Advanced Automatic Code Generation for Multiple Relaxation-Time Lattice Boltzmann Methods

The scientific code generation package lbmpy supports the automated design and the efficient implementation of lattice Boltzmann methods (LBMs) through metaprogramming. It is based on a new, concise calculus for describing multiple relaxation-time LBMs, including techniques that enable the numerically advantageous subtraction of the constant background component from the populations. These techniques are generalized to a wide range of collision spaces and equilibrium distributions. The article contains an overview of lbmpy's front-end and its code generation pipeline, which implements the new LBM calculus by means of symbolic formula manipulation tools and object-oriented programming. The generated codes have only a minimal number of arithmetic operations. Their automatic derivation rests on two novel Chimera transforms that have been specifically developed for efficiently computing raw and central moments. Information contained in the symbolic representation of the methods is further exploited in a customized sequence of algebraic simplifications, further reducing computational cost. When combined, these algebraic transformations lead to concise and compact numerical kernels. Specifically, with these optimizations, the advanced central moment- and cumulant-based methods can be realized with only little additional cost as when compared with the simple BGK method. The effectiveness and flexibility of the new lbmpy code generation system is demonstrated in simulating Taylor-Green vortex decay and the automatic derivation of an LBM algorithm to solve the shallow water equations.Comment: 23 pages, 6 figure

Generalized equilibria for color-gradient lattice Boltzmann model based on higher-order Hermite polynomials: A simplified implementation with central moments

We propose generalized equilibria of a three-dimensional color-gradient lattice Boltzmann model for two-component two-phase flows using higher-order Hermite polynomials. Although the resulting equilibrium distribution function, which includes a sixth-order term on the velocity, is computationally cumbersome, its equilibrium central moments (CMs) are velocity-independent and have a simplified form. Numerical experiments show that our approach, as in Wen et al. [{Phys. Rev. E \textbf{100}, 023301 (2019)}] who consider terms up to third order, improves the Galilean invariance compared to that of the conventional approach. Dynamic problems can be solved with high accuracy at a density ratio of 10; however, the accuracy is still limited to a density ratio of 1000. For lower density ratios, the generalized equilibria benefit from the CM-based multiple-relaxation-time model, especially at very high Reynolds numbers, significantly improving the numerical stability.Comment: 22 pages, 8 figure

Analysis and comparison of boundary condition variants in the free-surface lattice Boltzmann method

The accuracy of the free-surface lattice Boltzmann method (FSLBM) depends significantly on the boundary condition employed at the free interface. Ideally, the chosen boundary condition balances the forces exerted by the liquid and gas pressure. Different variants of the same boundary condition are possible, depending on the number and choice of the particle distribution functions (PDFs) to which it is applied. This study analyzes and compares four variants, in which (i) the boundary condition is applied to all PDFs oriented in the opposite direction of the free interface's normal vector, including or (ii) excluding the central PDF. While these variants overwrite existing information, the boundary condition can also be applied (iii) to only missing PDFs without dropping available data or (iv) to only missing PDFs but at least three PDFs as suggested in the literature. It is shown that neither variant generally balances the forces exerted by the liquid and gas pressure at the free surface. The four variants' accuracy was compared in five different numerical experiments covering various applications. These include a standing gravity wave, a rectangular and cylindrical dam break, a rising Taylor bubble, and a droplet impacting a thin pool of liquid. Overall, variant (iii) was substantially more accurate than the other variants in the numerical experiments performed in this study

A three-dimensional non-orthogonal multiple-relaxation-time phase-field lattice Boltzmann model for multiphase flows at large density ratios and high Reynolds numbers

This study proposes a three-dimensional non-orthogonal multiple-relaxation-time (NMRT) phase-field multiphase lattice Boltzmann (PFLB) model within a recently established unified lattice Boltzmann model (ULBM) framework [Luo et al., Phil. Trans. R. Soc. A 379, 20200397, 2021]. The conservative Allen-Cahn equation and the incompressible Navier-Stokes (NS) equations are solved. In addition, a local gradient calculation scheme for the order parameter of the Allen-Cahn equation is constructed with the non-equilibrium part of the distribution function. A series of benchmark cases are conducted to validate the proposed model, including the two-phase Poiseuille flow, Rayleigh-Taylor instability, binary liquid/metal droplet collision, and a bubble rise in water. The present simulation results are in good agreement with existing simulation and experimental data. In the simulation of the co-current two-phase Poiseuille flow, the present model is proven to resolve the discontinuity at the phase interface and provide accurate results at extremely high density ratios (i.e., up to ). Finally, the proposed model is adopted to simulate two challenging cases: (1) water droplet splashing during its impacting on a thin liquid film and (2) liquid jet breakup. The simulation results demonstrate an excellent agreement with previous experimental results, both qualitatively and quantitatively. In these simulations, the Weber number and Reynolds number reach 105 and 6000, respectively, and the viscosity can be as low as , in the lattice unit

Velocity Gradients Along Particle Trajectories in Turbulence

The creation of large spatial gradients in velocity by turbulent flows has important implications for a number of micro-physical applications that are sensitive to the straining and rotating influences of the immediate fluid environment. Because velocity gradients tend to be dominated by contributions from the smallest scales of motion in turbulence, their statistics enjoy many similarities across a wide range of natural and man-made flows and the canonical case of isotropic turbulence provides a simple flow in which to explore this aspect of turbulence in detail. In this thesis, the dynamics and kinematics of turbulent velocity gradients experienced while following Lagrangian trajectories are explored using fully resolved simulations and new, accurate techniques for inexpensive, reduced order models are developed. In particular, the cumulative stretching of infinitesimal material volumes is quantified statistically using large-deviation theory and compared with the stretching of vorticity. Following this, the dynamics of the velocity gradient itself are modeled using a stochastic approach. While some important terms are represented exactly in the Lagrangian formulation of velocity gradient dynamics, closure approximations are constructed systematically by applying a Lagrangian deformation map to Gaussian field statistics. This model is then extended to arbitrarily high Reynolds numbers using a multiple time scale expansion which faithfully represents energy cascade dynamics and the broad range of timescales present in high Reynolds number flows. It is also demonstrated that this stochastic modeling approach provides an accurate, an inexpensive way to model velocity gradients in coarse-grained simulations of inhomogeneous flows where the small scales of turbulence are not resolved. Finally, the restricted Euler model for Lagrangian velocity gradients is extended to inertial particle trajectories. While the model inherits the restricted Euler finite time singularity, qualitative features of velocity gradients on inertial particle trajectories are correctly predicted. Results point to the possibility for future developments of higher-fidelity models for applications where particle density differs significantly from that of the surrounding fluid

Photocatalytic oxidation of organic pollutants under visible light irradiation: from N-doped tio2 photocatalysts to the design of a continuous fixed bed reactor

2013 - 2014As a consequence of the rapid growth of population in urban areas, water use and reuse has become a major concern, leading to an urgent imperative of developing effective and affordable technologies for the treatment of water and wastewater. Traditional methods for water treatment are usually based on physical and biological processes but, unfortunately, some organic pollutants, classified as bio-recalcitrant, are not biodegradable. In this way heterogeneous photocatalysis may become an effective water treatment technology to remove organic pollutants hardly oxidised by conventional techniques. Photocatalysis represents one of the main challenges in the field of treatment and decontamination of water and air, because it is able to work at ambient temperature and atmospheric pressure. Heterogeneous photocatalysis is a catalytic process that uses the energy associated to a light source to activate a catalyst with semiconducting properties. The most common used photocatalyst is titanium dioxide (TiO2), which is able to oxidize a wide range of toxic organic compounds to harmless compounds such as CO2 and H2O. However, the following major factors limit both photocatalytic efficiency and activity of TiO2: a) the band gap of anatase TiO2 is 3.2 eV, i.e. it absorbs light in the UV region, so that only a small portion (5%) of sunlight can be used for a photocatalytic process. This is a great limitation in its use as photocatalyst for the conversion of solar into chemical energy; b) as in all semiconductors, photogenerated electron-hole couples undergo fast recombination in competition with charge transfer to adsorbed species on the catalyst surface; c) the use of slurry reactors limits the industrial applications of photocatalysis, since the necessary separation of catalyst powders after liquid phase reactions is troublesome and expensive. In this context, during this PhD project different routes have been explored to go beyond these limitations: 1. With respect to the use of visible light irradiation, doping with anions belonging to the p-block was investigated in recent years to sensitize TiO2 towards visible light, either by introducing newly created mid-gap energy states, or by narrowing the band gap itself. However, the role of titania dopants such as N, C, B, S, P, I and F is still not completely understood. The insertion of dopants in the crystalline structure of TiO2 may induce light absorption in the visible region, but also increases the rate of the undesired recombination of photogenerated charge carriers. This effect becomes relatively lower if the crystallinity of the oxide structure is higher... [edited by Author]XIII n.s

Bibliography of Lewis Research Center technical publications announced in 1993

This compilation of abstracts describes and indexes the technical reporting that resulted from the scientific and engineering work performed and managed by the Lewis Research Center in 1993. All the publications were announced in the 1993 issues of STAR (Scientific and Technical Aerospace Reports) and/or IAA (International Aerospace Abstracts). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses