Session R06: Computational Fluid Dynamics: LBM (5:00pm - 5:45pm CST)

Implementation of a generalised lattice Boltzmann method for external flow simulations

The lattice Boltzmann method is known for its computational efficiency and low numerical dissipation properties. Nonetheless, it is restricted to Cartesian grids, making this approach remarkably expensive for capturing boundary layers, and thereby impractical for external flow problems. A second-order finite difference numerical scheme is implemented to solve the discrete-velocity Boltzmann equation in generalised curvilinear coordinates to perform fluid flow simulations with non-uniform grids. Several test cases are used for verification, and the results have been compared with the available numerical and experimental literature with very favourable outcomes. Two-dimensional flows over a circular cylinder and NACA0012 aerofoil are specifically investigated to assess the accuracy and performance of the proposed approach. Additionally, the present method has been compared to our own standard Cartesian lattice Boltzmann solver with adaptive mesh refinement (AMROC-LBM) to demonstrate its advantages over the latter. The advantage of the present approach is capturing accurately large gradients in the wall vicinity with fewer mesh elements, which can lead to a dramatic reduction in computational effort over Cartesian lattice Boltzmann solvers.   

Study of a chain reaction in electrokinetic fluids with the Lattice Boltzmann Method

A 2D model is developed for a reactive electro-kinetic fluid in porous media based on the Lattice Boltzmann Method (LBM). The momentum, concentration and electric fields are simulated via the Navier-Stokes, advection-diffusion/Nernst-Planck and Poisson equations, respectively. With this model, the density, velocity, concentration and electric fields, and the interaction between the fields can be studied, which allows us to get an insight into the interplay between the chemistry, flow and geometry of the porous medium. In this work, two types of reactions are studied, namely, surface reactions and electric breakdown reactions. The results show that the conversion efficiency of both reactions can be strongly influenced by the flow and reaction parameters such as the fluid velocity, reactant concentration and the porosity of the porous media, which makes the reaction conversion efficiency display a non-trivial and non-monotonic behaviour as a function of the flow and reaction parameters. An analytical model of the chain reaction consisting of both reactions will be further studied. Using this model, one may be able to optimize the choice of the flow and reaction parameters in order to improve the performance of the reactions and achieve higher production rates.   

Cubature Rules for Off-Lattice Boltzmann Methods in Two and Three Dimensions

The discretization of the velocity space of on-lattice Boltzmann methods is primarily designed with focus on the regular lattice. However, the mostly used D2Q9, D3Q19, and D3Q27 low-degree cubature rules of the regular lattice Boltzmann method evoke errors in the stress tensor, which is one of the method's major drawbacks. We show that high-degree cubature rules cancel these errors, provided they integrate $e^{-\textbf{x}^2}$. Also we demonstrate that cubature rules significantly reduce the number of required abscissae in comparison to the obvious product rules of the one-dimensional Hermite quadrature. As an example, we were able to replace the degree-nine product rule D3Q125 by a D3Q45 velocity set. The properties of the introduced cubature rules are shown by using the semi-Lagrangian lattice Boltzmann method for test cases such as the two-dimensional shock-vortex interaction and the three-dimensional compressible Taylor-Green vortex.   

3-D Discrete Dynamical System Based on Volumetric Lattice Boltzmann Equation .

We develop a 3-D discrete dynamical system (DDS) using the volumetric lattice Boltzmann equation (VLBE). After providing a brief derivation of a ``poor man's VLBE'' (PMVLBE) for the DDS, we study time series, power spectra, and regime maps. Of specific interest is the ability of this DDS to produce expected physical fluid flow behaviors such as steady, periodic, and subharmonic patterns and, particularly, various turbulent phenomena including intermittencies. To derive the PMVLBE, we decomposed the VLBE into large-scale and subgrid-scale (SGS), and expanded the latter using Fourier series. A single mode from the Fourier representation of the SGS part is selected, and a forward Euler numerical integrator is used to discretize the resulting equation. In this study, the D3Q19 lattice model is used, from which 20 bifurcation parameters, all of which can be calculated from physical quantities (without models), are identified. This DDS will be employed to produce SGS information for use with the volumetric lattice Boltzmann method in the context of large-eddy simulation.   

Toward an Adaptive Mesh Refinement LBM for rough and porous media modelling

Flows over porous and rough media can be found in nature and in industrial devices. The combination of permeability and roughness effects leads to an outer flow that is significantly different than flows over impermeable flat or rough walls. However, the phenomena at play are still not fully understood. We employ the lattice Boltzmann method (LBM) with D3Q27 operator and adaptive mesh refinement (AMR) to enable accurate computation of turbulent structures generated by the porous medium. The aim of this paper is to assess the ability of LBM-AMR coupled with large eddy simulation (LES) to capture the flow in and over two porous media configurations. All calculations are made with our AMROC software. The first configuration consists of two layers made of spheres and is described in Stoesser (2006). The Reynolds number is 17,630. The second configuration is described in Kuwata (2016) and the porous media is made of several interlaced cubes layers. The Reynolds number is 2,900. Simulations realized with a Smagorinsky model accurately capture the flow outside of the porous media. However, some discrepancies, compared to the reference results, are still observed inside the media. More advanced LES models are introduced to improve the predictions of our LBM-AMR solver.   

Momentum fluctuations in coarse-grained fluid models

We investigate the equilibrium momentum fluctuations in the mesoscopic description of a two dimensional fluid. For a dilute Lennard-Jones gas, we measure momentum fluctuations using Molecular Dynamics simulations as well as the Molecular Dynamics Lattice Gas method. We compare these fluctuations to the corresponding ones obtained from the fluctuating lattice Boltzmann method. We find that the fluctuations are significantly different for different definitions of fluid momentum. We present the analytical expressions for the variances of the different fluctuations in the ideal gas limit.   

A Lattice Boltzmann Method for Electromagnetic Wave Scattering by Water Droplets

Understanding scattering of electromagnetic waves from water droplets in the sky is crucial for accurate estimation of rainfall. Scattering analysis and its signature depends on the shape, size and the distance of droplets as well as polarization of the wave. In this study, we solve Maxwell's equations of electromagnetism using the lattice Boltzmann method following the work of Hauser and Verhey (2017). Standard validations of electromagnetic waves by a dielectric interface and fluid mechanics problem have been performed. Scattered intensity is directly related to the droplets size and shape distribution. Therefore, this project is aimed at solving Maxwell’s equations of electromagnetism using the lattice Boltzmann method with the intention of accurately relating the shape and size distribution of the water droplets to calculate the scattered intensity. Error in the solutions was found to be minimal on comparing with analytical solutions. The applicability of the proposed numerical method towards analyzing scattering of electromagnetic waves by a three-dimensional scatterer, modelled on realistic water droplets, will be discussed.