Jonas Latt

Lattice Boltzmann method with regularized pre-collision distribution functions

An extended numerical scheme for the simulation of fluid flows by means of a lattice Boltzmann (LB) method is introduced. It is conceptually related to the lattice BGK scheme, which it enhances by a regularization step. The result is a numerical scheme that is both more accurate and more stable in the hydrodynamic regime.

Advances in multi-domain lattice Boltzmann grid refinement

Grid refinement has been addressed by different authors in the lattice Boltzmann method community. The information communication and reconstruction on grid transitions is of crucial importance from the accuracy and numerical stability point of view. While a decimation is performed when going from the fine to the coarse grid, a reconstruction must performed to pass form the coarse to the fine grid. In this context, we introduce a decimation technique for the copy from the fine to the coarse grid based on a filtering operation. We show this operation to be extremely important, because a simple copy of the information is not sufficient to guarantee the stability of the numerical scheme at high Reynolds numbers. Then we demonstrate that to reconstruct the information, a local cubic interpolation scheme is mandatory in order to get a precision compatible with the order of accuracy of the lattice Boltzmann method. These two fundamental extra-steps are validated on two classical 2D benchmarks, the 2D circular cylinder and the 2D dipole-wall collision. The latter is especially challenging from the numerical point of view since we allow strong gradients to cross the refinement interfaces at a relatively high Reynolds number of 5000. A very good agreement is found between the single grid and the refined grid cases. The proposed grid refinement strategy has been implemented in the parallel open-source library Palabos.

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.

A BENCHMARK CASE FOR LATTICE BOLTZMANN: TURBULENT DIPOLE-WALL COLLISION

A numerical experiment is presented that is taken from the recent literature. It has been devised as a benchmark case to test the quality of boundary conditions in numerical solvers for computational fluid dynamics. In this experiment, a two-dimensional system of two counter-rotating vortexes is brought into collision with a no-slip wall and rebounds from it. In the present paper, the benchmark is run with a lattice-Boltzmann numerical solver. Astonishingly accurate results are obtained with a straightforward boundary condition known under the name of bounce-back. This sample problem is also used to discuss techniques for the setup of an initial condition in the lattice Boltzmann method.

REDUCING THE COMPRESSIBILITY OF A LATTICE BOLTZMANN FLUID USING A REPULSIVE FORCE

This paper investigates the possibility to reduce the compressibility of lattice Boltzmann fluid models by introducing a repulsive force between nearest neighbor lattice Boltzmann particles. This new interaction is based on the Shan–Chen model. The interest of this approach is that it implements the physical mechanism responsible for the incompressibility of real fluids and retains the natural interpretation of the fluid density and fluid momentum. The new state equation shows that the compressibility factor decreases as the repulsive interaction increases. However, numerical instabilities limit the value of the acceptable repulsion. We investigate several situations, such as the Poiseuille flow with pressure gradient, a static fluid subject to gravity and the Womersley flow to evaluate the benefits of our approach. Globally, the compressibility of lattice Boltzmann fluids can be reduced by a factor of 4.

A LATTICE BOLTZMANN SIMULATION OF THE RHONE RIVER

We present a very detailed numerical simulation of the Rhone river in the Geneva area, using a Lattice Boltzmann (LB) modeling approach. The simulations of water ways are important to better predict and control their behavior when subject to exceptional event or new management strategies. Here, we investigate the current computing limits of using a three-dimensional (3D), free surface model to simulate a high resolution flow over a long section of the river, on a massively parallel computer. We argue that in a near future, computers will be powerful enough to tackle such a simulation. We also compare our results with a two-dimensional (2D) shallow water model to determine in which range a 3D free surface approach provides better insights. Finally, we discuss the advantage of a multi-scale approach for this type of problems.

THE OPENLB PROJECT: AN OPEN SOURCE AND OBJECT ORIENTED IMPLEMENTATION OF LATTICE BOLTZMANN METHODS

The OpenLB project aims at setting up an open source implementation of lattice Boltzmann methods in an object oriented framework. The code, which is written in C++, is intended to be used both by application programmers and by developers who may add their own particular dynamics. It supports advanced data structures that take into account complex geometries and parallel program executions. The programming concepts rely strongly on dynamic genericity through the use of object oriented interfaces as well as static genericity by means of templates. This design allows a straightforward and intuitive implementation of lattice Boltzmann models with almost no loss of efficiency. The aim of this paper is to introduce the OpenLB project and to depict the underlying structure leading to a powerful development tool for lattice Boltzmann methods.

Turbulence Effects on Kinetic Equations

It is well known that fluid dynamics can be derived from a kinetic (Boltzmann equation) framework. Here we propose that the variance of a fluctuating kinetic relaxation time be linked to turbulent time scales. It is further proposed that this connection be explored by direct numerical simulation of turbulence.

Lattice Boltzmann Modeling of Injection Moulding Process

Polymer injection in moulds with complicated shapes is common in todays industrial problems. A challenge is to optimize the mould design which leads to the most homogeneous filling. Current commercial softwares are able to simulate the process only partially. This paper proposes a preliminary study of the capability of a two-fluid Lattice-Boltzmann model to provide a simple and flexible approach which can be easily parallelized, will include correct contact angles and simulate the effect of the positioning of air-holes.

Simulating Time Harmonic Flows With The Regularized L-Bgk Method

A recent improvement of the lattice BGK model, based on a regularization of the precollision distribution function, is applied to three dimensional Womersley flow. The accuracy and the stability of the model are essentially improved by using this regularization. A good agreement with analytical Womersley solution is presented, as well as an improvement of the accuracy over standard L-BGK. Numerical stability of the scheme for a range of Reynolds and Womersley numbers is also presented, demonstrating an enhancement of the stability range of L-BGK for this type of flows.