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The sedimentation of two spherical solid objects in a viscous fluid has been extensively investigated and well understood. However, a pair of flat disks (in three dimensions) settling in the fluid shows more complex hydrodynamic behaviors. The present work aims to improve understanding of this phenomenon by performing Direct Numerical Simulations (DNS) and physical experiments. The present results show that the sedimentation processes are significantly influenced by disk shape, characterized by a dimensionless moment of inertia I*, and Reynolds number of the leading disk Re. For the flatter disks with smaller I*, steady falling with enduring contact transits to periodic swinging with intermittent contacts as Re increases. The disks with larger I* tend to fall in a Drafting-Kissing-Tumbling (DKT) mode at low Re and to remain separated at high Re. Based on I* and Re, a phase diagram is created to classify the two-disk falling into ten distinctive patterns. The planar motion or three-dimensional motion of the disks is determined primarily by Re. Turbulent disturbance flows at a high Re contribute to the chaotic three-dimensional rotation of the disks. The chance for the two disks to contact is increased when I* and Re are reduced., Comment: 51 pages, 28 figures

In this paper, we proposed a central moment discrete unified gas-kinetic scheme (DUGKS) for multiphase flows with large density ratio and high Reynolds number. Two sets of kinetic equations with central-moment-based multiple relaxation time collision operator are employed to approximate the incompressible Navier-Stokes equations and a conservative phase field equation for interface-capturing. In the framework of DUGKS, the first moment of the distribution function for the hydrodynamic equations is defined as velocity instead of momentum. Meanwhile, the zeroth moments of the distribution function and external force are also suitably defined such that a artificial pressure evolution equation can be recovered. Moreover, the Strang splitting technique for time integration is employed to avoid the calculation of spatial derivatives in the force term at cell faces. For the interface-capturing equation, two equivalent DUGKS methods that deal with the diffusion term differently using a source term as well as a modified equilibrium distribution function are presented. Several benchmark tests that cover a wide a range of density ratios (up to 1000) and Reynolds numbers (up to $10^5$) are subsequently carried out to demonstrate the capabilities of the proposed scheme. Numerical results are in good agreement with the reference and experimental data., 57 pages, 23 figures

In this paper, the mesoscopic representation of non-uniform forcing is investigated by an inverse design approach, for several MRT (multiple-relaxation-time) lattice Boltzmann models. First, the mesoscopic forcing representation of a standard LBM-MRT model on a square lattice is re-visited. By the multiscale Chapman–Enskog expansion, we derive the most general form of the representation by taking advantage of the MRT formulation. In particular, we show that there are three free components in the mesoscopic representation of forcing. Second, by the same methodology, the forcing scheme of two new rectangular MRT lattice Boltzmann models are derived based on the requirements of the Navier–Stokes equations. These theoretical results are then validated by numerical simulations of a forced Taylor–Green vortex flow, with several different forms of non-uniform forcing to alter the kinetic-energy evolution of the system. The numerical results are in excellent agreement with the corresponding time-dependent analytical solution of flow.

The standard lattice-Boltzmann method (LBM) for fluid flow simulation is based on a square (in 2D) or a cubic (in 3D) lattice grids. Recently, two new lattice Boltzmann schemes have been developed on a 2D rectangular grid using the MRT (multiple-relaxation-time) collision model, either by adding a free parameter in the definition of moments or by extending the equilibrium moments. These models satisfy all isotropy conditions and are fully consistent to the Navier–Stokes equations. Here we developed a lattice Boltzmann model on a 3D cuboid lattice, namely, a lattice grid with different grid lengths in different spatial directions. We designed the moment equations, derived from our MRT–LBM model through the Chapman–Enskog analysis, to be fully consistent with the Navier–Stokes equations. A second-order term is added to the equilibrium moments in order to not only satisfy all isotropy conditions but also to better accommodate different values of shear and bulk viscosities. The form of the second-order term and the coefficients of the extended equilibrium moments are determined through an inverse design process. An additional benefit of the model is that the shear viscosity can be adjusted, independent of the stress-moment relaxation parameter, thus potentially improving the numerical stability of the model. The resulting cuboid MRT–LBM model is then validated through benchmark simulations using the laminar channel flow, the turbulent channel flow, and the 3D time-dependent, energy-cascading Taylor–Green vortex flow. The second-order accuracy of the proposed model is also demonstrated. The aspect ratios for numerical stability appear to be constrained at high flow Reynolds numbers, especially for turbulent flow simulations, an aspect requiring further investigation.

In this paper, starting from the standard lattice BGK (LBGK) equation with an extended equilibrium distribution and applying the multiscale Chapman–Enskog (CE) analysis, we show theoretically that the correct Navier–Stokes (N–S) equations can be reproduced on a non-standard rectangular grid, using only the BGK collision model. The parameters in the extended equilibrium distribution are determined through an inverse design process. This new LBGK model is then validated using two benchmark cases, i.e., the 2D decaying Taylor–Green vortex flow and the lid-driven cavity flow. The accuracy and stability of the new model are discussed. The new model clearly extends the standard LBGK model as it was previously thought to be impossible to construct an LBGK model for the N–S equations on a rectangular grid.

Direct numerical simulations of an aggregation system composed of monosized spherical particles in homogeneous isotropic turbulence have been performed using Lattice Boltzmann method (LBM). The effects of hydrodynamics on the aggregation process were considered by directly resolving the disturbance flows around finite-size solid particles using an interpolated bounce-back scheme. A nonuniform time-dependent large-scale stochastic forcing scheme was implemented within the mesoscopic multiple-relaxation-time LBM approach to maintain turbulence intensity at targeted levels. To simulate particle interactions, the non-contact surface force and the contact force were taken into account using the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory and the soft-sphere model, respectively. This interface-resolved direct numerical simulation (IR-DNS) combined with the well-known DLVO theory was employed to obtain an insight into the aggregation process of micron-size particles. Specifically, the model was used to study the effects of solid volume fraction on aggregate growth. Aggregates of larger sizes formed in local regions of higher concentration of particles due to higher encountering probability between particles. The effects of aggregating particles of different volume fractions on the statistically stationary homogeneous isotropic turbulent flow were investigated. It was found that the presence of particles attenuated the turbulent kinetic energy at large scales and augmented the kinetic energy at the small scales. This effect is more apparent with increasing volume concentration of particles.

In order to treat immiscible two-phase flows at large density ratios and high Reynolds numbers, a three-dimensional code based on the discrete unified gas kinetic scheme (DUGKS) is developed, incorporating two major improvements. First, the particle distribution functions at cell interfaces are reconstructed using a weighted essentially non-oscillatory scheme. Second, the conservative lower-order Allen–Cahn equation is chosen instead of the higher-order Cahn–Hilliard equation to evolve the free-energy-based phase field governing the dynamics of two-phase interfaces. Five benchmark problems are simulated to demonstrate the capability of the approach in treating two-phase flows at large density ratios and high Reynolds numbers, including three two-dimensional problems (a stationary droplet, Rayleigh–Taylor instability, and a droplet splashing on a thin liquid film) and two three-dimensional problems (binary droplets collision and Rayleigh–Taylor instability). All results agree well with the previous numerical and experimental results. In these simulations, the density ratio and the Reynolds number can reach a large value of [Formula: see text]. Our improved approach sets the stage for the DUGKS scheme to handle realistic two-phase flow problems.

Nearly half of the global energy consumption goes toward the heating and cooling of buildings and processes. This quantity could be considerably reduced through the addition of advanced thermal energy storage systems. One emerging pathway for thermal energy storage is through nano-engineered phase change materials, which have very high energy densities and enable several degrees of design freedom in selecting their composition and morphology. Although the literature has indicated that these advanced materials provide a clear thermodynamic boost for thermal energy storage, they are subject to much more complex multiscale governing phenomena (e.g., non-uniform temperatures across the medium). This review highlights the most promising configurations that have been proposed for improved heat transfer along with the critical future needs in this field. We conclude that significant effort is still required to move up the technological readiness scale and to create commercially viable novel nano-engineered phase change systems.

The lattice Boltzmann method is employed to conduct direct numerical simulations of turbulent open channel flows with the presence of finite-size spherical sediment particles. The uniform particles have a diameter of approximately 18 wall units and a density of ρp=2.65ρf, where ρp and ρf are the particle and fluid densities, respectively. Three low particle volume fractions ϕ=0.11%, 0.22%, and 0.44% are used to investigate the particle-turbulence interactions. Simulation results indicate that particles are found to result in a more isotropic distribution of fluid turbulent kinetic energy (TKE) among different velocity components, and a more homogeneous distribution of the fluid TKE in the wall-normal direction. Particles tend to accumulate in the near-wall region due to the settling effect and they preferentially reside in low-speed streaks. The vertical particle volume fraction profiles are self-similar when normalized by the total particle volume fractions. Moreover, several typical transport modes of the sediment particles, such as resuspension, saltation, and rolling, are captured by tracking the trajectories of particles. Finally, the vertical profiles of particle concentration are shown to be consistent with a kinetic model.

Discrete unified gas-kinetic scheme (DUGKS) has been developed recently as a general method for simulating flows at all Knudsen numbers. In this study, we extend DUGKS to simulate fully compressible thermal flows. We introduce a source term to the Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) collision model [1] to adjust heat flux and thus the Prandtl number. The fully compressible Navier-Stokes equations can be recovered by the current model. As a mesoscopic CFD approach, it requires an accurate mesoscopic implementation of the boundary conditions. Using the Chapman-Enskog approximation, we derive the “bounce-back” expressions for both temperature and velocity distribution functions, which reveal the need to consider coupling terms between the velocity and thermal fields. To validate our scheme, we first reproduce the Boussinesq flow results by simulating natural convection in a square cavity with a small temperature difference ( ϵ = 0.01 ) and a low Mach number. Then we perform simulations of steady natural convection ( R a = 1.0 × 10 6 ) in a square cavity with differentially heated side walls and a large temperature difference ( ϵ = 0.6 ) , where the Boussinesq approximation becomes invalid. Temperature, velocity profiles, and Nusselt number distribution are obtained and compared with the benchmark results from the literature. Finally, the unsteady compressible natural convection with R a = 5.0 × 10 9 , ϵ = 0.6 is studied and the turbulent fluctuation statistics are computed and analyzed.

We investigate the dynamics of inertial particles in homogeneous isotropic turbulence, under one-way momentum coupling, using a new computational approach that incorporates the effect of long-range many-body aerodynamic interactions along with the short-range lubrication forces. The implementation couples hybrid direct numerical simulations (HDNS) with the analytical solutions of two rigid spheres moving in an unbounded fluid. Concerning the velocity field seen by the particles, the algorithm switches from the flow solution in terms of HDNS to analytical formulae when the separation distance between particles becomes comparable to their average radius. Standard HDNS is unable to correctly represent the short-range interactions since this method is based on the superposition of the Stokes solutions for single spheres. Our results show that for the turbulent kinetic energy dissipation rates typical of atmospheric clouds, the radial relative velocities (RRVs) of the droplets increase, and the radial distribution function (RDF) decreases in the near-contact region if the lubrication forces are taken into account. These changes are more pronounced when the effect of gravity is considered. Away from the contact region, there is not much change in RRVs and RDFs. For turbulent clouds with lower dissipation rates lubrication forces significantly enhance the average RRV in the limit of low Stokes number. This enhancement, however, is statistically insignificant because the number of particle pairs at close proximity is very small. The effect of mass loading on the collision statistics is also investigated, demonstrating an increase in RRV and a reduction in RDF with the droplet concentration.

In the present study, the magnetic field induced self-assembly processes of magnetic microparticles in an aqueous liquid (the pure magnetic fluid) and nonmagnetic microparticles in ferrofluid (the inverse magnetic fluid) are experimentally investigated The microparticles are formed into chain-like microstructures in both the pure magnetic fluid and the inverse magnetic fluid by applying the external magnetic field The fluorescence parameters of these self-assembled chain-like microstructures are measured and compared to those without the effect of magnetic field It is found that the fluorescence in the pure magnetic fluid is weakened, because the scattering and illuminating areas are reduced in the microstructures On the contrary, the fluorescence in the inverse magnetic fluid is enhanced, because more fluorescent nonmagnetic microparticles are enriched and become detectable under the effect of the magnetic dipole force and the magnetic levitational force, and their unnecessary scattering can be absorbed by the surrounding ferrofluid The average enhancement of the fluorescence area ratio in the inverse magnetic fluid with 3 μm nonmagnetic microparticles reaches 112 92% The present work shows that the inverse magnetic fluid has advantages such as low cost, no scattering effect, stable fluorescence intensity, and relatively low magnetic resistance In the end, a prototype design for the novel detection of coronavirus disease 2019 based on the magnetic field induced self-assembly in the inverse magnetic fluid is proposed, which could support the epidemic prevention and control © 2021 Author(s)

The enhancement of heat transfer between parallel surfaces, including parallel plates, parallel disks, and two concentric pipes, is vital because of their wide applications ranging from lubrication systems to water purification processes. Various techniques can be utilized to enhance heat transfer in such systems. Adding nanoparticles to the conventional working fluids is an effective solution that could remarkably enhance the heat transfer rate. No published review article focuses on the recent advances in nanofluid flow between parallel surfaces; therefore, the present paper aims to review the latest experimental and numerical studies on the flow and heat transfer of nanofluids (mixtures of nanoparticles and conventional working fluids) in such configurations. For the performance analysis of thermal systems composed of parallel surfaces and operating with nanofluids, it is necessary to know the physical phenomena and parameters that influence the flow and heat transfer characteristics in these systems. Significant results obtained from this review indicate that, in most cases, the heat transfer rate between parallel surfaces is enhanced with an increase in the Rayleigh number, the Reynolds number, the magnetic number, and Brownian motion. On the other hand, an increase in thermophoresis parameter, as well as flow parameters, including the Eckert number, buoyancy ratio, Hartmann number, and Lewis number, leads to heat transfer rate reduction.

The recent discovery of superconductivity in doped infinite-layer nickelates has stimulated intensive interest, especially for similarities and differences compared to that in cuprate superconductors. In contrast to cuprates, although earlier magnetization measurement reveals a Curie-Weiss-like behavior in undoped infinite-layer nickelates, there is no magnetic ordering observed by elastic neutron scattering down to liquid helium temperature. Until now, the nature of the magnetic ground state in undoped infinite-layer nickelates was still elusive. Here, we perform a nuclear magnetic resonance (NMR) experiment through 139La nuclei to study the intrinsic spin susceptibility of infinite-layer LaNiO2. First, the signature for magnetic ordering or freezing is absent in the 139La NMR spectrum down to 0.24 K, which unambiguously confirms a paramagnetic ground state in LaNiO2. Second, a pseudogap-like behavior instead of Curie-Weiss-like behavior is observed in both the temperature-dependent Knight shift and nuclear spin-lattice relaxation rate (1/T1), which is widely observed in both underdoped cuprates and iron-based superconductors. Furthermore, the scaling behavior between the Knight shift and 1/T1T has also been discussed. Finally, the present results imply a considerable exchange interaction in infinite-layer nickelates, which sets a strong constraint for the proposed theoretical models., 14 pages, 4 figures, accepted by Physical Review Letters

In this paper, we present a general framework for the inverse-design of mesoscopic models based on the Boltzmann equation. Starting from the single-relaxation-time Boltzmann equation with an additional source term, two model Boltzmann equations for two reduced distribution functions are obtained, each then also having an additional undetermined source term. Under this general framework and using Navier-Stokes-Fourier (NSF) equations as constraints, the structures of the distribution functions are obtained by the leading-order Chapman-Enskog analysis. Next, five basic constraints for the design of the two source terms are obtained in order to recover the Navier-Stokes-Fourier system in the continuum limit. These constraints allow for adjustable bulk-to-shear viscosity ratio, Prandtl number as well as a thermal energy source. The specific forms of the two source terms can be determined through proper physical considerations and numerical implementation requirements. By employing the truncated Hermite expansion, one design for the two source terms is proposed. Moreover, three well-known mesoscopic models in the literature are shown to be compatible with these five constraints. In addition, the consistent implementation of boundary conditions is also explored by using the Chapman-Enskog expansion at the NSF order. Finally, based on the higher-order Chapman-Enskog expansion of the distribution functions, we derive the complete analytical expressions for the viscous stress tensor and the heat flux. Some underlying physics can be further explored under this framework.

Two case studies of marine stratocumulus (one nocturnal and drizzling, the other daytime and nonprecipitating) are simulated by the UCLA large-eddy simulation model with bin microphysics for comparison with aircraft in situ observations. A high-bin-resolution variant of the microphysics is implemented for closer comparison with cloud drop size distribution (DSD) observations and a turbulent collision–coalescence kernel to evaluate the role of turbulence on drizzle formation. Simulations agree well with observational constraints, reproducing observed thermodynamic profiles (i.e., liquid water potential temperature and total moisture mixing ratio) as well as liquid water path. Cloud drop number concentration and liquid water content profiles also agree well insofar as the thermodynamic profiles match observations, but there are significant differences in DSD shape among simulations that cause discrepancies in higher-order moments such as sedimentation flux, especially as a function of bin resolution. Counterintuitively, high-bin-resolution simulations produce broader DSDs than standard resolution for both cases. Examination of several metrics of DSD width and percentile drop sizes shows that various discrepancies of model output with respect to the observations can be attributed to specific microphysical processes: condensation spuriously creates DSDs that are too wide as measured by standard deviation, which leads to collisional production of too many large drops. The turbulent kernel has the greatest impact on the low-bin-resolution simulation of the drizzling case, which exhibits greater surface precipitation accumulation and broader DSDs than the control (quiescent kernel) simulations. Turbulence effects on precipitation formation cannot be definitively evaluated using bin microphysics until the artificial condensation broadening issue has been addressed.

Background Effect of hydrodynamic heterogeneity on particle dispersion in a Taylor-Couette flow (TC) reactor with variable configurations of inner cylinder has been investigated using CFD modelling. Methods Particle dispersion was tracked based on the Eulerian-Lagrangian approach, where the reactant solution phase was solved in the Eulerian reference frame, while the particle dispersion was calculated by tracking a large number of particles with consideration of the hydrodynamic forces acting on particles and adopting actual particle properties measured from the particle synthesis experiments. Significant Findings The simulation reveals that particle dispersion is significantly enhanced by increasing the inner cylinder rotational speed, characterized by particle distribution for both circular inner cylinder Taylor-Couette flow reactor (CTC) and lobed cross-section inner cylinder Taylor-Couette flow reactor (LTC). Particle trajectories or dispersion are influenced by the turbulent Taylor vortices. Particle radial dispersion affects the particle classification by presenting different particle axial velocities in radial direction, while particle axial dispersion can be seen as an indicator for global mixing occurring in the TC reactor, which is enhanced at high rotational speed, especially in the LTC. The calculated dispersion coefficient is found to be similar to the shape of particle size distribution found in the experiments.

In this work, an immersed boundary-discrete unified gas kinetic scheme (IB-DUGKS) is proposed and presented for the simulation of natural convection with a curved body surface. In this method, two distribution functions are employed for velocity and temperature field, respectively, and they are coupled under the Boussinesq approximation. The IB-DUGKS provides an effective way for the DUGKS to treat a curved boundary. The Strang-splitting method is used to handle the IB force, and its accuracy is first validated by comparing with another implementation method for the base case of natural convection in a square cavity. The widely used direct-forcing immersed boundary method is adopted due to its simplicity, with an iteration procedure to ensure the accuracy of no-slip condition on the immersed boundary. Natural convection between an outer square and an inner circular cylinder is then simulated under different geometric configurations, including different aspect ratios and locations of the cylinder relative to the cavity. The numerical results are in excellent agreement with the results from the literature, confirming the accuracy and robustness of the proposed method.

In this paper, turbulent pipe flows laden with finite-size particles are investigated, using the direct numerical simulations based on the lattice Boltzmann method. Our focus is on the modulation of turbulence statistics in the pipe due to the presence of finite-size neutrally buoyant particles, and the question if the characteristics of modulation differ from those in a turbulent channel flow under comparable system parameters in order to reveal the effect of curved walls in the pipe. The mechanisms responsible for modulations of the turbulent intensity in the pipe flow are clarified through a quantitative budget analysis of the turbulent kinetic energy.

A lattice Boltzmann model (LBM) for two-phase flows with liquid-vapor phase transition based on a dynamic van der Waals theory [Phys. Rev. Lett. 94, 054501 (2005)] is proposed. The proposed model consists of two lattice Boltzmann equations (LBE): one for the Navier-Stokes-Korteweg (NSK) equations and the other for the temperature equation. In the thermal LBE, the equilibrium distribution function is redesigned by introducing a reference temperature, which is used to reduce the numerical errors of velocity divergence in the thermal LBE. A free-energy-based LBE is developed for the hydrodynamic equations and a novel force term is used to correctly recover the NSK equations. Several numerical simulations, including the liquid-vapor coexistence curve, phase separation, stationary droplet, droplet on partially wetting surface, droplet evaporation and bubble nucleate and departure, are conducted to validate the capability and performance of the present model. The numerical results of the proposed model are found to be in excellent agreement with the results of theoretical and/or the hybrid method. It is also shown that numerical stability and accuracy of the present models can be greatly improved by adjusting the reference temperature. The present models provide an effective predictive tool for two-phase flows involving phase change.

Recently, the COVID-19 virus pandemic has led to many studies on the airborne transmission of expiratory droplets. While limited experiments and on-site measurements offer qualitative indication of potential virus spread rates and the level of transmission risk, the quantitative understanding and mechanistic insights also indispensably come from careful theoretical modeling and numerical simulation efforts around which a surge of research papers has emerged. However, due to the highly interdisciplinary nature of the topic, numerical simulations of the airborne spread of expiratory droplets face serious challenges. It is essential to examine the assumptions and simplifications made in the existing modeling and simulations, which will be reviewed carefully here to better advance the fidelity of numerical results when compared to the reality. So far, existing review papers have focused on discussing the simulation results without questioning or comparing the model assumptions. This review paper focuses instead on the details of the model simplifications used in the numerical methods and how to properly incorporate important processes associated with respiratory droplet transmission. Specifically, the critical issues reviewed here include modeling of the respiratory droplet evaporation, droplet size distribution, and time-dependent velocity profile of air exhaled from coughing and sneezing. According to the literature review, another problem in numerical simulations is that the virus decay rate and suspended viable viral dose are often not incorporated; therefore here, empirical relationships for the bioactivity of coronavirus are presented. It is hoped that this paper can assist researchers to significantly improve their model fidelity when simulating respiratory droplet transmission.

Face masks play a critical role in reducing the transmission risk of COVID-19 and other respiratory diseases. Masks made with nanofibers have drawn increasingly more attention because of their higher filtration efficiency, better comfort, and lower pressure drop. However, the interactions and consequences of the nanofibers and microwater droplets remain unclear. In this work, the evolution of fibers made of polymers with different contact angles, diameters, and mesh sizes under water aerosol exposure is systematically visualized. The images show that capillarity is very strong compared with the elasticity of the nanofiber. The nanofibers coalesce irreversibly during the droplet capture stage as well as the subsequent liquid evaporation stage. The fiber coalescence significantly reduces the effective fiber length for capturing aerosols. The nanofiber mesh that undergoes multiple droplet capture/evaporation cycles exhibits a fiber coalescing fraction of 40%–58%. The hydrophobic and orthogonally woven fibers can reduce the capillary forces and decrease the fiber coalescing fraction. This finding is expected to assist the proper design, fabrication, and use of face masks with nanofibers. It also provides direct visual evidence on the necessity to replace face masks frequently, especially in cold environments.

The dynamics of a single or a group of slippery spheres settling under gravity in a Newtonian fluid is studied numerically. We focus particularly on the effect of particle surface slip on the sedimentation behavior. The flows containing moving slippery spheres are solved by a three-dimensional lattice Boltzmann model where a kinetic boundary condition is used to handle the slip phenomenon at the curved particle surface. The method is first validated by simulating the slip flow in a cylindrical tube, and the no-slip flows around one and two spheres settling in a container. The hydrodynamic behaviors of one, two and multiple slippery spheres settling under gravity are then investigated. The results for a single sphere show that the surface slip makes the sphere fall faster than a no-slip particle and the wall correction factor decreases as the level of particle-surface slip is increased, indicating a drag reduction caused by the slip condition. For two settling spheres, when the no-slip particle is placed below the slip one, the two spheres will enter into the kissing phase earlier; on the contrary, deploying the no-slip particle above the slip one, the DKT process does not occur beyond a critical slip level and initial gap distance. If the two spheres are both slippery, the settling dynamics are similar to the no-slip case, but the time duration of the kissing phase decreases. As for the sedimentation of multiple spheres, it is found that the initial geometric arrangement has a significant impact on the sedimentation behavior. In general, slippery spheres in a cluster will experience larger fluctuations in the vertical velocity and position in the accelerated-falling stage, and smaller fluctuations in the decelerated-falling stage.

Knowledge of the soil water retention curve (SWRC) is critical to mathematical modeling of soil water dynamics in the vadose zone. Traditional SWRC models were developed based on bundles of cylindrical capillaries (BCCs) using a residual water content, which fail to accurately describe the dry end of the curve. This study improved and expanded on the traditional BCC models. Specifically, the total water retention was treated as a weighed superposition of capillary and adsorptive components. We proposed a mathematical continuous expression for water retention from saturation to oven dryness, which also allowed for a partition of capillary and adsorptive retention. We further evaluated six capillary retention functions using different probability laws for pore‐size distribution—namely, the log‐logistic, Weibull, lognormal, two‐parameter van Genuchten (VG), three‐parameter VG (or Dagum), and Fredlund–Xing (FX) distributions. Model testing against 144 experimental data showed better agreement of the proposed model with experimental observations than the traditional approaches that use the residual water content. The Dagum and FX distributions, which have one more degree of freedom, provided better agreement with experimental data than the other four distributions. The log‐logistic and lognormal distributions fitted the experimental data better than the Weibull and VG distribution for loam soils. In addition, the fitted weighting factor w using the log‐logistic and lognormal distributions better correlated to soil clay content than the other four distributions. Our study suggests that the log‐logistic and lognormal distributions are more suitable to model soils’ pore‐size distribution than other tested distributions.

The spurious currents observed in multiphase flow simulations with pseudo-potential lattice Boltzmann (LB) models are usually understood to be the result of the lack of isotropy of the model-generated interaction force between phases. Remedies have been proposed to utilize larger stencils to compute the interaction force with higher orders of isotropy. In this document, we point out the incompleteness in the current understanding and propose a new consistent implementation to more effectively suppress the spurious currents. We also demonstrate theoretically that certain low-level spurious currents cannot be eliminated by increasing isotropy if the local hydrostatic balance inside the diffuse interface is not established in the LB models.

We investigate three-dimensional natural convection flow in an air-filled, differentially heated cubical cavity. The vertical wall on the left is heated and the vertical wall on the right is cooled, with the remaining four walls being adiabatic. We performed direct numerical simulations of the natural convection flow using discrete unified gas-kinetic scheme (DUGKS), with an improved implementation of boundary conditions. Thin boundary layers are developed along the two isothermal walls. The laminar to turbulent flow transition inside the boundary layers is studied in this paper. The simulations are conducted at three Rayleigh numbers of 1.5 × 10 9 , 1.0 × 10 10 , 1.0 × 10 11 using nonuniform grids with resolution up to 320 3 . The Prandtl number is fixed at 0.71. We provide a detailed analysis of the transition from laminar to turbulent flow inside the vertical boundary layers and its influence on the rate of heat transfer. Time traces of temperature and velocity, time-averaged flow field, statistics of fluctuation fields are presented to illustrate distinct behaviors in the laminar and turbulent thermal boundary layer, as well as to determine the transition location at different R a numbers. The average Nusselt numbers for different R a numbers are compiled and compared to previous results. A guideline of the resolution requirement is suggested based on the R a scaling of laminar thermal boundary layer.

A multiple-relaxation time (MRT) lattice Boltzmann (LB) model on a D2Q9 rectangular grid is designed theoretically and validated numerically in the present work. By introducing stress components into the equilibrium moments, this MRT-LB model restores the isotropy of diffusive momentum transport at the macroscopic level (or in the continuum limit), leading to moment equations that are fully consistent with the NavierStokes equations. The model is derived by an inverse design process which is described in detail. Except one moment associated with the energy square, all other eight equilibrium moments can be theoretically and uniquely determined. The model is then carefully validated using both the two-dimensional decaying TaylorGreen vortex flow and lid-driven cavity flow, with different grid aspect ratios. The corresponding results from an earlier model (Bouzidi et al. (2001) [28]) are also presented for comparison. The results of Bouzidi et al.'s model show problems associated with anisotropy of viscosity coefficients, while the present model exhibits full isotropy and is accurate and stable.

Accurate simulations of moving particles in a viscous flow require an adequate grid resolution near the surface of a moving particle. Within the framework of the lattice Boltzmann approach, inadequate grid resolution could also lead to numerical instability and large fluctuations of the computed hydrodynamic force and torque. Here we explore the use of local grid refinement around a moving particle to improve the simulation results using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). We first re-examine the necessary relationships, within MRT LBM, between the relaxation parameters and the distribution functions on the coarse and fine grids, in order to meet the physical requirements of the fluid hydrodynamics.We also propose additional relationships based on the Chapman–Enskog multi-scaling analysis. Several aspects of the implementation details are discussed, including the treatment of interface buffer nodes, the method to transfer information between the coarse domain and fine domain, and the computation of macroscopic variables including stress components. Our approach is then applied in two numerical tests to demonstrate that the local grid refinement can significantly improve the physical results with a high computational efficiency. We compare simulation results from three grid configurations: a uniformly coarse grid, a uniformly coarse grid with local refinement, and a uniformly fine grid. For the lid-driven cavity flow, the local refinement essentially yields a local flow field that is comparable to the use of uniformly fine grid, but with much less computational cost. In the Couette flow with a moving cylinder, the local refinement suppresses the level of force fluctuations. In these tests, the stress profiles are carefully examined to help illustrate the benefits of local grid refinement. We also confirm that the coarse-fine grid relationships between the non-equilibrium moments of energy square and energy fluxes do not affect the simulation results.