Modeling epidemics by the lattice Boltzmann method

In this paper, we demonstrate that the lattice Boltzmann method can be successfully adopted to investigate the dynamics of epidemics. Numerical simulations prove the excellent accuracy properties of the approach, which recovers the solution of the popular SIR model. Because spatial effects are naturally accounted for in the lattice Boltzmann formulation, the present scheme appears to be more competitive than traditional solution procedures. Interestingly, it allows us to simulate scenarios characterized by selective lockdown configurations.

Central-Moments-Based Lattice Boltzmann for Associating Fluids: A New Integrated Approach

Dynamic and thermodynamic behaviors of associating fluids play a crucial role in various science and engineering disciplines. Cubic plus association equation of state (CPA EOS) is implemented in a central-moments-based lattice Boltzmann method (LBM) in order to mimic the thermodynamic behavior of associating fluids. The pseudopotential approach is selected to model the multiphase thermodynamic characteristics such as reduced density of associating fluids. The priority of central-moments-based approach over multiple-relaxation-time collision operator is highlighted by performing double shear layers. The integration of central-moments-based LBM and CPA EOS is useful to simulate the dynamic and thermodynamic characteristics of associating fluids at high flow rate conditions, which is extended to high-density ratio scenarios by increasing the anisotropy order of gradient operator. In order to increase the stability of the model, a higher anisotropy order of the gradient operator is implemented; about 34 present reduction in spurious velocities is noticed in some cases. The type of gradient operator considerably affects the model thermodynamic consistency. Finally, the model is validated by observing a straight line in the Laplace law test. Prediction of thermodynamic behaviors of associating fluids is of significance in various applications including biological processes as well as fluid flow in porous media.

Role of higher-order Hermite polynomials in the central-moments-based lattice Boltzmann framework

The cascaded lattice Boltzmann method decomposes the collision stage on a basis of central moments on which the equilibrium state is assumed equal to that of the continuous Maxwellian distribution. Such a relaxation process is usually considered as an assumption, which is then justified a posteriori by showing the enhanced Galilean invariance of the resultant algorithm. An alternative method is to relax central moments to the equilibrium state of the discrete second-order truncated distribution. In this paper, we demonstrate that relaxation to the continuous Maxwellian distribution is equivalent to the discrete counterpart if higher-order (up to sixth) Hermite polynomials are used to construct the equilibrium when the D3Q27 lattice velocity space is considered. Therefore, a theoretical a priori justification of the choice of the continuous distribution is formally provided for the first time.

Color-gradient lattice Boltzmann model with nonorthogonal central moments: Hydrodynamic melt-jet breakup simulations

We develop a lattice Boltzmann (LB) model for immiscible two-phase flow simulations with central moments (CMs). This successfully combines a three-dimensional nonorthogonal CM-based LB scheme [De Rosis, Phys. Rev. E 95, 013310 (2017)2470-004510.1103/PhysRevE.95.013310] with our previous color-gradient LB model [Saito, Abe, and Koyama, Phys. Rev. E 96, 013317 (2017)2470-004510.1103/PhysRevE.96.013317]. Hydrodynamic melt-jet breakup simulations show that the proposed model is significantly more stable, even for flow with extremely high Reynolds numbers, up to O(10^{6}). This enables us to investigate the phenomena expected under actual reactor conditions.

Preconditioned lattice Boltzmann method for steady flows: A noncascaded central-moments-based approach

We present a concise yet effective central-moments-based lattice Boltzmann method with an accelerated convergence to the steady state through preconditioning. It is demonstrated that the proposed scheme reduces to a slight modification of the unaccelerated one, as the preconditioning affects only the equilibrium state. Different from previous efforts carried out within the lattice Boltzmann community, the present scheme is built on an original model. In fact, the corresponding collision operator loses the pyramidal orchestrated nature that is typical of the cascaded scheme, hence we coin the name "noncascaded." Our model is very general, characterized by highly intelligible formulations, simple to implement, and it can be derived for any lattice velocity space.

Transport of ellipsoid fibers in oscillatory shear flows: Implications for aerosol deposition in deep airways

It is widely acknowledged that inhaled fibers, e.g. air pollutants and anthropogenic particulate matter, hold the ability to deposit deep into the lungs reaching the distal pulmonary acinar airways as a result of their aerodynamic properties; these particles tend to align with the flow and thus stay longer airborne relative to their spherical counterpart, due to higher drag forces that resist sedimentation. Together with a high surface-to-volume ratio, such characteristics may render non-spherical particles, and fibers in particular, potentially attractive airborne carriers for drug delivery. Until present, however, our understanding of the dynamics of inhaled aerosols in the distal regions of the lungs has been mostly limited to spherical particles. In an effort to unravel the fate of non-spherical aerosols in the pulmonary depths, we explore through numerical simulations the kinematics of ellipsoid-shaped fibers in a toy model of a straight pipe as a first step towards understanding particle dynamics in more intricate acinar geometries. Transient translational and rotational motions of micron-sized ellipsoid particles are simulated as a function of aspect ratio (AR) for laminar oscillatory shear flows mimicking various inhalation maneuvers under the influence of aerodynamic (i.e. drag and lift) and gravitational forces. We quantify transport and deposition metrics for such fibers, including residence time and penetration depth, compared with spherical particles of equivalent mass. Our findings underscore how deposition depth is largely independent of AR under oscillatory conditions, in contrast with previous works where AR was found to influence deposition depth under steady inspiratory flow. Overall, our efforts underline the importance of modeling oscillatory breathing when predicting fiber deposition in the distal lungs, as they are inhaled and exhaled during a full inspiratory cycle. Such physical insight helps further explore the potential of fiber particles as attractive carriers for deep airway targeting.

Alternative formulation to incorporate forcing terms in a lattice Boltzmann scheme with central moments

Within the framework of the central-moment-based lattice Boltzmann method, we propose a strategy to account for external forces in two and three dimensions. Its numerical properties are evaluated against consolidated benchmark problems, highlighting very high accuracy and optimal convergence. Moreover, our derivations are light and intelligible.

Nonorthogonal central-moments-based lattice Boltzmann scheme in three dimensions

We present an alternative three-dimensional lattice Boltzmann collision operator consisting of a nonorthogonal basis of central moments. Our formulation is characterized by an intelligible derivation with a relatively simple and quite general implementation. It is successfully validated against several established, well-consolidated, well-defined benchmark problems, showing excellent properties in terms of accuracy and convergence. If compared to the adoption of the classical Bhatnagar-Gross-Krook operator, our model possesses superior stability.

Fluid forces enhance the performance of an aspirant leader in self-organized living groups

In this paper, the performance of an individual aiming at guiding a self-organized group is numerically investigated. A collective behavioural model is adopted, accounting for the mutual repulsion, attraction and orientation experienced by the individuals. Moreover, these represent a set of solid particles which are supposed to be immersed in a fictitious viscous fluid. In particular, the lattice Boltzmann and Immersed boundary methods are used to predict the fluid dynamics, whereas the effect of the hydrodynamic forces on particles is accounted for by solving the equation of the solid motion through the time discontinuous Galerkin scheme. Numerical simulations are carried out by involving the individuals in a dichotomous process. On the one hand, an aspirant leader (AL) additional individual is added to the system. AL is forced to move along a prescribed direction which intersects the group. On the other hand, these tend to depart from an obstacle represented by a rotating lamina which is placed in the fluid domain. A numerical campaign is carried out by varying the fluid viscosity and, as a consequence, the hydrodynamic field. Moreover, scenarios characterized by different values of the size of the group are investigated. In order to estimate the AL's performance, a proper parameter is introduced, depending on the number of individuals following AL. Present findings show that the sole collective behavioural equations are insufficient to predict the AL's performance, since the motion is drastically affected by the presence of the surrounding fluid. With respect to the existing literature, the proposed numerical model is enriched by accounting for the presence of the encompassing fluid, thus computing the hydrodynamic forces arising when the individuals move.