Santosh Ansumali

• PhD
• Professor (Associate) at Jawaharlal Nehru Centre for Advanced Scientific Research

The hydrodynamic limit of a discrete kinetic equation is intrinsically connected with the symmetry of the lattices used in construction of a discrete velocity model. On mixed lattices composed of standard lattices the sixth-order (and higher) moment is often not isotropic and thus they are insufficient to ensure correct imposition of the hydrodynam...

This study aims to evaluate the performance of the Entropic Lattice Boltzmann Method (ELBM) in predicting the aerodynamic forces on a NACA0012 airfoil at high angles of attack. To validate the accuracy of the ELBM results, we compare the lift coefficient obtained from simulations with wind tunnel experiments conducted by Sandia National Laboratorie...

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 obs...

Background & objectives Coronary artery disease (CAD) is one of the leading causes of mortality worldwide and contributes significantly to the disease burden in India. The dearth of datasets for Indian patients with CAD is an obstacle to further development and collaborative work in clinical research. The purpose of this study was to create a compr...

Kinetic models of polyatomic gas typically account for the internal degrees of freedom at the level of the two-particle distribution function. However, close to the hydrodynamic limit, the internal (rotational) degrees of freedom tend to be well represented just by rotational kinetic energy density. We account for the rotational energy by augmentin...

In the late 90's and early 2000's the concept of a discrete H theorem and Lyapunov functionals as a way to ensure stability of lattice Boltzmann solvers was a shift of paradigm in the construction of discrete kinetic solvers and opened the door for new discussions and perspectives on the matter. The entropic construction proposed to reorganize the...

In the late 90’s and early 2000’s the concept of a discrete H theorem and Lyapunov functionals as a way to ensure stability of lattice Boltzmann solvers was a shift of paradigm in the construction of discrete kinetic solvers and opened the door for new discussions and perspectives on the matter. The entropic construction proposed to reorganize the...

The objective of the current work is to calculate the combined roll Dynamic Stability Derivative (DSD) of the SACCON UAV (Unmanned Aerial Vehicle) by numerically replicating the forced oscillation experiment conducted at NASA Langley 14x22-foot wind tunnel. This test-case is characterized by inherent unsteadiness, which makes it essential to captur...

In the pharmaceutical and biopharmaceutical industry, stirred-tank reactors are extensively used for production of Active Pharmaceutical Ingredients (APIs). Characterization of the stirred-tank reactor and proper understanding of the mixing process is essential for streamlining the production of APIs. Several experimental techniques like Laser Dopp...

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. We demonstrate that n...

We revisit force evaluation methodologies on rigid solid particles suspended in a viscous fluid and simulated via lattice Boltzmann method (LBM). We point out the non-commutativity of streaming and collision operators in the force evaluation procedure and provide a theoretical explanation for this observation. Based on this analysis, we propose a d...

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. The...

This work investigates the transonic flow over a 65◦ swept-back delta wing with a sharp leading edge. The behaviour of vortex breakdown in cross-flow shocks makes the problem setup highly complex in contrast to subsonic vortical flows. It has been reported that increasing the Angle of Attack (AoA) leads to a complex interaction of the strong vortex...

This work analyzes the aeroacoustics of M219 cavity flow using the model-free higher- order lattice Boltzmann method. We have simulated an unsteady transonic flow over an open cavity with a length-to-depth ratio of 5:1 and the depth-to-width ratio of 1:1. The Mach and Reynolds number based on cavity length considered for this simulation are 0.85 an...

The main objective of the present work is to assess higher-order Entropic Lattice Boltzmann Method (ELBM) for separated and transitional flows without the use of any explicit turbulence model. For this, we chose to simulate two cases of T106 Low-Pressure Turbine (LPT) cascade -- T106A and T106C -- representing incompressible and compressible flow r...

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. We demonstrate that ne...

We provide a Boltzmann-type kinetic description for dilute polymer solutions based on two-fluid theory. This Boltzmann-type description uses a quasi-equilibrium 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. The...

Kinetic models of polyatomic gas typically account for the internal degrees of freedom at the level of the two-particle distribution function. However, close to the hydrodynamic limit, the internal (rotational) degrees of freedom tend to be well represented just by rotational kinetic energy density. We account for the rotational energy by augmentin...

View Video Presentation: https://doi.org/10.2514/6.2021-3485.vid The main objective of the present work is to assess higher-order Entropic Lattice Boltzmann Method (ELBM) for separated and transitional flows without the use of any explicit turbulence model. For this, we chose to simulate two cases of T106 Low-Pressure Turbine (LPT) cascade--T106A a...

Universal vaccination on an urgent basis is a way of controlling COVID-19 infections and deaths. Vaccine shortage and practical deployment rates on the field necessitate prioritization. The global strategy has been to prioritize those with high personal risk due to their age or comorbidities, and those who constitute the essential workforce of the...

Immediate and universal vaccination is a way of controlling the COVID-19 infections and deaths. Shortages of vaccine supplies and practical deployment rates on the field necessitate prioritization. The global strategy has been to prioritize those with a high personal risk due to their age or comorbidities and those who constitute the essential work...

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...

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 E does not infect the susceptible group S. A distinguishing feature of COVID-19 is that, unlike with previous vira...

Background. By mid-September of 2020, the number of daily new infections in India have crossed 95,000. To facilitate an intuition for the spatio-temporal development of the pandemic and to help resource deployment planning, we analyze and describe how the disease burden almost-predictably shifted from large metropolitan districts to sub-urban distr...

Fokker–Planck model for binary mixtures - Volume 899 - Samarth Agrawal, S. K. Singh, S. Ansumali

Current epidemiological models can in principle model the temporal evolution of a pandemic. However, any such model will rely on parameters that are unknown, which in practice are estimated using stochastic and poorly measured quantities. As a result, an early prediction of the long-term evolution of a pandemic will quickly lose relevance, while a...

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 giv...

Lattice differential operators are known to preserve key properties of their analytical counterpart, such as isotropy, fundamental vector identities due to the symmetries of the discrete kinetic lattice. Here, we present the idea of discrete lattice operators derived on a Body-Centered-Cubic(BCC) lattice. These operators show quite a high degree of...

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 lockdown and resulting spatial migration of population due to announcement of lockdown. A method is presented for estimating the model parameters from real-world data....

When actively taking measures to control an epidemic, an important indicator of success is crossing the "peak" of daily new infections. The peak is a positive sign which marks the end of the exponential phase of infection spread and a transition into a phase that is a manageable. Most countries or provinces with similar but independent growth traje...

Current epidemiological models can in principle model the temporal evolution of a pandemic. However, any such model will rely on parameters that are unknown, which in practice are estimated using stochastic and poorly measured quantities. As a result, an early prediction of the long-term evolution of a pandemic will quickly lose relevance, while a...

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 fl...

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 E does not infect the susceptible group S. A distinguishing feature of COVID-19 is that, unlike with previous viruses, there is a distinct “asymptomatic” group...

In dilute gas kinetic theory, model collision dynamics such as Bhatnagar-Gross-Krook (BGK) model is often used to get a better insight and numerical modelling. BGK model and its variants assume that highly nonlinear collision term can be replaced by a simple relaxation dynamics towards Maxwell-Boltzmann distribution. Lebowitz et al., proposed an al...

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 fl...

We show that collective chaotic behavior emerging from the Boltzmann picture of gases provides an alternate conceptual framework to analyze and create apparent randomness on computers. For instance, at equilibrium the distribution of various physical quantities such as position or velocities or two-dimensional projection of kinetic energy can be us...

We present an energy conserving lattice Boltzmann model on a body-centered-cubic arrangement for thermohydrodynamics. It exhibits accurate thermohydrodynamic behavior with a high degree of accuracy and is therefore capable of simulating compressible and thermal hydrodynamics. The theoretical requirements and the methodology to construct this 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 corre...

We present a new lattice Boltzmann formulation for elastic solids and analyse the issue of conservation laws for solids. This new formulation allows tunable Poisson ratio. As a first benchmark problem, we consider an elastic wave propagating in an infinite homogeneous medium with point force and point dipole Ricker wavelet as the source. The method...

The dynamics of thermally fluctuating conserved order parameters are described by stochastic conservation laws. Thermal equilibrium in such systems requires the dissipative and stochastic components of the flux to be related by detailed balance. Preserving this relation in spatial and temporal discretization is necessary to obtain solutions that ha...

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...

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...

It is shown that the combination of generalized Van der Waals equations of state with high-order discrete velocity lattices, permits to simulate the dynamics of liquid droplets at air-water density ratios, with very moderate levels of spurious currents near the droplet interface. Satisfactory agreement with experimental data on droplet collisions a...

We present a phenomenological description of the hydrodynamics in terms of the Fokker-Planck (FP) equation for one-particle distribution function. Similar to the Boltzmann equation or the Bhatnager-Gross-Krook (BGK) model, this approach is thermodynamically consistent and has the H theorem. In this model, transport coefficients as well as the equat...

We study the evolution of shock waves in a dilute granular gas which is modelled using three variants of hydrodynamic equations: Euler, 10-moment and 14-moment models. The one-dimensional shock-wave problem is formulated and the resulting equations are solved numerically using a relaxation-type scheme. Focusing on the specific case of blast waves,...

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...

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...

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...

We propose a modified direct simulation Monte Carlo (DSMC) method, which extends the validity of DSMC from rarefied to dense system of hard spheres (HSs). To assess this adapted method, transport properties of hard-sphere (HS) systems have been predicted both at dense states as well as dilute, and we observed the excellent accuracy over existing DS...

Recently, it was shown that energy conserving (EC) lattice Boltzmann (LB) model is more accurate than athermal LB model for high-resolution simulations of athermal flows. However, in the sub-grid (SG) domain, the behavior is found to be opposite. In this work, we show that via multi-relaxation model, it is possible to preserve the accuracy of the E...

We present a vector-friendly blocked computing strategy for the lattice Boltzmann method (LBM). This strategy, along with a recently developed data structure, Structure of Arrays of Structures (SoAoS), is implemented for multi-relaxation type lattice Boltzmann (LB). The proposed methodology enables optimal memory bandwidth utilization in the advect...

Numerical results from large-scale, long-time, simulations of decaying homogeneous turbulence are reported, which indicate that blow-up of inviscid flows is tamed by the emergence of collective dynamics of coherent structures. The simulations also suggest that this collective dynamics might lead to universal behaviour during the transient evolution...

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 dire...

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,...

We present a general scheme to derive lattice differential operators from the discrete velocities and associated Maxwell-Boltzmann distributions used in lattice hydrodynamics. Such discretizations offer built-in isotropy and lend themselves to recursive techniques to enhance the convergence order. The result is a simple and elegant procedure to der...

Lattice Boltzmann method (LBM) modelling of thermal flows, compressible and micro flows requires an accurate velocity space discretization. The sub optimality of Gauss-Hermite quadrature in this regard is well known [1]. Most of the thermal LBM in the past have suffered from instability due to lack of proper H-theorem and accuracy [2]. Motivated fr...

In this paper, we highlight the benefits resulting from imposing energy conserving equilibria in entropic lattice Boltzmann models for isothermal flows. The advantages are documented through a series of numerical simulations, such as Taylor-Green vortices, cavity flow and flow past a sphere.

We present a general scheme to derive lattice differential operators from the discrete velocities and associated Maxwell-Boltzmann distributions used in lattice hydrodynamics. Such discretizations offer built-in isotropy and recursive techniques to increase the convergence order. This provides a simple and elegant procedure to derive isotropic and...

In this work, lattice Boltzmann method (LBM) is developed for efficient and accurate solution of multi-dimensional population balance equations (PBEs) used to model crystallization processes with growth and nucleation. Detailed derivation of LBM for multi-dimensional advection equation is presented, where the velocity is a function of space coordin...

We show that discrete schemes developed for lattice hydrodynamics provide an elegant and physically transparent way of deriving Laplacians with isotropic discretisation error. Isotropy is guaranteed whenever the Laplacian weights follow from the discrete Maxwell-Boltzmann equilibrium since these are, by construction, isotropic on the lattice. We al...

Lattice Boltzmann method (LBM) is developed for solution of one-dimensional population balance equations (PBEs) with simultaneous growth, nucleation, aggregation and breakage. Aggregation and breakage, which act as source terms in PBEs, are included as force terms in LBM formulation. The force terms representing aggregation and breakage are evaluat...

An alternate BGK type formulation of the Enskog equation has been recently proposed [1]. It was shown that the new model has a valid H-theorem and correct thermal conductivity. We propose Lattice Boltzmann (LB) formulation of this new Enskog-BGK model. The molecular nature of the model is verified in case of shear flow by comparing the predicted no...

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 i...

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 equ...

The exact solution to the hierarchy of nonlinear lattice Boltzmann kinetic equations, for the stationary planar Couette flow for any Knudsen number was pre-sented by S. Ansumali et al. [Phys. Rev. Lett., 98 (2007), 124502]. In this paper, sim-ulation results at a non-vanishing value of the Knudsen number are compared with the closed-form solutions...

The production of ethanol for the energy market has traditionally been from corn and sugar cane biomass. The use of such biomass as energy feedstocks has recently been criticised as ill-fated due to competitive threat against food supplies. At the same time, ethanol production from cellulosic biomass is becoming increasingly popular. In this paper,...

Population balances equations (PBEs) have become an indispensable tool for scientists and engineers in a wide range of disciplines [1]. PBEs are hyperbolic partial differential equations used to model processes, such as crystallization, where the entities of interest are distributed along property coordinates. Many crystallization processes require...

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 wor...

A lattice Boltzmann method (LBM) is introduced for accurate simulation of crystallization processes modelled using one-dimensional population balance equations (PBEs) with growth and nucleation phenomena. LBM for PBEs with size independent growth is developed by identifying their similarity with the advection equation. To obtain an efficient method...

High-resolution (HR) finite-volume methods can provide an accurate numerical solution of population balance equations describing crystallization processes. To satisfy the stability requirements, the time step (Δt) for the available HR methods needs to be selected conservatively, rendering them computationally expensive for processes with size-depen...

Crystallization is widely used in chemical, pharmaceutical, food and semiconductor industries as a method of separation and purification. In industrial crystallization processes, the control of crystal shape and size is of key importance as these properties not only affect the product qualities, e.g. bioavailability, but also the efficacy of the do...

We introduce a novel scheme obtained by distorting energy level of the velocity shells, which give rise to additional degree of freedom for the same number of discrete velocities. We claim that the proposed model is the smallest known 3-dimensional system in terms of the number of velocities for the accuracy of full sixth-order moments. Velocity pr...

Recently, analytical solutions for the nonlinear Couette flow demonstrated the relevance of the lattice Boltzmann (LB) models to hydrodynamics beyond the continuum limit [S. Ansumali, Phys. Rev. Lett. 98, 124502 (2007)]. In this paper, we present a systematic study of the simplest LB kinetic equation-the nine-bit model in two dimensions--in order t...

I propose an extension to Boltzmann BGK equation for Hard Spheres. The present model has an $H$-theorem and it allows choice of Prandtl number as an independent parameter. I show that similar to Enskog equation this equation can reproduce dynamics of hard spheres in dense systems.

Recently, another approach to study incompressible fluid flow was suggested [S. Ansumali, I. Karlin, and H. Ottinger, Phys. Rev. Lett. 94, 080602 (2005)]-the kinetically reduced local Navier-Stokes (KRLNS) equations. We consider a simplified two-dimensional KRLNS system and compare it with Chorin's artificial compressibility method. A comparison of...

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 exa...

Concepts of the lattice Boltzmann method are discussed in detail for the one-dimensional kinetic model. Various techniques of constructing lattice Boltzmann models are discussed, and novel collision integrals are derived. Geometry of the kinetic space and the role of the thermodynamic projector is elucidated.

A general lattice Boltzmann method for simulation of fluids with tailored transport coefficients is presented. It is based on the recently introduced quasi-equilibrium kinetic models, and a general lattice Boltzmann implementation is developed. Lattice Boltzmann models for isothermal binary mixtures with a given Schmidt number, and for a weakly com...

The exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at nonvanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of moments with boundary conditions for populations enables us to derive closed-form solutions for all higher...

Exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at non-vanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of moments with boundary conditions for populations enables to derive closed-form solutions for all higher-order...

Is it possible to solve Boltzmann-type kinetic equations using only a small number of particles velocities? We introduce a novel techniques of solving kinetic equations with (arbitrarily) large number of particle velocities using only a lattice Boltzmann method on standard, low-symmetry lattices. The renormalized kinetic equation is validated with...

A general lattice Boltzmann method for simulation of fluids with tailored transport coefficients is presented. It is based on the recently introduced quasi-equilibrium kinetic models, and a general lattice Boltzmann implementation is developed. Lattice Boltzmann models for isothermal binary mixtures with a given Schmidt number, and for a weakly com...

Engineering applications of computational fluid dynamics typically require specification of the boundary conditions at the inlet and at the outlet. It is known that the accuracy and stability of simulations is greatly influenced by the boundary conditions even at moderate Reynolds numbers. In this paper, we derive a new outflow boundary condition f...

A lattice Boltzman model for the simulation of binary mixtures is presented. Contrary to previous models, the present formulation is able to simulate mixtures with different Schmidt numbers and arbitrary molecular mass ratio of the components. In the hydrodynamic limit, the Navier-Stokes and the Stefan-Maxwell binary diffusion equations are recover...

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-Stoke...

A new kinetic model for binary mixtures and its Lattice Boltzman (LB) discretiza- tion is presented. In the hydrodynamic limit the model recovers the Navier-Stokes and the Stefan-Maxwell binary diusion equations. The thermodynamic consistency is ensured by the dened non-negative entropy production within the domain of ap- plicability of the model....

A new thermal entropic lattice Boltzmann model on the standard two-dimensional nine-velocity lattice is introduced for simulation of weakly compressible flows. The new model covers a wider range of flows than the standard isothermal model on the same lattice, and is computationally efficient and stable.

This paper opens a series of papers aimed at finalizing the development of the lattice Boltzmann method for complex hydrodynamic systems. The lattice Boltz-mann method is introduced at the elementary level of the linear advection equation. Details are provided on lifting the target macroscopic equations to a kinetic equation, and, after that, to th...

Efficient, nonlinearly stable entropic lattice Boltzmann models for computational fluid dynamics are presented. A new method of fast evaluation of equilibria to machine precision is proposed. Analytical solution is found for the collision step which guarantees stability and thermodynamic consistency of the scheme. As an example, a novel 15-velocity...

One of the classical questions of non-equilibrium thermodynamics is the validity of various closure approximations in nontrivial flows. We study this question for a lid-driven cavity flow using a minimal molecular model derived from the Boltzmann equation. In this nontrivial flow, we quantify the model as a superset of the Grad moment approximation...