We investigate the sedimentation dynamics of a binary mixture, the species of which differ by their Stokes coefficients but are identical otherwise. We analyze the sedimentation dynamics and the morphology of the final deposits using Brownian dynamics simulations for mixtures with a range of sedimentation velocities of both species. In addition, we use the lattice Boltzmann method to study hydrodynamic effects. We found a threshold in the difference of the sedimentation velocities above which the species in the final deposit are segregated. The degree of segregation increases with the difference in the Stokes coefficients or the sedimentation velocities above the threshold. We propose a simple analytical model that captures the main features of the simulated deposits.

The effect of the thickness of the dielectric boundary layer that connects a material of refractive index $n_1$ to another of index $n_2$ is considered for the propagation of an electromagnetic pulse. A qubit lattice algorithm (QLA), which consists of a specially chosen non-commuting sequence of collision and streaming operators acting on a basis set of qubits, is theoretically determined that recovers the Maxwell equations to second-order in a small parameter $\epsilon.$ For very thin but continuous boundary layer the scattering properties of the pulse mimics that found from the Fresnel discontinuous jump conditions for a plane wave - except that the transmission to incident amplitudes are augmented by a factor of $\sqrt{ n_2/n_1}.$ As the boundary layer becomes thicker one finds deviations away from the discontinuous Fresnel conditions and eventually one approaches the expected WKB limit. However there is found a small but unusual dip in part of the transmitted pulse that persists in time. Computationally, the QLA simulations still recover the solutions to Maxwell equations even when this parameter $\epsilon → 1.$ On examining the pulse propagation in medium $n_1 , \epsilon$ corresponds to the dimensionless speed of the pulse (in lattice units).

We propose a multiple relaxation time entropic realization of a recent two-phase flow lattice Boltzmann model [S.A. Hosseini, B. Dorschner, and I. V. Karlin, Journal of Fluid Mechanics 953 (2022)]. While the original model with a single relaxation time allows us to reach large density ratios, it is limited in terms of stability with respect to non-dimensional viscosity and velocity. Here we show that the entropic multiple relaxation time model extends the stability limits of the model significantly, which allows us to reach larger Reynolds numbers for a given grid resolution. The thermodynamic properties of the solver, using the Peng–Robinson equation of state, are studied first using simple configurations. Co-existence densities and temperature scaling of both the interface thickness and the surface tension are shown to agree well with theory. The model is then used to simulate the impact of a drop onto a thin liquid film with density and viscosity ratios matching those of water and air both in two and three dimensions. The results are in very good agreement with theoretically predicted scaling laws and experimental data.

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Physiological solvent flows surround biological structures triggering therein collective motions. Notable examples are virus/host-cell interactions and solvent-mediated allosteric regulation. The present work describes a multiscale approach joining the Lattice Boltzmann fluid dynamics (for solvent flows) with the all-atom atomistic molecular dynamics (for proteins) to model functional interactions between flows and molecules. We present, as an applicative scenario, the study of the SARS-CoV-2 virus spike glycoprotein protein interacting with the surrounding solvent, modeled as a mesoscopic fluid. The equilibrium properties of the wild-type spike and of the Alpha variant in implicit solvent are described by suitable observables. The mesoscopic solvent description is critically compared to the all-atom solvent model, to quantify the advantages and limitations of the mesoscopic fluid description.

Mandelic acid is an enantiomer of interest in many areas, in particular for the pharmaceutical industry. One of the approaches to produce enantiopure mandelic acid is through crystallization from an aqueous solution. We propose in this study a numerical tool based on lattice Boltzmann simulations to model crystallization dynamics of (S)-mandelic acid. The solver is first validated against experimental data. It is then used to perform parametric studies concerning the effects of important parameters such as supersaturation and seed size on the growth rate. It is finally extended to investigate the impact of forced convection on the crystal habits. Based on there parametric studies, a modification of the reactor geometry is proposed that should reduce the observed deviations from symmetrical growth with a five-fold habit.

We present the development of a non-reflecting boundary condition, based on the Local One-Dimensional Inviscid (LODI) approach, for Lattice Boltzmann Models working with multi-speed stencils.
We test and evaluate the LODI implementation with numerical benchmarks, showing significant accuracy gains with respect to the results produced by a simple zero-gradient condition. We also implement a simplified approach, which allows handling the unknown distribution functions spanning several layers of nodes in a unified way, still preserving a comparable level of accuracy with respect to the standard formulation.

We numerically study the dynamics of quasi-two dimensional cholesteric liquid crystal droplets in the presence of a time-dependent electric field, rotating at constant angular velocity. A surfactant sitting at the droplet interface is also introduced to prevent droplet coalescence. The dynamics is modeled following a hybrid numerical approach, where a standard lattice Boltzmann technique solves the Navier-Stokes equation and a finite difference scheme integrates the evolution equations of liquid crystal and surfactant. Our results show that, once the field is turned on, the liquid crystal rotates coherently triggering a concurrent orbital motion of both droplets around each other, an effect due to the momentum transfer to the surrounding fluid. In addition the topological defects, resulting from the conflict orientation of the liquid crystal within the drops, exhibit a chaotic-like motion in cholesterics with a high pitch, in contrast with a regular one occurring along circular trajectories observed in nematics drops. Such behavior is found to depend on magnitude and frequency of the applied field as well as on the anchoring of the liquid crystal at the droplet interface. These findings are quantitatively evaluated by measuring the angular velocity of fluid and drops for various frequencies of the applied field.

PonD is a method to extend LBM calculations to arbitrary ranges of Mach number and temperature. The current work was motivated by the issue of mass, momentum and energy conservation in the PonD method for LBM. The collision guarantees their conservation, thus, the study involves all aspects of the streaming step: both coordinate and velocity space discretizations, gauge transfer method, resolution of the scheme implicitness. After obtaining the expressions for the change of moments in the system in a time update of the scheme, it was found that the scheme can be formulated as explicit in some cases. Thus, we found the sufficient conditions to make Pond/RegPonD computations explicit and mass, momentum, and energy conserving. The scheme was implemented in the explicit form, and validated for several test cases.

In this work we provide analytic and numerical solutions for the Bjorken flow, a standard benchmark in relativistic hydrodynamics providing a simple model for the bulk evolution of matter created in collisions between heavy nuclei.
We consider relativistic gases of both massive and massless particles, working in a (2+1) and (3+1) Minkowski space-time coordinate system. The numerical results from a recently developed lattice kinetic scheme show excellent agreement with the analytic solutions.

In this study, we develop computational models and a methodology for accurate multicomponent flow simulation in underresolved multiscale porous structures [1]. It is generally impractical to fully resolve the flow in porous structures with large length-scale differences due to the tremendously high computational expense. The flow contributions from underresolved scales should be taken into account with proper physics modeling and simulation processes. Using precomputed physical properties such as the absolute permeability, $K_0,$ the capillary pressure-saturation curve, and the relative permeability, $K_r,$ in typical resolved porous structures, the local fluid force is determined and applied to simulations in the underresolved regions, which are represented by porous media. In this way, accurate flow simulations in multiscale porous structures become feasible.
To evaluate the accuracy and robustness of this method, a set of benchmark test cases are simulated for both single-component and two-component flows in artificially constructed multiscale porous structures. Using comparisons with analytic solutions and results with much finer resolution resolving the porous structures, the simulated results are examined. Indeed, in all cases, the results successfully show high accuracy with proper input of $K_0,$ capillary pressure, and $K_r.$ Specifically, imbibition patterns, entry pressure, residual component patterns, and absolute/relative permeability are accurately captured with this approach.

A design of a new heterogeneous code for LBM simulations is proposed. By heterogeneous computing we mean a collaborative computation on CPU and GPU, which is characterized by the following features: the data is distributed between CPU and GPU memory spaces taking advantage of both parallel hierarchies; the capabilities of both SIMT GPU and SIMD GPU parallelization are used for calculations; the algorithms in use efficiently conceal the CPU-GPU data exchange; the subdivision of the computing task is performed with an account for the strong points of both processing units: high performance of GPU, low latency, and advanced memory hierarchy of CPU. This code is a continuation of our work in the development of LRnLA codes for LBM. Previous LRnLA codes had good efficiency both for CPU and GPU computing, and allowed GPU simulation performed on data stored in CPU RAM without performance loss on CPU-GPU data transfer. In the new code, we use methods and instruments that can be flexibly adapted to GPU and CPU instruction sets. We present the theoretical study of the performance of the proposed code and suggest implementation techniques. The bottlenecks are identified. As a result, we conclude that larger problems can be simulated with higher efficiency in the heterogeneous system.

Magnetohydrodynamics couples the Navier–Stokes and Maxwell’s equations to describe the flow of electrically conducting fluids in magnetic fields. Maxwell’s equations require the divergence of the magnetic field to vanish, but this condition is typically not preserved exactly by numerical algorithms. Solutions can develop artifacts because structural properties of the magnetohydrodynamic equations then fail to hold. Magnetohydrodynamics with hyperbolic divergence cleaning permits a nonzero divergence that evolves under a telegraph equation, designed to both damp the divergence, and propagate it away from any sources, such as poorly resolved regions with large spatial gradients, without significantly increasing the computational cost. We show that existing lattice Boltzmann algorithms for magnetohydrodynamics already incorporate hyperbolic divergence cleaning, though they typically use parameter values for which it reduces to parabolic divergence cleaning under a slowly-varying approximation. We recover hyperbolic divergence cleaning by adjusting the relaxation rate for the trace of the tensor that represents the electric field, and absorb the contribution from the symmetric-traceless part of this tensor using a change of variables. Numerical experiments confirm that the qualitative behaviour changes from parabolic to hyperbolic when the relaxation time for the trace of the electric field tensor is increased.

We detail some of the understudied aspects of the flow inside and around the Hexactinellid Sponge Euplectella aspergillum. By leveraging the flexibility of the Lattice Boltzmann Method, High Performance Computing simulations are performed to dissect the complex conditions corresponding to the actual environment at the bottom of the ocean, at depths between 100 and 1,000 m. These large-scale simulations unveil potential clues on the evolutionary adaptations of these deep-sea sponges in response to the surrounding fluid flow, and they open the path to future investigations at the interface between physics, engineering and biology.

Recently, we have validated a three-dimensional, single framework multicomponent lattice Boltzmann method, modified to generate vesicles (rather than drops) [“Three-dimensional single framework multicomponent lattice Boltzmann equation method for vesicle hydrodynamics,” Phys. Fluids 33, 077110 (2021)]. This approach implements an immersed boundary force distribution, characterised by bending rigidity, surface tension, preferred curvature and conserved membrane area, in which work we successfully validated isolated vesicle flows against other methodologies and experiment. Like most immersed boundary algorithms, our method relies on numerical computation of high-order spatial derivatives and an intricate body force density. The next step is to verify that it has sufficient numerical stability to address the anticipated application of high volume fraction flows of highly deformable objects in intimate interaction. It is this in silico verification – of both the class of fluid object attainable and the stability of the later in strong, straining and shearing flows which is at issue, here. We extend our method to simulate multiple variously deflated vesicles and multiple liquid droplets still within a single framework, from which our fluid objects emerge as particular parameterisations. We present data from simulations containing up to four vesicles (five immiscible fluid species), which threshold verifies that simulations containing unlimited fluid objects are possible [“Modeling the flow of dense suspensions of deformable particles in three dimensions,” Phys. Rev. E 75, 066707 (2007)]. These data also assure the ability of our immersed boundary forcing to preserve the character and integrity of fluid objects in interactions characterised by large local velocity gradients (intimate squeezing, shearing and elongational straining). Throughout, we take interfacial or membrane area, $A,$ as a proxy for stability and physical veracity.

The performance of a single or the collection of microswimmers strongly depends on the hydrodynamic coupling among their constituents and themselves. We present a numerical study for a single and a pair of microswimmers based on lattice Boltzmann method (LBM) simulations. Our numerical algorithm consists of two separable parts. Lagrange polynomials provide a discretization of the microswimmers and the lattice Boltzmann method captures the dynamics of the surrounding fluid. The two components couple via an immersed boundary method. We present data for a single swimmer system and our data also show the onset of collective effects and, in particular, an overall velocity increment of clusters of swimmers.

Multicomponent models based on the Lattice Boltzmann Method (LBM) have clear advantages with respect to other approaches, such as good parallel performances and scalability and the automatic resolution of breakup and coalescence events. Multicomponent flow simulations are useful for a wide range of applications, yet many multicomponent models for LBM are limited in their numerical stability and therefore do not allow exploration of physically relevant low viscosity regimes. Here we perform a quantitative study and validations, varying parameters such as viscosity, droplet radius, domain size and acceleration for stationary and translating droplet simulations for the color-gradient method with central moments (CG-CM) formulation, as this method promises increased numerical stability with respect to the non-CM formulation. We focus on numerical stability and on the effect of decreasing grid-spacing, i.e. increasing resolution, in the extremely low viscosity regime for stationary droplet simulations. The effects of small- and large-scale anisotropy, due to grid-spacing and domain-size, respectively, are investigated for a stationary droplet. The effects on numerical stability of applying a uniform acceleration in one direction on the domain, i.e. on both the droplet and the ambient, is explored into the low viscosity regime, to probe the numerical stability of the method under dynamical conditions.

The immersed boundary method has emerged as an efficient approach for the simulation of finite-sized solid particles in complex fluid flows. However, one of the well known shortcomings of the method is the limited support for the simulation of light particles, i.e. particles with a density lower than that of the surrounding fluid, both in terms of accuracy and numerical stability.
Although a broad literature exists, with several authors reporting different approaches for improving the stability of the method, most of these attempts introduce extra complexities and are very costly from a computational point of view.
In this work, we introduce an effective force stabilizing technique, allowing to extend the stability range of the method by filtering spurious oscillations arising when dealing with light-particles, pushing down the particle-to-fluid density ratio as low as 0.04. We thoroughly validate the method comparing with both experimental and numerical data available in literature.