Sébastien Leclaire

Progress and investigation on lattice Boltzmann modeling of multiple immiscible fluids or components with variable density and viscosity ratios

Lattice Boltzmann models for simulating multiphase flows are relatively new, and much work remains to be done to demonstrate their ability to solve fundamental test cases before they are considered for engineering problems. From this perspective, a hydrodynamic lattice Boltzmann model for simulating immiscible multiphase flows with high density and high viscosity ratios, up to O(1000)O(1000) and O(100)O(100) respectively, is presented and validated against analytical solutions. The method is based on a two phase flow model with operators extended to handle N immiscible fluids. The current approach is O(N)O(N) in computational complexity for the number of different gradient approximations. This is a major improvement, considering the O(N2)O(N2) complexity found in most works. A sequence of systematic and essential tests have been conducted to establish milestones that need to be met by the proposed approach (as well as by other methods). First, the method is validated qualitatively by demonstrating its ability to address the spinodal decomposition of immiscible fluids. Second, the model is quantitatively verified for the case of multilayered planar interfaces. Third, the multiphase Laplace law is studied for the case of three fluids. Fourth, a quality index is developed for the three-phase Laplace–Young’s law, which concerns the position of the interfaces between the fluids resulting from the different surface tensions. The current model is compatible with the analytical solution, and is shown to be first order accurate in terms of this quality index. Finally, the multilayered Couette’s flow is studied. In this study, numerical results can recover the analytical solutions for all the selected test cases, as long as unit density ratios are considered. For high density and high viscosity ratios, the analytical solution is recovered for all tests, except that of the multilayered Couette’s flow. Numerical results and a discussion are presented for this unsuccessful test case. It is believed that other LB models may have the same problem in addressing the simulation of multiphase flows with variable density ratios.

Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media

This article presents a three-dimensional numerical framework for the simulation of fluid-fluid immiscible compounds in complex geometries, based on the multiple-relaxation-time lattice Boltzmann method to model the fluid dynamics and the color-gradient approach to model multicomponent flow interaction. New lattice weights for the lattices D3Q15, D3Q19, and D3Q27 that improve the Galilean invariance of the color-gradient model as well as for modeling the interfacial tension are derived and provided in the Appendix. The presented method proposes in particular an approach to model the interaction between the fluid compound and the solid, and to maintain a precise contact angle between the two-component interface and the wall. Contrarily to previous approaches proposed in the literature, this method yields accurate solutions even in complex geometries and does not suffer from numerical artifacts like nonphysical mass transfer along the solid wall, which is crucial for modeling imbibition-type problems. The article also proposes an approach to model inflow and outflow boundaries with the color-gradient method by generalizing the regularized boundary conditions. The numerical framework is first validated for three-dimensional (3D) stationary state (Jurins law) and time-dependent (Washburns law and capillary waves) problems. Then, the usefulness of the method for practical problems of pore-scale flow imbibition and drainage in porous media is demonstrated. Through the simulation of nonwetting displacement in two-dimensional random porous media networks, we show that the model properly reproduces three main invasion regimes (stable displacement, capillary fingering, and viscous fingering) as well as the saturating zone transition between these regimes. Finally, the ability to simulate immiscible two-component flow imbibition and drainage is validated, with excellent results, by numerical simulations in a Berea sandstone, a frequently used benchmark case used in this field, using a complex geometry that originates from a 3D scan of a porous sandstone. The methods presented in this article were implemented in the open-source PALABOS library, a general C++ matrix-based library well adapted for massive fluid flow parallel computation.

An implementation of the Spalart-Allmaras turbulence model in a multi-domain lattice Boltzmann method for solving turbulent airfoil flows

A methodology for solving turbulent airfoil flows based on the lattice Boltzmann method is proposed. It employs a multi-domain grid refinement approach, the cascaded collision operator, and a finite-difference implementation of the Spalart-Allmaras turbulence model. It is validated for the flow over a NACA0012 airfoil at a Reynolds number of 5×105, and over the low Reynolds S1223 and E387 airfoils, both at Re = 2 × 10 5 . The results for the NACA0012 airfoil, in terms of force coefficients, pressure coefficients, and velocity profiles, compare favorably with the numerical results of two other studies, both of which use the Spalart-Allmaras turbulence model. The results for the other two airfoils successfully capture the experimental lift and drag profiles reported in the literature. Overall, the proposed methodology is shown to be appropriate for solving turbulent airfoil flows, provided the grid is sufficiently refined near the walls.

Convolution Kernel for Fast CPU/GPU Computation of 2D/3D Isotropic Gradients on a Square/Cubic Lattice

Edge detection, which is widely performed in image analysis, is an operation that requires gradient calculation. Commonly used edge detection methods are Canny, Prewitt, Roberts and Sobel, which can be found in MATLAB’s platform. In this field, edge detection techniques rely on the application of convolution masks to provide a filter or kernel to calculate gradients in two perpendicular directions. A threshold is then applied to obtain an edge shape.

Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models

In this paper, a lattice Boltzmann color-gradient method is compared with a multi-component pseudo-potential lattice Boltzmann model for two test problems: a droplet deformation in a shear flow and a rising bubble subject to buoyancy forces. With the help of these two problems, the behavior of the two models is compared in situations of competing viscous, capillary and gravity forces. It is found that both models are able to generate relevant scientific results. However, while the color-gradient model is more complex than the pseudo-potential approach, numerical experiments show that it is also more powerful and suffers fewer limitations.

Forward and backward finite differences for isotropic gradients on a square lattice derived from a rectangular lattice formulation

In this research, forward and backward isotropic finite differences for the gradient operator are developed up to fourth order. Isotropic gradients are characterized by error terms which have small directional preference. Currently, only centred finite differences are available for isotropic discretization in the scientific literature; however, these finite differences are not suited for evaluation on domain boundaries or at multilevel lattice interfaces. We show that the order of accuracy with respect to the gradient direction with isotropic discretizations can be higher in some situations, and, at the same time, use neighbours that are closer to the evaluation point than with standard discretizations. The isotropic discretizations presented here were developed for a special rectangular lattice formulation, and general stencil weights are provided. When the rectangular lattice has a certain aspect ratio, forward and backward isotropic gradients can be obtained on a square lattice.