An interaction potential based lattice Boltzmann method with adaptive mesh refinement (AMR) for two-phase flow simulation

Brief history of the lattice Boltzmann method In recent years, the lattice Boltzmann method (LBM) (Chen and Doolen, 1998; Succi, 2001) has become a popular numerical scheme for simulating fluid flows and modeling physics in fluids. The lattice Boltzmann method is based on a simplified mesoscopic equation, i.e. the discrete Boltzmann equation. By starting from mesoscopic modeling, instead of doing numerical discretizations of macroscopic continuum equations, the LBM can easily incorporate underlying physics into numerical solutions. By developing a simplified version of the kinetic equation, one avoids solving complicated kinetic equations such as the full Boltzmann equation. The kinetic feature of the LBM provides additional advantages of mesoscopic modeling, such as easy implementation of boundary conditions and fully parallel algorithms. This is arguably the major reason why the LBM has been quite successful in simulating multiphase flows. Furthermore, because of the availability of very fast and massively parallel computers, there is a current trend to use codes that can exploit the intrinsic features of parallelism. The LBM fulfills these requirements in a straightforward manner. The lattice Boltzmann method was first proposed by McNamara and Zanetti in 1988 in an effort to reduce the statistical noise in lattice gas automaton (LGA) simulations (Rothman and Zaleski, 2004). The difference is that LBM uses real numbers to count particle population, while LGA only allows integers. The result has been phenomenal: the lattice Boltzmann model substantially reduced the statistic noise observed in LGA simulations.

The pseudopotential method has grown as a powerful tool for multiphase fluid flow simulations within the lattice Boltzmann method framework. We consider that due to its simplicity and computational efficiency, the pseudopotential method could be explored also inside the framework of more traditional Computational Fluid Dynamic methods such as Finite Difference, Finite Volume or Finite Element methods. Following this idea, in this work we start from the macroscopic equations resulting from the pseudopotential lattice Boltzmann method and discretize it by a simple Finite Difference scheme. This pseudopotential based finite difference method is then tested in different benchmark problems such as a planar interface, a smooth droplet oscillation, and a single droplet evaporation. Excellent results were obtained in all tests. One of the advantages of the proposed method is that mesh refinement is straightforward, and converged solutions can be used as a tool of validation for the lattice Boltzmann method. Results indicate that the pseudopotential method is suitable to be used with standard discretization methods such as Finite Difference and that in future works more robust discretizations can be used to further enhance the pseudopotential method application.

Surface tension plays a crucial role in governing interfacial dynamics during phase change phenomena spanning natural systems and industrial applications. The phase-field lattice Boltzmann (LB) method has emerged as a powerful approach for modeling phase change, particularly due to its inherent ability to capture interfacial tension effects in multiphase systems. However, there has been no three-dimensional phase-field LB method capable of simulating phase change initialed from a single-phase medium. In this study, we propose a phase-field-based LB method for modeling thermal phase change. A source term is derived to accurately describe phase change. A key distinguishing feature of our model is its capability to initiate phase change driven by the sensible heat of superheated or supercooled phases, thereby enabling the presence of superheated liquid and supercooled vapor. To validate the proposed model, we perform a series of benchmark tests using D3Q19 LB models with density ratios up to 1:1000. These include (i) a comparison between numerical results and analytical solutions of the one-dimensional Stefan problem and (ii) a quantitative evaluation of bubble departure diameter against the Fritz relation for bubble generation in a pure liquid phase under wall heating. The results demonstrate agreement with theoretical predictions, underscoring the accuracy and robustness of the proposed approach. This study extends the applicability of the LB method to scenarios requiring consideration of both surface tension and thermal phase change, offering a valuable tool for simulating complex multiphase systems.

Numerical simulations using the lattice Boltzmann (LB) method are presented for the two-dimensional channel flow with/without sudden expansion. Ninevelocity square lattice model is used. In order to improve computational efficiency of the LB method, nonuniform mesh is used, and residual averaging and mutigrid method are also incorporated into the LB method. By using these techniques, convergence to a steady state was considerably accelerated.

This study is aimed at developing a novel computational framework that seamlessly incorporates the feedback forcing model and adaptive mesh refinement mesh refinement (AMR) techniques in the immersed-boundary (IB) lattice Boltzmann method (LBM) approach, so that challenging problems, including the interactions between flowing fluids and moving objects, can be numerically investigated. Owing to the feedback forcing based IB model, the advantages, such as simple mechanics principle, explicit interpolations, and inherent satisfaction of no-slip boundary condition for solid surfaces are fully exhibited. Additionally, the "bubble' function is employed in the local mesh refinement process, so that the solution of second order accuracy at newly generated nodes can be obtained only by the spatial interpolation but no temporal interpolation. Focusing on both steady and unsteady flow around a single cylinder and bi-cylinders, a number of test cases performed in this study have demonstrated the usefulness and effectiveness of the present AMR IB-LBM approach.

Depth-averaged Lattice Boltzmann and Finite Element methods for single-phase flows in fractures with obstacles

Lattice Boltzmann Method (LBM) is a powerful numerical simulation method of the fluid flow. With its data parallel nature, it is a promising candidate for a parallel implementation on a GPU. The LBM, however, is heavily data intensive and memory bound. In particular, moving the data to the adjacent cells in the streaming computation phase incurs a lot of uncoalesced accesses on the GPU which affects the overall performance. Furthermore, the main computation kernels of the LBM use a large number of registers per thread which limits the thread parallelism available at the run time due to the fixed number of registers on the GPU. In this paper, we develop high performance parallelization of the LBM on a GPU by minimizing the overheads associated with the uncoalesced memory accesses while improving the cache locality using the tiling optimization with the data layout change. Furthermore, we aggressively reduce the register uses for the LBM kernels in order to increase the run-time thread parallelism. Experimental results on the Nvidia Tesla K20 GPU show that our approach delivers impressive throughput performance: 1210.63 Million Lattice Updates Per Second (MLUPS).

In this paper, we present a reliable micro‐to‐macroscale framework to model multiphase fluid flow through fractured porous media. This is based on utilizing the capabilities of the lattice Boltzmann method (LBM) within the phase‐field modeling (PFM) of fractures in multiphase porous media. In this, we propose new physically motivated phase‐field‐dependent relationships for the residual saturation, the intrinsic as well as relative permeabilities. In addition, an anisotropic, phase‐field‐dependent intrinsic permeability tensor for the fractured porous domains is formulated, which relies on the single‐ and multiphasic LBM flow simulations. Based on these results, new relationships for the variation of the macroscopic theory of porous media (TPM)–PFM model parameters in the transition zone are proposed. Whereby, a multiscale concept for the coupling between the multiphasic flow through the crack on one hand and the porous ambient, on the other hand, is achieved. The hybrid model is numerically applied on a real microgeometry of fractured porous media, extracted via X‐ray microcomputed tomography data of fractured Berea Sandstone. Moreover, the model is utilized for the calculation of the fluid leak‐off from the crack to the intact zones. Additionally, the effects of the depth of the transition zone and the orientation of the crack channels on the amount of leakage flow rates are studied. The outcomes of the numerical model proved the reliability of the multiscale model to simulate multiphasic fluid flow through fractured porous media.

Lattice Boltzmann simulation for unsteady shock wave/boundary layer interaction in a shock tube

Lattice Boltzmann method (LBM) has recently been receiving considerable attention as a possible alternative to conventional computational fluid dynamics (CFD) approaches in many areas related to complex fluid flows. It is of great promise for simulating flows in topologically complicated geometries, such as those encountered in porous media, and for simulations of multi-component and/or multiphase flow conjugated with heat and mass transfer. In these particular areas, there are few viable conventional CFD methods for using. The present chapter deals with LBM numerical investigation to heat and mass transfer in flows with multiple components and/or phases encountered in the rotating packed-bed or nucleate pool boiling. In the following section 2 the LB multi-component model is adapted for simulating the mixing process in a rotating packed-bed with a serial competitive reaction (A+B→R, B+R→S; A, B, R, and S denote different components.) occurred inside. The serial competitive reaction in the main filling area of a rotating packed-bed is simulated and the mass transfer with forced convection caused by a cylindrical filler (to mimic the packing material) is studied as well. The obtained results provide some guidance for further studying the forced mass-transfer in and for the design of the real rotating packed-bed in industries. In section 3, a hybrid LBM model is constructed. In combination with a lattice Boltzmann thermal model, the lattice Boltzmann multiphase model being capable of handling a large density ratio between phases is extended to describe the phenomenon of phase change with mass and heat transferring through the interface. Based on the Stefan boundary condition, the phase change is considered as change of the phase order parameter and is treated as a source term in the Cahn-Hilliard(C-H) equation. The evolution of the interfacial position is thereby tracked. With an improved Briant’s treatment to the partial wetting boundaries, this hybrid model is used to simulate the growth of a single vapour bubble on and its departure from a heated wall. Numerical results exhibit similar parametric dependence of the bubble departure diameter in comparison with the experimental correlation available in recent literatures. Furthermore, parametric studies on the growth, coalescence and departure of a pair of twin-bubbles on a heated wall are conducted as well.

The lattice Boltzmann method for isothermal micro-gaseous flow and its application in shale gas flow: A review

In the subsurface, fluids play a critical role by transporting dissolved minerals, colloids, and contaminants (sometimes over long distances); by mediating dissolution and precipitation processes; and by enabling chemical transformations in solution and at mineral surfaces. Although the complex geometries of fracture apertures, fracture networks, and pore spaces may make it difficult to accurately predict fluid flow in saturated (single‐phase) subsurface systems, well‐developed methods are available. The simulation of multiphase fluid flow in the subsurface is much more challenging because of the large density and/or viscosity ratios found in important applications (water/air in the vadose zone; water/oil, water/gas, gas/oil, and water/oil/gas in hydrocarbon reservoirs; water/air/nonaqueous phase liquids (nonaqueous phase liquids/dense nonaqueous phase liquids) in contaminated vadose zone systems; and gas/molten rock in volcanic systems, for example). In addition, the complex behavior of fluid‐fluid‐solid contact lines and their impact on dynamic contact angles must also be taken into account and coupled with the fluid flow. Here we review the methods that are currently being used to simulate pore‐scale multiphase fluid flow and reactive transport in fractured and porous media. After the introduction, the review begins with an overview of the fundamental physics of multiphase fluids flow followed by a more detailed discussion of the complex dynamic behavior of contact lines and contact angles, an important barrier to accurate pore‐scale modeling and simulation. The main part of the review focuses on five different approaches: pore network models, lattice gas and lattice Boltzmann methods, Monte Carlo methods, particle methods (molecular dynamics, dissipative particle dynamics, and smoothed particle hydrodynamics), and traditional grid‐based computational fluid dynamics coupled with interface tracking and a contact angle model. Finally, the review closes with a discussion of future trends and challenges.

This document contains a summary of the work performed under the LDRD project entitled 'Interface Physics in Microporous Media'. The presence of fluid-fluid interfaces, which can carry non-zero stresses, distinguishes multiphase flows from more readily understood single-phase flows. In this work the physics active at these interfaces has been examined via a combined experimental and computational approach. One of the major difficulties of examining true microporous systems of the type found in filters, membranes, geologic media, etc. is the geometric uncertainty. To help facilitate the examination of transport at the pore-scale without this complication, a significant effort has been made in the area of fabrication of both two-dimensional and three-dimensional micromodels. Using these micromodels, multiphase flow experiments have been performed for liquid-liquid and liquid-gas systems. Laser scanning confocal microscopy has been utilized to provide high resolution, three-dimensional reconstructions as well as time resolved, two-dimensional reconstructions. Computational work has focused on extending lattice Boltzmann (LB) and finite element methods for probing the interface physics at the pore scale. A new LB technique has been developed that provides over 100x speed up for steady flows in complex geometries. A new LB model has been developed that allows for arbitrary density ratios, which has been a significant obstacle in applying LB to air-water flows. A new reduced order model has been developed and implemented in finite element code for examining non-equilibrium wetting in microchannel systems. These advances will enhance Sandia's ability to quantitatively probe the rich interfacial physics present in microporous systems.

Challenges and opportunities in modelling of proton exchange membrane fuel cells (PEMFC)

Development and assessment of the interface lattice Boltzmann flux solvers for multiphase flows