Explicit time marching method with enhanced stability.

Recent developments in distributed computing architecture are slowly changing the way we develop partial differential equation solvers for simulating complex industrial and natural systems. Since achieving perfect parallelization of implicit temporal schemes is quite challenging, there is a growing interest in using explicit procedures with enhanced stability limits. The current work focuses on one such enhancement obtained by modifying an asynchronous delayed difference method.

Flow force calculation in the lattice Boltzmann method.

We revisit force evaluation methodologies on rigid solid particles suspended in a viscous fluid that is simulated via the lattice Boltzmann method (LBM). We point out the noncommutativity of streaming and collision operators in the force evaluation procedure due to the presence of a solid boundary, and provide a theoretical explanation for this observation. Based on this analysis, we propose a discrete force calculation scheme with enhanced accuracy.

Essentially entropic lattice Boltzmann model: Theory and simulations.

We present a detailed description of the essentially entropic lattice Boltzmann model. The entropic lattice Boltzmann model guarantees unconditional numerical stability by iteratively solving the nonlinear entropy evolution equation. In this paper we explain the construction of closed-form analytic solutions to this equation.

Two-fluid kinetic theory for dilute polymer solutions.

We provide a Boltzmann-type kinetic description for dilute polymer solutions based on two-fluid theory. This Boltzmann-type description uses a quasiequilibrium based relaxation mechanism to model collisions between a polymer dumbbell and a solvent molecule. The model reproduces the desired macroscopic equations for the polymer-solvent mixture.

Estimating the herd immunity threshold by accounting for the hidden asymptomatics using a COVID-19 specific model.

A quantitative COVID-19 model that incorporates hidden asymptomatic patients is developed, and an analytic solution in parametric form is given. The model incorporates the impact of lock-down and resulting spatial migration of population due to announcement of lock-down. A method is presented for estimating the model parameters from real-world data, and it is shown that the various phases in the observed epidemiological data are captured well.

Modelling a pandemic with asymptomatic patients, impact of lockdown and herd immunity, with applications to SARS-CoV-2.

The SARS-CoV-2 is a type of coronavirus that has caused the pandemic known as the Coronavirus Disease of 2019, or COVID-19. In traditional epidemiological models such as SEIR (Susceptible, Exposed, Infected, Removed), the exposed group does not infect the susceptible group . A distinguishing feature of COVID-19 is that, unlike with previous viral diseases, there is a distinct "asymptomatic" group , which does not show any symptoms, but can nevertheless infect others, at the same rate as infected symptomatic patients.

The lattice Fokker-Planck equation for models of wealth distribution.

Recent work on agent-based models of wealth distribution has yielded nonlinear, non-local Fokker-Planck equations whose steady-state solutions describe empirical wealth distributions with remarkable accuracy using only a few free parameters. Because these equations are often used to solve the 'inverse problem' of determining the free parameters given empirical wealth data, there is much impetus to find fast and accurate methods of solving the 'forward problem' of finding the steady state corresponding to given parameters. In this work, we derive and calibrate a lattice Boltzmann equation for this purpose.

Lattice Boltzmann model for weakly compressible flows.

We present an energy conserving lattice Boltzmann model based on a crystallographic lattice for simulation of weakly compressible flows. The theoretical requirements and the methodology to construct such a model are discussed. We demonstrate that the model recovers the isentropic sound speed in addition to the effects of viscous heating and heat flux dynamics.

Modelling the COVID-19 Pandemic: Asymptomatic Patients, Lockdown and Herd Immunity.

The SARS-Cov-2 is a type of coronavirus that has caused the COVID-19 pandemic. In traditional epidemiological models such as SEIR (Susceptible, Exposed, Infected, Removed), the exposed group does not infect the susceptible group A distinguishing feature of COVID-19 is that, unlike with previous viruses, there is a distinct "asymptomatic" group who do not show any symptoms, but can nevertheless infect others, at the same rate as infected patients. This situation is captured in a model known as SAIR (Susceptible, Asymptomatic, Infected, Removed), introduced in Robinson and Stilianakis (2013).

Essentially Entropic Lattice Boltzmann Model.

The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality.

Gaseous microflow modeling using the Fokker-Planck equation.

We present a comparative study of gaseous microflow systems using the recently introduced Fokker-Planck approach and other methods such as: direct simulation Monte Carlo, lattice Boltzmann, and variational solution of Boltzmann-BGK. We show that this Fokker-Plank approach performs efficiently at intermediate values of Knudsen number, a region where direct simulation Monte Carlo becomes expensive and lattice Boltzmann becomes inaccurate. We also investigate the effectiveness of a recently proposed Fokker-Planck model in simulations of heat transfer, as a function of relevant parameters such as the Prandtl, Knudsen numbers.

Crystallographic Lattice Boltzmann Method.

Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling.

Delayed difference scheme for large scale scientific simulations.

We argue that the current heterogeneous computing environment mimics a complex nonlinear system which needs to borrow the concept of time-scale separation and the delayed difference approach from statistical mechanics and nonlinear dynamics. We show that by replacing the usual difference equations approach by a delayed difference equations approach, the sequential fraction of many scientific computing algorithms can be substantially reduced. We also provide a comprehensive theoretical analysis to establish that the error and stability of our scheme is of the same order as existing schemes for a large, well-characterized class of problems.

Diffused bounce-back condition and refill algorithm for the lattice Boltzmann method.

A solid-fluid boundary condition for the lattice Boltzmann (LB) method, which retains the simplicity of the bounce-back method and leads to positive definite populations similar to the diffusive boundary condition, is presented. As a refill algorithm, it is proposed that quasi-equilibrium distributions be used to model distributions at fluid nodes uncovered due to solid movement. The method is tested for flow past an impulsively started cylinder and demonstrates considerable enhancement in the accuracy of the unsteady force calculation at moderate and high Reynolds numbers.

Data structure and movement for lattice-based simulations.

We show that for the lattice Boltzmann model, the existing paradigm in computer science for the choice of the data structure is suboptimal. In this paper we use the requirements of physical symmetry necessary for recovering hydrodynamics in the lattice Boltzmann description to propose a hybrid data layout for the method. This hybrid data structure, which we call a structure of an array of structures, is shown to be optimal for the lattice Boltzmann model.

Lattice Fokker Planck for dilute polymer dynamics.

We show that the actual diffusive dynamics, governing the momentum relaxation of a polymer molecule, and described by a Fokker-Planck equation, may be replaced by a BGK-type relaxation dynamics without affecting the slow (Smoluchowski) dynamics in configuration space. Based on the BGK-type description, we present a lattice-Boltzmann (LB) based direct discretization approach for the phase-space description of inertial polymer dynamics. We benchmark this formulation by determining the bulk rheological properties for both steady and time-dependent shear and extensional flows at moderate to large Weissenberg numbers.

A lattice Boltzmann method for dilute polymer solutions.

We present a lattice Boltzmann approach for the simulation of non-Newtonian fluids. The method is illustrated for the specific case of dilute polymer solutions. With the appropriate local equilibrium distribution, phase-space dynamics on a lattice, driven by a Bhatnagar-Gross-Krook (BGK) relaxation term, leads to a solution of the Fokker-Planck equation governing the probability density of polymer configurations.

Efficient lattice Boltzmann algorithm for Brownian suspensions.

A lattice Boltzmann (LB)-based hybrid method is developed to simulate suspensions of Brownian particles. The method uses conventional LB discretization (without fluid- level fluctuations) for suspending fluid, and treats Brownian particles as point masses with a stochastic thermal noise. LB equations are used to compute the velocity perturbations induced by the particle motion.

Higher-order Galilean-invariant lattice Boltzmann model for microflows: single-component gas.

We introduce a scheme which gives rise to additional degree of freedom for the same number of discrete velocities in the context of the lattice Boltzmann model. We show that an off-lattice D3Q27 model exists with correct equilibrium to recover Galilean-invariant form of Navier-Stokes equation (without any cubic error). In the first part of this work, we show that the present model can capture two important features of the microflow in a single component gas: Knudsen boundary layer and Knudsen Paradox.

Renormalization of the lattice Boltzmann hierarchy.

Is it possible to solve Boltzmann-type kinetic equations using only a small number of particle velocities? We introduce a technique of solving kinetic equations with a (arbitrarily) large number of particle velocities using only a lattice Boltzmann method on standard, low-symmetry lattices. The renormalized kinetic equation is validated with an exact solution of the planar Couette flow at moderate Knudsen numbers.

Kinetically reduced local Navier-Stokes equations: an alternative approach to hydrodynamics.

An alternative approach, the kinetically reduced local Navier-Stokes (KRLNS) equations for the grand potential and the momentum, is proposed for the simulation of low Mach number flows. The Taylor-Green vortex flow is considered in the KRLNS framework, and compared to the results of the direct numerical simulation of the incompressible Navier-Stokes equations. The excellent agreement between the KRLNS equations and the incompressible nonlocal Navier-Stokes equations for this nontrivial time-dependent flow indicates that the former is a viable alternative for computational fluid dynamics at low Mach numbers.

Consistent lattice Boltzmann method.

Lack of energy conservation in lattice Boltzmann models leads to unrealistically high values of the bulk viscosity. For this reason, the lattice Boltzmann method remains a computational tool rather than a model of a fluid. A novel lattice Boltzmann model with energy conservation is derived from Boltzmann's kinetic theory.