The study of the underlying physics of soft flowing materials depends heavily on numerical simulations, due to the complex structure of the governing equations reflecting the competition of concurrent mechanisms acting at widely disparate scales in space and time. A full-scale computational modelling remains a formidable challenge since it amounts to simultaneously handle six or more spatial decades in space and twice as many in time. Coarse-grained methods often provide a viable strategy to significantly mitigate this issue, through the implementation of mesoscale supramolecular forces designed to capture the essential physics at a fraction of the computational cost of a full-detail description.
Here, we review some recent advances in the design of a lattice Boltzmann mesoscale approach for soft flowing materials, inclusive of near-contact interactions (NCI) between dynamic interfaces, as they occur in high packing-fraction soft flowing crystals.
The method proves capable of capturing several aspects of the rheology of soft flowing crystals, namely, i) a 3/2 power-law dependence of the dispersed phase flow rate on the applied pressure gradient, ii) the structural transition between an ex-two and ex-one (bamboo) configurations with the associated drop of the flow rate, iii) the onset of interfacial waves once NCI is sufficiently intense.
A novel hybrid computational method based on the discrete-velocity (DV) approximation, including the lattice-Boltzmann (LB) technique, is proposed. Numerical schemes for the kinetic equations are used in regions of rarefied flows, and LB schemes are employed in continuum flow zones. The schemes are written under the finite-volume (FV) formulation to achieve the flexibility of local mesh refinement. The truncated Hermite polynomial expansion is used for matching of DV and LB solutions. Special attention is paid to preserving conservation properties in the coupling algorithm. The test results ob…
Boltzmann transport equation (BTE) is an ideal tool to describe the multiscale phonon transport phenomena, which are critical to applications like microelectronics cooling. Numerically solving phonon BTE is extremely computationally challenging due to the high dimensionality of such problems, especially when mode-resolved properties are considered. In this work, we demonstrate the use of physics-informed neural networks (PINNs) to efficiently solve phonon BTE for multiscale thermal transport problems with the consideration of phonon dispersion and polarization. In particular, a PINN framework …
A hybrid computational method coupling the lattice-Boltzmann (LB) method and a Langevin-dynamics (LD) method is developed to simulate nanoscale particle and polymer (NPP) suspensions in the presence of both thermal fluctuation and long-range many-body hydrodynamic interactions (HI). Brownian motion of the NPP is explicitly captured by a stochastic forcing term in the LD method. The LD method is two-way coupled to the non-fluctuating LB fluid through a discrete LB forcing source distribution to capture the long-range HI. To ensure intrinsically linear scalability with respect to the number of p…
We present a mesoscale representation of near-contact interactions between colliding droplets which permits to reach up to the scale of full microfluidic devices, where such droplets are produced. The method is demonstrated for the case of colliding droplets and the formation of soft flowing crystals in flow-focussing microfluidic devices. This model may open up the possibility of multiscale simulation of microfluidic devices for the production of new droplet/bubble-based mesoscale porous materials.
We propose a mesoscopic model of binary fluid mixtures with tunable viscosity ratio based on a two-range pseudo-potential lattice Boltzmann method, for the simulation of soft flowing systems. In addition to the short range repulsive interaction between species in the classical single-range model, a competing mechanism between the short-range attractive and mid-range repulsive interactions is imposed within each species. Besides extending the range of attainable surface tension as compared with the single-range model, the proposed scheme is also shown to achieve a positive disjoining pressure, …
The direct simulation of the dynamics of second sound in graphitic materials remains a challenging task due to lack of methodology for solving the phonon Boltzmann equation in such a stiff hydrodynamic regime. In this work, we aim to tackle this challenge by developing a multiscale numerical scheme for the transient phonon Boltzmann equation under Callaway's dual relaxation model which captures well the collective phonon kinetics. Comparing to traditional numerical methods, the present multiscale scheme is efficient, accurate and stable in all transport regimes attributed to avoiding the use o…
The deformation and dynamics of a single droplet in isotropic turbulence is studied using a Lattice Boltzmann diffuse interface model involving exact boundary flow conditions to allow for the creation of an external turbulent flow. We focus on a small, sub-Kolmogorov droplet, whose scale is much smaller than the Kolmogorov length scale of the turbulent flow. The external flow field is obtained via pseudo-spectral simulation data describing the trajectory of a passive tracer in isotropic turbulence. In this way we combine the microscopic scale of the droplet and the macroscopic scale of the tur…
Molecular simulation is a scientific tool dealing with challenges in material science and biology. This is reflected in a permanent development and enhancement of algorithms within scientific simulation packages. Here, we present computational tools for multiscale modeling developed and implemented within the ESPResSo++ package. These include the latest applications of the adaptive resolution scheme, the hydrodynamic interactions through a lattice Boltzmann solvent coupled to particle-based molecular dynamics, the implementation of the hierarchical strategy for equilibrating long-chained polym…
A unified gas-kinetic framework from Boltzmann to Navier-Stokes scales
Huazhong University of Science and Technology（华中科技大学）；Hong Kong University of Science and Technology（香港科技大学）；Shanghai Suochen Information Technology Co., Ltd（上海速晨信息技术有限公司）
In this work we discuss the coupling of two mesoscopic approaches for fluid dynamics, namely the lattice Boltzmann method (LB) and the multiparticle collision dynamics (MPCD) \cite{kapral2008multiparticle} to design a new class of flexible and efficient multiscale schemes based on a dual representation of the fluid observables. At variance with other commonly used multigrid methods, mostly oriented to high Reynolds and turbulent flows, the present approach is designed to capture the physics at the smallest scales whenever the lattice Boltzmann alone falls short of providing the correct physica…
The present work investigates the application of Artificial Neural Networks (ANNs) to estimate the Reynolds ($Re$) number for flows around a cylinder. The data required to train the ANN was generated with our own implementation of a Lattice Boltzmann Method (LBM) code performing simulations of a 2-dimensional flow around a cylinder. As results of the simulations, we obtain the velocity field ($\vec{v}$) and the vorticity ($\vec{\nabla}\times\vec{v}$) of the fluid for 120 different values of $Re$ measured at different distances from the obstacle and use them to teach the ANN to predict the $Re$…
Phonon Boltzmann transport equation (BTE) is a key tool for modeling multiscale phonon transport, which is critical to the thermal management of miniaturized integrated circuits, but assumptions about the system temperatures (i.e., small temperature gradients) are usually made to ensure that it is computationally tractable. To include the effects of large temperature non-equilibrium, we demonstrate a data-free deep learning scheme, physics-informed neural network (PINN), for solving stationary, mode-resolved phonon BTE with arbitrary temperature gradients. This scheme uses the temperature-depe…
The deformability of soft condensed matter often requires modelling of hydrodynamical aspects to gain quantitative understanding. This, however, requires specialised methods that can resolve the multiscale nature of soft matter systems. We review a number of the most popular simulation methods that have emerged, such as Langevin dynamics, dissipative particle dynamics, multi-particle collision dynamics, sometimes also referred to as stochastic rotation dynamics, and the lattice-Boltzmann method. We conclude this review with a short glance at current compute architectures for high-performance c…
We discuss the Lattice Boltzmann-Particle Dynamics (LBPD) multiscale paradigm for the simulation of complex states of flowing matter at the interface between Physics, Chemistry and Biology. In particular, we describe current large-scale LBPD simulations of biopolymer translocation across cellular membranes, molecular transport in ion channels and amyloid aggregation in cells. We also provide prospects for future LBPD explorations in the direction of cellular organization, the direct simulation of full biological organelles, all the way to up to physiological scales of potential relevance to fu…
Blood flowing through microvascular bifurcations has been an active research topic for many decades, while the partitioning pattern of nanoscale solutes in the blood remains relatively unexplored. Here, we demonstrate a multiscale computational framework for direct numerical simulation of the nanoparticle (NP) partitioning through physiologically-relevant vascular bifurcations in the presence of red blood cells (RBCs). The computational framework is established by embedding a newly-developed particulate suspension inflow/outflow boundary condition into a multiscale blood flow solver. The compu…
Uni-Flow: a unified autoregressive-diffusion model for complex multiscale flows
Centre for Computational Science, University College London, London, UK；Department of Earth Science；Engineering, Imperial College London, London, UK；Department of Chemical Engineering, University College London, London, UK；Department of Physics, Eindhoven University of Technology, Eindhoven, Netherlands；School of Civil \& Environmental Engineering, Queensland University of Technology, Brisbane, Australia；Australian Centre for Water；Environmental Biotechnology, The University of Queensland, Brisbane, Australia；Institute for Mechanics, Computational Mechanics Group, Technical University of Darmstadt, Germany；Centre for Advanced Research Computing, University College London, London, UK
The non-equilibrium gas dynamics is described by the Boltzmann equation, which can be solved numerically through the deterministic and stochastic methods. Due to the complicated collision term of the Boltzmann equation, many kinetic relaxation models have been proposed and used in the past seventy years for the study of rarefied flow. In order to develop a multiscale method for the rarefied and continuum flow simulation, by adopting the integral solution of the kinetic model equation a DVM-type unified gas-kinetic scheme (UGKS) has been constructed. The UGKS models the gas dynamics on the cell…
For theoretical gas dynamics, the flow regimes are classified according to the Knudsen number. For computational fluid dynamics (CFD), the numerical flow field is the projection of the physical flow field onto the discrete space and time, which is related to the cell Knudsen number. The real representable flow regimes are controlled by these two parameters. According to the values of Knudsen number and cell Knudsen number, we study the classification of the numerical flow regimes. In the process of mesh refinement, the numerical experiments show the change of numerical flow regime from continu…
Lattice Boltzmann Methods for Navier-Stokes Equations in General Orthogonal Coordinates for Efficient Flow Simulations using Nonuniform Clustered Grids
Active gel theory has recently been very successful in describing biologically active materials such as actin filaments or moving bacteria in temporally fixed and simple geometries such as cubes or spheres. Here we develop a computational algorithm to compute the dynamic evolution of an arbitrarily shaped, deformable thin membrane of active material embedded in a 3D flowing liquid. For this, our algorithm combines active gel theory with the classical theory of thin elastic shells. To compute the actual forces resulting from active stresses, we apply a parabolic fitting procedure to the triangu…
