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Numerical solutions of the reaction–diffusion system of equations in three dimensions provide a systematic procedure to generate a variety of porous media structures of a chosen porosity. A way to characterize such geometries is by their Minkowski functional densities and their average pore diameter. We generated multiple porous geometries of the granular and foam-like types. Hydraulic flow through these series of geometries is simulated to study the dependence of the permeability k and the Forchheimer parameter β on the chosen geometrical identifiers. Both k and β exhibit two distinct behaviors aligned with the two distinct generated types of geometries when scaled with the Euler characteristic. A good correlation for dimensionless k as a function of the Minkowski functional densities and the average pore diameter was found for both types of geometries with an accuracy of 15% and 18%, respectively, while no good correlation was found for β , implying that more geometrical information is needed beyond the proposed one. From the correlations, it was found that, together with the porosity, the mean curvature is also a good parameter to characterize the permeability. Article Highlights: Porous media generation based on solutions to reaction-diffusion equations Model porous structures characterized through Minkowski functionals and average pore diameter Scaling based on the Euler characteristic reveals two distinct flow behaviors. [ABSTRACT FROM AUTHOR]

The permeability of complex porous materials is of interest to many engineering disciplines. This quantity can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as the simulation domains become less porous or more heterogeneous. Semi-analytical models that rely on averaged structural properties (i.e., porosity and tortuosity) have been proposed, but these features only partly summarize the domain, resulting in limited applicability. On the other hand, data-driven machine learning approaches have shown great promise for building more general models by virtue of accounting for the spatial arrangement of the domains' solid boundaries. However, prior approaches building on the convolutional neural network (ConvNet) literature concerning 2D image recognition problems do not scale well to the large 3D domains required to obtain a representative elementary volume (REV). As such, most prior work focused on homogeneous samples, where a small REV entails that the global nature of fluid flow could be mostly neglected, and accordingly, the memory bottleneck of addressing 3D domains with ConvNets was side-stepped. Therefore, important geometries such as fractures and vuggy domains could not be modeled properly. In this work, we address this limitation with a general multiscale deep learning model that is able to learn from porous media simulation data. By using a coupled set of neural networks that view the domain on different scales, we enable the evaluation of large ( > 512 3 ) images in approximately one second on a single graphics processing unit. This model architecture opens up the possibility of modeling domain sizes that would not be feasible using traditional direct simulation tools on a desktop computer. We validate our method with a laminar fluid flow case using vuggy samples and fractures. As a result of viewing the entire domain at once, our model is able to perform accurate prediction on domains exhibiting a large degree of heterogeneity. We expect the methodology to be applicable to many other transport problems where complex geometries play a central role. [ABSTRACT FROM AUTHOR]

In the emerging field of 3D bioprinting, cell damage due to large deformations is considered a main cause for cell death and loss of functionality inside the printed construct. Those deformations, in turn, strongly depend on the mechano-elastic response of the cell to the hydrodynamic stresses experienced during printing. In this work, we present a numerical model to simulate the deformation of biological cells in arbitrary three-dimensional flows. We consider cells as an elastic continuum according to the hyperelastic Mooney–Rivlin model. We then employ force calculations on a tetrahedralized volume mesh. To calibrate our model, we perform a series of FluidFM ® compression experiments with REF52 cells demonstrating that all three parameters of the Mooney–Rivlin model are required for a good description of the experimental data at very large deformations up to 80%. In addition, we validate the model by comparing to previous AFM experiments on bovine endothelial cells and artificial hydrogel particles. To investigate cell deformation in flow, we incorporate our model into Lattice Boltzmann simulations via an Immersed-Boundary algorithm. In linear shear flows, our model shows excellent agreement with analytical calculations and previous simulation data. [ABSTRACT FROM AUTHOR]

Purpose: Cerebral aneurysms are one of the prevalent cerebrovascular disorders in adults worldwide and caused by a weakness in the brain artery. The most impressive treatment for a brain aneurysm is interventional radiology treatment, which is extremely dependent on the skill level of the radiologist. Hence, accurate detection and effective therapy for cerebral aneurysms still remain important clinical challenges. In this work, we have introduced a pipeline for cerebral blood flow simulation and real-time visualization incorporating all aspects from medical image acquisition to real-time visualization and steering. Methods: We have developed and employed an improved version of HemeLB as the main computational core of the pipeline. HemeLB is a massive parallel lattice-Boltzmann fluid solver optimized for sparse and complex geometries. The visualization component of this pipeline is based on the ray marching method implemented on CUDA capable GPU cores. Results: The proposed visualization engine is evaluated comprehensively and the reported results demonstrate that it achieves significantly higher scalability and sites updates per second, indicating higher update rate of geometry sites' values, in comparison with the original HemeLB. This proposed engine is more than two times faster and capable of 3D visualization of the results by processing more than 30 frames per second. Conclusion: A reliable modeling and visualizing environment for measuring and displaying blood flow patterns in vivo, which can provide insight into the hemodynamic characteristics of cerebral aneurysms, is presented in this work. This pipeline increases the speed of visualization and maximizes the performance of the processing units to do the tasks by breaking them into smaller tasks and working with GPU to render the images. Hence, the proposed pipeline can be applied as part of clinical routines to provide the clinicians with the real-time cerebral blood flow-related information. [ABSTRACT FROM AUTHOR]

Wave energy from the ocean is currently a very popular renewable energy, and its development has primarily focused on the shape of the wave energy converter (WEC) used to efficiently convert wave energy into electrical energy. However, the free surface ocean wave problem is very complex and the parameters affecting WEC behavior are difficult to understand. In this paper, based on the Lattice-Boltzmann method, we present particle-based CFD simulation results for the pivoted-type WEC that exhibits both vertical and horizontal motions. In this method, the computation domain need not be a mesh and complex geometry is not a limiting factor. Using a free-surface turbulence model, we simulated the fluid–structure interaction. We detail our simulation results, which show good agreement with those in the literature. [ABSTRACT FROM AUTHOR]

A Kozeny-Carman-based model of permeability for fibrous networks is proposed: the original model is extended by incorporating information about the local structure of the void space. Furthermore, it is demonstrated how in practice this added structural information can be retrieved from a three-dimensional digital image of a fibrous material. The proposed model is then validated for both foam- and water-deposited laboratory sheets of bleached kraft pulp (Scots pine) and chemi-thermo-mechanical pulp (CTMP, Norway spruce). The validation is carried out by comparing the model predictions against computationally determined permeability values. The related fluid-flow simulations are executed using the lattice-Boltzmann method together with high-resolution X-ray microtomography images. For both pulp materials, the sample sets had nearly equal porosities, but deviated substantially in their permeabilities. The proposed model was shown to improve prediction of permeability for the fibrous materials considered: the deviation between the predicted and computationally determined values was no more than 8%. [ABSTRACT FROM AUTHOR]

Electroosmotic flow and dispersion in open and closed packed beds were investigated using Nuclear Magnetic Resonance (NMR) spectroscopy and pore-scale simulation. A series of NMR spectroscopy experiments were conducted to measure the effect of electroosmotic pressure on dispersion in packed spheres as a function of diameter and electric field strength. The experiments confirm earlier observations by others of superdiffusive transport in closed media. However, superdiffusive behavior is observed even at small pore sizes, contrary to earlier results and simulations in fixed sphere packs, and is conjectured to result from pressure-induced rearrangement of the particles. Simulations also support the existence of pore size-independent velocity distributions in closed media. The distribution of reverse velocities is also similar, apart from a difference in sign, to pressure-driven flow in open porous media. [ABSTRACT FROM AUTHOR]

The effects of roughness geometries and relative roughness height at the slip flow regime to investigate the thermal and hydraulic performances of microchannel have been considered in the present article using a thermal Lattice Boltzmann Method (TLBM). A two dimensional 9-bit (D2Q9) single relaxation time (SRT) model is used to simulate this problem. In micro-flows, the local density variation is still relatively small, but the total density changes, therefore, in order to account this density variation and its effect on the kinematic viscosity v, a new relaxation time proposed by Niu et al.[13] is used. The roughness geometry is modeled as a series of square and circular riblets with a relative roughness height from 0% to 10% of the channel height. The friction coefficients in terms of Poiseuille number (Pn) and the dimensionless heat transfer rate in terms of Nusselt number (Nu) have been discussed in order to analyze the roughness effects. The thermal-hydraulic performance ( η) is calculated considering the simultaneous effects of thermal and fluid friction (pressure drop) at the slip flow regime at Knudsen number, Kn, ranging from 0.01 to 0.10 with other controlling parameters for both kind of geometries. The results have been compared with previous published works and it is found to be in very good agreement. [ABSTRACT FROM AUTHOR]

Lattice-Boltzmann equation (LBE)-Discrete element method (DEM) coupled simulation of a two-dimensional gas-solid cross jet is performed, focusing on the gas-particle two-way coupling effect on heat transfer characteristics. The Reynolds number is 1000, and particle Stokes numbers are 10, 25, and 50 under the same number flow rate of particles. The gas phase temperature field and particle distribution as well as the inter-phase heat transfer characteristics are studied and analyzed. The dominating effects, i.e. the mean temperature difference and mean heat transfer coefficient between the gas-solid phases, for the pre- and post- collision stages of the cross jets are illustrated respectively. The change of dominating roles is related to the dynamical response characteristics of particles. [ABSTRACT FROM AUTHOR]

The relationship between the 3D morphology of gas-diffusion layers (GDL) of HT-PEFCs and their functionality is analyzed. A stochastic model describing the microstructure of paper-type GDL is combined with the Lattice-Boltzmann method (LBM) to simulate gas transport within the GDL microstructure. Virtual 3D microstructures representing paper-type GDL are generated by a stochastic model, where the binder morphology is systematically modified. On these structures, single phase single component gas flow is computed by the LBM. Quality criteria evaluating the spatial homogeneity of gas supply are introduced and related to the binder morphology. The spatial homogeneity of the gas supply is analyzed by a parametrized stochastic model describing the gas flow at the exit of the GDL. This approach gives insight into the spatial structure of the gas flow at the GDL exit. The quality of gas supply is quantified by characterizing size and arrangement of regions with high gas supply. This stochastic gas flow model predicts the quality of gas supply for further binder morphologies. Analyzing the quality criteria and the stochastic evaluation of the spatial structure of the gas flow field at the GDL exit, it is found that the binder morphology has an essential influence on the gas supply. [ABSTRACT FROM AUTHOR]

An investigation of margination dependence on hematocrit, platelet shape, and viscosity ratio of plasma to cytoplasm is presented. Whole blood is modeled as a suspension of deformable red blood cells (RBCs) and rigid platelets in a viscous liquid. The fluid phase is simulated using the lattice-Boltzmann method, the RBC membranes are modeled with a coarse-grained spectrin-link method, and the dynamics of rigid particles are updated using Newton's equations of motion for axisymmetric shapes. The results emphasize that an increase in hematocrit increases the rate of margination. The viscosity ratio between the interior cytoplasm and suspending fluid can considerably alter the rate of margination. The aspect ratio of surrogate platelet particles influences the rate of margination as well. Spherical particles tend to migrate more quickly than disks. Highly viscous or rigid RBCs slow down margination. [ABSTRACT FROM AUTHOR]

The Lattice–Boltzmann method (LBM) is a distribution-function based approach to numerical fluid mechanics. Due to the simple formulation of the underlying algorithm this method is well suited for parallelization and hardware acceleration using general purpose graphical processing units (GPGPU). Within this work LBM has been implemented in a new code with multi-GPU support and physically validated for a flow around a sphere. The performance analysis shows a remarkable speed-up of 1840% using 3 GPU’s in comparison to a single socket multi core CPU calculation. Moreover the validation for the test case chosen shows excellent agreement with available reference data. [ABSTRACT FROM AUTHOR]

A method of coupling grids of different mesh size is developed for classical Lattice-Boltzmann (LB) algorithms on uniform grids. The approach is based on an asymptotic analysis revealing suitable quantities equalized along the grid interfaces for exchanging information between the subgrids. In contrast to other couplings the method works without overlap zones. Moreover the grid velocity (Mach number) is not kept constant, as the time step depends not linearly but quadratically on the grid spacing. To illustrate the basic idea we use a simple LB algorithm solving the advection-diffusion equation. The proposed grid coupling is validated by numerical convergence studies indicating, that the coupling does not affect the second-order convergence behavior of the LB algorithm which is observed on uniform grids. In order to demonstrate its principal applicability to other LB models, the coupling is generalized to the standard D2P9 model for (Navier-)Stokes flow and tested numerically. As we use analytic tools different from the Chapman-Enskog expansion, the theoretical background material is given in two appendices. In particular, the results of numerical experiments are confirmed with a consistency analysis. [ABSTRACT FROM AUTHOR]

The lattice Boltzmann model is a simplified kinetic method based on the particle distribution function. We use this method to simulate problems in MEMS, in which the velocity slip near the wall plays an important role. It is demonstrated that the lattice Boltzmann method can capture the fundamental behaviors in micro-channel flow, including velocity slip, nonlinear pressure drop along the channel and mass flow rate variation with Knudsen number. The Knudsen number dependence of the position of the vortex center and the pressure contour in micro-cavity flows is also demonstrated. [ABSTRACT FROM AUTHOR]

We report results of extensive two-phase lattice-Boltzmann simulations of capillary rise dynamics. We demonstrate that the method can be used to model the hydrodynamic behaviour inside a capillary tube provided that the diameter of the tube is large enough, typically at least 30 lattice units. We also present results for the dependence of the cosine of the dynamic contact angle on the capillary number Ca. Its deviation from the static advancing contact angle has a power-law form, with the value of the exponent very close to 3/2 for capillary rise at zero gravity, while behaviour is more complex in the presence of gravity. [ABSTRACT FROM AUTHOR]

The mechanisms of momentum transfer and shear stress of liquid-particle suspensions in two-dimensional Couette flow are studied using direct numerical simulation by lattice-Boltzmann techniques. The results obtained display complex flow phenomena that arise from the two-phase nature of the fluid including a nonlinear velocity profile, layering of particles, and apparent slip near the solid walls. The general rheological behaviour of the suspension is dilatant. A detailed study of the various momentum transfer mechanisms that contribute to the total shear stress indicates that the observed shear thickening is related to enhanced relative solid phase stress for increasing shear rates. [ABSTRACT FROM AUTHOR]

This paper reviews applications of the lattice-Boltzmann method to simulations of particle-fluid suspensions. We first summarize the available simulation methods for colloidal suspensions together with some of the important applications of these methods, and then describe results from lattice-gas and lattice-Boltzmann simulations in more detail. The remainder of the paper is an update of previously published work,(69, 70) taking into account recent research by ourselves and other groups. We describe a lattice-Boltzmann model that can take proper account of density fluctuations in the fluid, which may be important in describing the short-time dynamics of colloidal particles. We then derive macro-dynamical equations for a collision operator with separate shear and bulk viscosities, via the usual multi-time-scale expansion. A careful examination of the second-order equations shows that inclusion of an external force, such as a pressure gradient, requires terms that depend on the eigenvalues of the collision operator. Alternatively, the momentum density must be redefined to include a contribution from the external force. Next, we summarize recent innovations and give a few numerical examples to illustrate critical issues. Finally, we derive the equations for a lattice-Boltzmann model that includes transverse and longitudinal fluctuations in momentum. The model leads to a discrete version of the Green–Kubo relations for the shear and bulk viscosity, which agree with the viscosities obtained from the macro-dynamical analysis. We believe that inclusion of longitudinal fluctuations will improve the equipartition of energy in lattice-Boltzmann simulations of colloidal suspensions. [ABSTRACT FROM AUTHOR]