. As these three CG models have not previously been compared, there remains some debate, however, about the best practice in the application of CG in CFD-DEM simulations. In this paper, we evaluate the performance of three typical CG methods based on simulations of a bubbling fluidised bed. This is achieved through the use of a numerical validation framework, which makes full use of the high-resolution 3D positron emission particle tracking (PEPT) measurements to rigorously validate the outputs of CFD-DEM simulations conducted using various different coarse-graining models, and various different degrees of coarse-graining. The particle flow behaviours in terms of the particle occupancy field, velocity field, circulation time, and bubble size and velocity, are comprehensively analysed. It is shown that the CG simulation starts to fail when the size ratio between the bed chamber and the particles decreases to approximately 20. It is also observed, somewhat surprisingly, that the specific CG approach applied to interparticle contact parameters does not have a substantial effect on the simulation results for the bubbling bed simulations across a wide range of CG factors.     

Soot primary particle formation from multiscale coarse-grained molecular dynamics simulation

A new multiscale coarse-graining procedure is used to study carbonaceous nanoparticle agglomeration in combustion environments. The computational methodology is applied to an ensemble of 10,000 nanoparticles (or effectively 2 million total carbon atoms) to simulate, for the first time, the agglomeration of carbonaceous nanoparticles using coarse-grained atomistic-scale information. In particular, with the coarse-graining approach we are able to assess the influence of nanoparticle morphology and temperature on the agglomeration process. The coarse-graining of the interparticle force field is accomplished applying a force-matching procedure to data obtained from trajectories and forces from all-atom MD simulations. The coarse-grained MD results show rich and varied clustering behaviors for different particle morphology and, in some cases, the formation of primary particles with a diameter around 15 nm are observed for the first time by molecular simulation techniques.     

Predictions of the P1 approximation for radiative heat transfer in heterogeneous granular media

The P1 approximation is a computationally efficient model for thermal radiation. Here, we present a P1 formulation in the context of the combined computational fluid dynamics and discrete element method (CFD-DEM), including closures for dependent scattering and coarse-graining. Using available analytical and semi-analytical solutions, we find agreement for steady-state and transient quantities in size-disperse systems. Heat flux is identified as the most sensitive quantity to predict, displaying unphysical spatial oscillations. These oscillations are due to a temperature slip at the locations of abrupt change in solid fraction. We propose two techniques that mitigate this effect: smoothing of the radiative properties, and pseudo-scattering. Furthermore, using up to a million times enlarged particles, we demonstrate practically limitless compatibility with coarse-graining. Finally, we compare predictions made with our code to experimental data for a pebble bed under vacuum conditions, and in presence of nitrogen. We find that a carefully calibrated simulation can replicate trends observed in experiments, with relative temperature error of less than 10%.