Goncalo Silva

Universidade de Évora | uevora · Deparment of Mechatronics

This work presents a detailed theoretical analysis of the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM), formulated on central moment (CM) space, for the numerical modeling of the one-dimensional advection-diffusion equation (ADE) with a constant velocity and diffusion coefficient, based on the D1Q3 lattice. Other LBM collision oper...

This study aims to assess the influence of root canal preparation, irrigation needle design and its placement depth in the irrigation flow of confluent canals during syringe irrigation. A mandibular molar presenting two confluent canals in its mesial root was sequentially prepared and scanned by micro-computed tomography after mechanical preparatio...

The goal of this work is to advance the characteristics of existing lattice Boltzmann Dirichlet velocity boundary schemes in terms of the accuracy, locality, stability, and mass conservation for arbitrarily grid-inclined straight walls, curved surfaces, and narrow fluid gaps, for both creeping and inertial flow regimes. We reach this objective with...

This work presents a detailed numerical analysis of one-dimensional, time-dependent (linear) reaction–diffusion type equations modeled with the lattice Boltzmann method (LBM), using the two-relaxation-time (TRT) scheme, for the D1Q3 lattice. The interest behind this study is twofold. First, because it applies to the description of many engineering...

Aim: This study aimed to experimentally validate a computational fluid dynamics (CFD) model, using micro-particle image velocimetry (micro-PIV) measurements of the irrigation flow velocity field developed in confluent canals during irrigation with a side-vented needle. Methodology: A microchip with confluent canals, manufactured in polydimethyls...

Slip flows in ducts are important in numerous engineering applications, most notably in microchannel flows. Compared to the standard no‐slip Dirichlet condition, the case of slip formulates as a Robin‐type condition for the fluid tangential velocity. Such an increase in mathematical complexity is accompanied by a more challenging numerical transcri...

A physics‐based medical image segmentation method is developed. Specifically, the image greyscale intensity is used to infer the voxel partial volumes and subsequently formulate a porous medium analogy. The method involves first translating the medical image volumetric data into a three‐dimensional computational domain of a porous material. A veloc...

We introduce two new approaches, called A-LSOB and N-MR, for boundary and interface-conjugate conditions on flat or curved surface shapes in the advection-diffusion lattice Boltzmann method (LBM). The Local Second-Order, single-node A-LSOB enhances the existing Dirichlet and Neumann normal boundary treatments with respect to locality, accuracy, and...

The two-relaxation-times collision benefits the steady lattice Boltzmann method by yielding viscosity-independent numerical errors. We present in a new, intuitive way, how to incorporate popular force methods into the two-relaxation-times collision. We subsequently rewrite force methods into a generic equation to reveal commonalities and difference...

This work addresses the Dirichlet boundary condition for momentum in the lattice Boltzmann method (LBM), with focus on the steady-state Stokes flow modelling inside non-trivial shaped ducts. For this task, we revisit a local and highly accurate boundary scheme, called the local second-order boundary (LSOB) method. This work reformulates the LSOB wi...

This work concerns with the clean inclusion of the forcing term in the lattice Boltzmann method (LBM) for the modeling of non-uniform body forces in steady hydrodynamics. The study is conducted for the two-relaxation-time (TRT) scheme. Here, we consider a simple, but yet sufficiently generic, flow configuration driven by a spatially varying body fo...

Blood-side resistance to oxygen transport in extracorporeal membrane blood oxygenators (MBO) depends on fluid mechanics governing the laminar flow in very narrow channels, particularly the hemodynamics controlling the cell free layer (CFL) built-up at solid/blood interfaces. The CFL thickness constitutes a barrier to oxygen transport from the membr...

We comment on the truncation error analysis and numerical artifacts of the D3Q19 lattice Boltzmann model reported in Silva et al. [3]. We present corrections for specific spatial truncation error terms in the momentum conservation equations. By introducing an improved discrete equilibrium for the D3Q19 stencil, we show that the reported spurious cu...

The measurement of microfluidic flows is an essential instrument to understand the governing physical mechanisms at small scales. This fact has motivated the adaptation of well-established “macroscale” experimental technics to deal with the specificities of microfluidic flows; a prominent example is the micro particle image velocimetry (micro-PIV)t...

Gaseous flows inside microfluidic devices often fall in the slip-flow regime. According to this theoretical description, the Navier-Stokes model remains applicable in bulk, while at solid walls a slip velocity boundary model shall be considered. Physically, it is well established that, to properly account for the wall curvature, the wall slip veloc...

After reading this chapter, you will be familiar with how the “lattice units” usually used in simulations and articles can be related to physical units through unit conversion or through dimensionless numbers such as the Reynolds number. Additionally, you will be able to make good choices of simulation parameters and simulation resolution. As these...

After reading this chapter, you will be familiar with the basics of lattice Boltzmann boundary conditions. After also having read Chap. 3, you will be able to implement fluid flow problems with various types of grid-aligned boundaries, representing both no-slip and open surfaces. From the boundary condition theory explained in this chapter together...

After reading this chapter, you will understand the fundamentals of high-performance computing and how to write efficient code for lattice Boltzmann method simulations. You will know how to optimise sequential codes and develop parallel codes for multi-core CPUs, computing clusters, and graphics processing units. The code listings in this chapter a...

After reading this chapter, you will be able to add forces to lattice Boltzmann simulations while retaining their accuracy. You will know how a forcing scheme can be derived by including forces in the derivation of the lattice Boltzmann equation, though you will also know that there are a number of other forcing schemes available. You will understa...

After reading this chapter, you will be familiar with many in-depth aspects of the lattice Boltzmann method. You will have a detailed understanding of how the Chapman-Enskog analysis can be used to determine how the lattice Boltzmann equation and its variations behave on the macroscopic Navier-Stokes level. You will know a number of such variations...

After reading this chapter, you will understand how the lattice Boltzmann equation can be adapted from flow problems to advection-diffusion problems with only small changes. These problems include thermal flows, and you will know how to simulate these as two interlinked lattice Boltzmann simulations, one for the flow and one for the thermal advecti...

After reading this chapter, you will have a working understanding of the equations of fluid mechanics, which describe a fluid’s behaviour through its conservation of mass and momentum. You will understand the basics of the kinetic theory on which the lattice Boltzmann method is founded. Additionally, you will have learned about how different descri...

After reading this chapter, you will understand the fundamentals of sound propagation in a viscous fluid as they apply to lattice Boltzmann simulations, and you will know why sound waves in these simulations do not necessarily propagate according to the “speed of sound” lattice constant. You will have insight into why sound waves can appear spontan...

After reading this chapter, you will have a solid understanding of the general principles of multiple-relaxation-time (MRT) and two-relaxation-time (TRT) collision operators. You will know how to implement these and how to choose the various relaxation times in order to increase the stability, the accuracy, and the possibilities of lattice Boltzman...

After reading this chapter, you will have insight into a number of other fluid simulation methods and their advantages and disadvantages. These methods are divided into two categories. First, conventional numerical methods based on discretising the equations of fluid mechanics, such as finite difference, finite volume, and finite element methods. S...

After reading this chapter, you will be able to expand lattice Boltzmann simulations by including non-ideal fluids, using either the free-energy or the Shan-Chen pseudopotential method. This will allow you to simulate fluids consisting of multiple phases (e.g. liquid water and water vapour) and multiple components (e.g. oil and water). You will als...

After reading this chapter, you will have insight into a large number of more complex lattice Boltzmann boundary conditions, including advanced bounce-back methods, ghost methods, and immersed boundary methods. These boundary conditions will allow you to simulate things like curved boundaries, flows in media with sub-grid porosity, rigid but moveab...

After reading this chapter, you will know the basics of the lattice Boltzmann method, how it can be used to simulate fluids, and how to implement it in code. You will have insight into the derivation of the lattice Boltzmann equation, having seen how the continuous Boltzmann equation is discretised in velocity space through Hermite series expansion...

The first nonequilibrium effect experienced by gaseous flows in contact with solid surfaces is the slip-flow regime. While the classical hydrodynamic description holds valid in bulk, at boundaries the fluid-wall interactions must consider slip. In comparison to the standard no-slip Dirichlet condition, the case of slip formulates as a Robin-type co...

This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamen...

An analytical study is devised for the problem of bimodal porous flow across a periodic array of permeable cylindrical inclusions. Such a configuration is particularly relevant for porous media systems of dual granulometry, an idealization often taken, e.g. in the modelling of membranes and fibrous applications. The double-porosity system is govern...

This work demonstrates that in advection–diffusion Lattice Boltzmann schemes, the local mass-conserving boundary rules, such as bounce-back and local specular reflection, may modify the transport coefficients predicted by the Chapman–Enskog expansion when they enforce to zero not only the normal, but also the tangential boundary flux. In order to a...

Using as a benchmark the porous flow in a square array of solid or permeable cylindrical obstacles, we evaluate the numerical performance of the two-relaxation-time lattice Boltzmann method (TRT–LBM) and the linear finite element method (FEM). We analyze the bulk, boundary and interface properties of the Brinkman-based schemes in staircase discreti...

This work focuses on the numerical solution of the Stokes-Brinkman equation for a voxel-type porous-media grid, resolved by one to eight spacings per permeability contrast of 1 to 10 orders in magnitude. It is first analytically demonstrated that the lattice Boltzmann method (LBM) and the linear-finite-element method (FEM) both suffer from the visc...

The isothermal Navier–Stokes equations are determined by the leading three velocity moments of the lattice Boltzmann method (LBM). Necessary conditions establishing the hydrodynamic consistency of these moments are provided by multiscale asymptotic techniques, such as the second-order Chapman–Enskog expansion. However, for simulating incompressible...

When the lattice Boltzmann (LB) method is used to solve hydrodynamic problems containing a body force term varying in space and/or time, its modelling at the mesoscopic scale must be verified in terms of consistency in order to avoid the appearance of non-hydrodynamic error terms at the macroscopic scale. In the present work it is shown that the mo...

Capillary valves are used as pressure barriers to control flow sequencing in microfluidic devices. Influence of valves height on liquid flow pattern and critical pressure are studied through flow visualization and CFD predictions (Gambit® 2.2.30 and FLUENT® 6.2.16). Both hydrophilic and hydrophobic walls are studied. Results show that the surface t...

The precise characterization of microgeometries is a crucial task in the study of flow phenomena at these scales. Since the use of conventional optical microscopes is somehow limited in terms of accuracy, the present work studies the use of micro-PIV measurements to characterize a rather irregular microchannel cross-section. The micro-PIV is employ...

Microfluidics is a promising technology, although the governing physical mechanisms are still not quite understood due to the difficulties arising in measuring at such small scales. This work intends to bring some insight on the influence of surface phenomena in microscale flows by proposing a different method to quantify such influence. In this ne...

Microfluidics is a promising technology, although the governing physical mechanisms are still not quite understood due to the difficulties arising in measuring at such small scales. This work intends to bring some insight on the influence of surface phenomena in microscale flows by proposing a different method to quantify such influence. In this ne...