General mechanisms for stabilizing weakly compressible models.

Many weakly compressible models with intrinsic mechanisms for stabilizing computation have been proposed to simulate incompressible flows. The present paper analyzes several weakly compressible models to establish general mechanisms that incorporate them into a unified and simple framework. It is found that all these models contain some identical numerical dissipation terms, mass diffusion terms in the continuity equation, and bulk viscosity terms in the momentum equation. They are proven to provide general mechanisms for stabilizing computation. Referring to the general mechanisms and the computational procedures of the lattice Boltzmann flux solver, two general weakly compressible solvers for isothermal flows and thermal flows are proposed. They can be directly derived from standard governing equations and implicitly introduce those numerical dissipation terms. Detailed numerical investigations demonstrate that the two general weakly compressible solvers have good numerical stability and accuracy for both isothermal and thermal flows, which validates the general mechanisms further and the general approach of constructing general weakly compressible solvers.

Analysis and reconstruction of the multiphase lattice Boltzmann flux solver for multiphase flows with large density ratios.

The multiphase lattice Boltzmann flux solver (MLBFS) has been proposed to tackle complex geometries with nonuniform meshes. It also has been proven to have good numerical stability for multiphase flows with large density ratios. However, the reason for the good numerical stability of MLBFS at large density ratios has not been well established. The present paper reveals the relation between MLBFS and the macroscopic weakly compressible multiphase model by recovering the macroscopic equations of MLBFS (MEs-MLBFS) with actual numerical dissipation terms. By directly solving MEs-MLBFS, the reconstructed MLBFS (RMLBFS) that involves only macroscopic variables in the computational processes is proposed. The analysis of RMLBFS indicates that by combining the predictor step, the corrector step of MLBFS introduces some numerical dissipation terms which contribute to the good numerical stability of MLBFS. By retaining these numerical dissipation terms, RMLBFS can maintain the numerical stability of MLBFS even at large density ratios.

Mesoscopic Lattice Boltzmann Modeling of the Liquid-Vapor Phase Transition.

We develop a mesoscopic lattice Boltzmann model for liquid-vapor phase transition by handling the microscopic molecular interaction. The short-range molecular interaction is incorporated by recovering an equation of state for dense gases, and the long-range molecular interaction is mimicked by introducing a pairwise interaction force. Double distribution functions are employed, with the density distribution function for the mass and momentum conservation laws and an innovative total kinetic energy distribution function for the energy conservation law. The recovered mesomacroscopic governing equations are fully consistent with kinetic theory, and thermodynamic consistency is naturally satisfied.

Evolution of SLA-Based Al2O3 Microstructure During Additive Manufacturing Process.

Evolution of additively manufactured (AM) ceramics' microstructure between manufacturing stages is a hardly explored topic. These data are of high demand for advanced numerical modeling. In this work, 3D microstructural models of Al2O3 greenbody, brownbody and sintered material are presented and analyzed, for ceramic samples manufactured with SLA-based AM workflow, using a commercially available ceramic paste and 3D printer. The novel data, acquired at the micro- and mesoscale, using Computed Tomography (CT), Scanning Electron Microscopy (SEM) and Focused Ion-Beam SEM (FIB/SEM) techniques, allowed a deep insight into additive ceramics characteristics. We demonstrated the spatial 3D distribution of ceramic particles, an organic binder and pores at every stage of AM workflow. The porosity of greenbody samples (1.6%), brownbody samples (37.3%) and sintered material (4.9%) are analyzed. Pore distribution and possible originating mechanisms are discussed. The location and shape of pores and ceramic particles are indicative of specific physical processes driving the ceramics manufacturing. We will use the presented microstructural 3D models as input and verification data for advanced numerical simulations developed in the project.

Effect of Mach number on droplet aerobreakup in shear stripping regime.

ABSTRACT: The present experimental study investigates the shear stripping breakup of single droplets in subsonic and supersonic gaseous flows. In contrast to most research that places emphasis on the Weber number (We), we focus on the individual effects exerted by flow Mach (M ∞) and Reynolds numbers (Re). Millimeter-sized droplets made of either ethylene glycol or water are exposed to shock-induced flows. Shadowgraph and schlieren images of the breakup process are recorded by an ultra-high-speed camera. The experimental We is constrained at 1100, while M ∞ is varied from 0.3 to 1.19 and Re from 2600 to 24,000. A systematic analysis of the experiment series reveals that the breakup pattern alters with M ∞ although a constant We is maintained. The classical stripping behavior with fine mist shed from the peripheral sheet changes to rupture of multiple bags along the periphery at M ∞ = 0.63, and further to stretching of ligament structures from the leeward surface at M ∞ = 1.19. The corresponding breakup initiation is delayed and the resultant fragments are sized less uniformly and distributed over a narrower spread. In terms of the early-stage deformation, droplets experience less intense flattening and slower sheet growth at higher M ∞. The change of Re introduces additional variations, but only to a minor extent.

Density gradient calculation in a class of multiphase lattice Boltzmann models.

The multiphase lattice Boltzmann (LB) models based on pairwise interactions show great potential for simulating multiphase flows due to the conceptual and computational simplicity. Although the dynamics of multiphase flows are reproduced by the pairwise interaction force, the gradient of density (or effective density, i.e., pseudopotential) is implicitly involved in these models via the specialized forcing scheme or the consistent scheme for ɛ^{3}-order term. This work focuses on the calculation of density gradient in this class of multiphase LB models. Theoretical analyses are first carried out to reveal the involvement and calculation of density gradient. On the basis of a low Mach number approximation, an improved scheme is then proposed to calculate the density gradient for the recent LB model with self-tuning equation of state. Analytical and numerical calculations show that the improved scheme is more accurate and can help to reduce the numerical error when the reduced temperature is relatively low.

Implicit atomistic viscosities in smoothed dissipative particle dynamics.

We apply a standard nonequilibrium dynamics microscopic analysis of transport coefficients to the smoothed dissipative particle dynamics (SDPD) method of steady-shear flow conditions. Extending the research of Ellero et al. [Phys. Rev. E 82, 046702 (2010)PRESCM1539-375510.1103/PhysRevE.82.046702] for smoothed particle hydrodynamics (SPH), we focus, in particular, on velocity and acceleration statistics and on mean-density phenomena. Implicit and explicit fluctuations affect non-Gaussian statistics and effective viscosities whereas only explicit fluctuations affect large-scale dissipation through the fluctuation-dissipation relation. SDPD facilitates the simulation of mesoscopic systems as the resolution scale is defined by the scaling of the random fluctuations. In the kinetic regime, SDPD recovers the behavior of SPH. In the diffusive regime, non-Gaussian behavior occurs, in contrast to SPH. We observe the formation of isotropic randomly oriented structures with high density which are related to the magnitude of thermal fluctuations. It is demonstrated that SDPD produces non-Gaussian acceleration PDF corresponding to that of a turbulent flow field.

Lattice Boltzmann model with self-tuning equation of state for multiphase flows.

A lattice Boltzmann (LB) model for multiphase flows is developed that complies with the thermodynamic foundations of kinetic theory. By directly devising the collision term for the LB equation at the discrete level, a self-tuning equation of state is achieved, which can be interpreted as the incorporation of short-range molecular interaction. A pairwise interaction force is introduced to mimic the long-range molecular interaction, which is responsible for interfacial dynamics. The derived pressure tensor is naturally consistent with thermodynamic theory, and surface tension and interface thickness can be independently prescribed. Numerical tests, including static and dynamic cases, are carried out to validate the present model and good results are obtained. As a further application, head-on collision of equal-sized droplets is simulated and the elusive "bouncing" regime is successfully reproduced.

Eliminating cubic terms in the pseudopotential lattice Boltzmann model for multiphase flow.

It is well recognized that there exist additional cubic terms of velocity in the lattice Boltzmann (LB) model based on the standard lattice. In this work, elimination of these cubic terms in the pseudopotential LB model for multiphase flow is investigated, where the force term and density gradient are considered. By retaining high-order (≥3) Hermite terms in the equilibrium distribution function and the discrete force term, as well as introducing correction terms in the LB equation, the additional cubic terms of velocity are entirely eliminated. With this technique, the computational simplicity of the pseudopotential LB model is well maintained. Numerical tests, including stationary and moving flat and circular interface problems, are carried out to show the effects of such cubic terms on the simulation of multiphase flow. It is found that the elimination of additional cubic terms is beneficial to reduce the numerical error, especially when the velocity is relatively large. Numerical results also suggest that these cubic terms mainly take effect in the interfacial region and that the density-gradient-related cubic terms are more important than the other cubic terms for multiphase flow.

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.

Analysis of intermittency in under-resolved smoothed-particle-hydrodynamics direct numerical simulations of forced compressible turbulence.

We perform three-dimensional under-resolved direct numerical simulations of forced compressible turbulence using the smoothed particle hydrodynamics (SPH) method and investigate the Lagrangian intermittency of the resulting hydrodynamic fields. The analysis presented here is motivated by the presence of typical stretched tails in the probability density function (PDF) of the particle accelerations previously observed in two-dimensional SPH simulations of uniform shear flow [Ellero et al., Phys. Rev. E 82, 046702 (2010)]. In order to produce a stationary isotropic compressible turbulent state, the real-space stochastic forcing method proposed by Kida and Orszag is applied, and the statistics of particle quantities are evaluated. We validate our scheme by checking the behavior of the energy spectrum in the supersonic case where the expected Burgers-like scaling is obtained. By discretizing the continuum equations along fluid particle trajectories, the SPH method allows us to extract Lagrangian statistics in a straightforward fashion without the need for extra tracer particles. In particular, Lagrangian PDF of the density, particle accelerations as well as their Lagrangian structure functions and local scaling exponents are analyzed. The results for low-order statistics of Lagrangian intermittency in compressible turbulence demonstrate the implicit subparticle-scale modeling of the SPH discretization scheme.

Implicit atomistic viscosities in smoothed particle hydrodynamics.

We consider a standard microscopic analysis of the transport coefficients, commonly used in nonequilibrium molecular dynamics techniques, and apply it to the smoothed particle hydrodynamics method in steady-shear flow conditions. As previously suggested by Posch [Phys. Rev. E 52, 1711 (1995)], we observe the presence of nonzero microscopic (kinetic and potential) contributions to the total stress tensor in addition to its dissipative part coming from the discretization of the Navier-Stokes continuum equations. Accordingly, the dissipative part of the shear stress produces an output viscosity equal to the input model parameter. On the other hand, the nonzero atomistic viscosities can contribute significantly to the overall output viscosity of the method. In particular, it is shown that the kinetic part, which acts similarly to an average Reynolds-like stress, becomes dominant at very low viscous flows where large velocity fluctuations occur. Remarkably, in this kinetic regime the probability distribution function of the particle accelerations is in surprisingly good agreement with non-gaussian statistics observed experimentally.

Particle-layering effect in wall-bounded dissipative particle dynamics.

Dissipative particle dynamics (DPD) is a mesoscopic simulation method that describes "clusters" of molecules as a single numerical particle. DPD is a very effective method but it introduces numerical artifacts through the coarse-graining procedure, such as particle ordering in the near-wall region. These artifacts can result in nonphysical phenomena during a simulation of a polymer tethered to the wall undergoing shear flow: polymer sticking and overextension for higher shear rates. In this paper we report that a version of DPD with a so-called solidification boundary formulation and conservative-force interactions based on the equation of state allows to reduce number density fluctuations in near-wall region significantly.

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.

Smoothed dissipative particle dynamics model for polymer molecules in suspension.

We present a model for a polymer molecule in solution based on smoothed dissipative particle dynamics (SDPD) [Español and Revenga, Phys. Rev. E 67, 026705 (2003)]. This method is a thermodynamically consistent version of smoothed particle hydrodynamics able to discretize the Navier-Stokes equations and, at the same time, to incorporate thermal fluctuations according to the fluctuation-dissipation theorem. Within the framework of the method developed for mesoscopic multiphase flows by Hu and Adams [J. Comput. Phys. 213, 844 (2006)], we introduce additional finitely extendable nonlinear elastic interactions between particles that represent the beads of a polymer chain. In order to assess the accuracy of the technique, we analyze the static and dynamic conformational properties of the modeled polymer molecule in solution. Extensive tests of the method for the two-dimensional (2D) case are performed, showing good agreement with the analytical theory. Finally, the effect of confinement on the conformational properties of the polymer molecule is investigated by considering a 2D microchannel with gap H varying between 1 and 10 microm , of the same order as the polymer gyration radius. Several SDPD simulations are performed for different chain lengths corresponding to N=20-100 beads, giving a universal behavior of the gyration radius R_{G} and polymer stretch X as functions of the channel gap when normalized properly.