Lattice Boltzmann Method Algorithm Research Articles

A quantum algorithm for the lattice-Boltzmann method advection-diffusion equation

We present a versatile and efficient quantum algorithm based on the Lattice Boltzmann method (LBM) approximate solution of the linear advection-diffusion equation (ADE). We emphasize that the LBM approximation modifies the diffusion term of the underlying exact ADE and leads to a modified equation (mADE). Due to its versatility in terms of operator splitting, the proposed quantum LBM algorithm for the mADE provides a building block for future quantum algorithms to solve the linearized Navier-Stokes equation on quantum computers. We split the algorithm into four operations: initialization, collision, streaming, and calculation of the macroscopic quantities. We propose general quantum building blocks for each operator, which adapt intrinsically from the general three-dimensional case to smaller dimensions and apply to arbitrary lattice-velocity sets. Based on (sub-linear) amplitude data encoding, we propose improved initialization and collision operations with reduced complexity and efficient sampling-based simulation. Quantum streaming algorithms are based on previous developments. The proposed quantum algorithm allows for the computation of successive time steps, requiring full state measurement and reinitialization after every time step. It is validated by comparison with a digital implementation and based on analytical solutions in one and two dimensions. Furthermore, we demonstrate the versatility of the quantum algorithm for two cases with non-uniform advection velocities in two and three dimensions. Various velocity sets are considered to further highlight the flexibility of the algorithm. We benchmark our optimized quantum algorithm against previous methods employed in sampling-based quantum simulators. We demonstrate sampling efficiency, with sampling accelerated convergence requiring fewer shots.

Investigation of the lattice Boltzmann method to resolve combined radiation-conduction heat transfer in participating media with curved boundaries

PurposePresent study aims to extend the lattice Boltzmann method (LBM) to simulate radiation in geometries with curved boundaries, as the first step to simulate radiation in complex porous media. In recent years, researchers have increasingly explored the use of porous media to improve the heat transfer processes. The lattice Boltzmann method (LBM) is one of the most effective techniques for simulating heat transfer in such media. However, the application of the LBM to study radiation in complex geometries that contain curved boundaries, as found in many porous media, has been limited.Design/methodology/approachThe numerical evaluation of the effect of the radiation-conduction parameter and extinction coefficient on temperature and incident radiation distributions demonstrates that the proposed LBM algorithm provides highly accurate results across all cases, compared to those found in the literature or those obtained using the finite volume method (FVM) with the discrete ordinates method (DOM) for radiative information.FindingsFor the case with a conduction-radiation parameter equal to 0.01, the maximum relative error is 1.9% in predicting temperature along vertical central line. The accuracy improves with an increase in the conduction-radiation parameter. Furthermore, the comparison between computational performances of two approaches reveals that the LBM-LBM approach performs significantly faster than the FVM-DOM solver.Originality/valueThe difficulty of radiative modeling in combined problems involving irregular boundaries has led to alternative approaches that generally increase the computational expense to obtain necessary radiative details. To address the limitations of existing methods, this study presents a new approach involving a coupled lattice Boltzmann and first-order blocked-off technique to efficiently model conductive-radiative heat transfer in complex geometries with participating media. This algorithm has been developed using the parallel lattice Boltzmann solver.

Solving 2D damped Kuramoto-Sivashinsky with multiple relaxation time lattice Boltzmann method

Lattice Boltzmann method (LBM) is a powerful fluid flow solver. Using this method to solve other PDEs might be a difficult task. The first challenge is to find a suitable local equilibrium distribution function (EDF) capable of recovering the desired PDE. The next difficulty arises from the explicit nature of LBM. The conditional stability of the LBM algorithm affects the numerical solution accuracy. Damped Kuramoto–Sivashinsky (DKS) equation is a fourth–order PDE that recently challenged many numerical methods' abilities. This equation is highly sensitive to a parameter that causes three states of solutions in a small interval of freedom. In this paper, we challenged LBM to solve the two–dimensional DKS equation by finding EDF using the Chapman–Enskog analysis up to the fourth–order. Also, the von Neumann analysis and a simple genetic algorithm are applied to find reliable values for the free parameters. Furthermore, a modification on image-based ghost node method is proposed for implementation of the boundary conditions in the complex geometries.

Memory-efficient Lattice Boltzmann Method for low Reynolds number flows

The Lattice Boltzmann Method algorithm is simplified by assuming constant numerical viscosity (the relaxation time is fixed at τ=1). This leads to the removal of the distribution function from the computer memory. To test the solver the Poiseuille and Driven Cavity flows are simulated and analyzed. The error of the solution decreases with the grid size L as L−2. Compared to the standard algorithm, the presented formulation is simpler and shorter in implementation. It is less error-prone and needs significantly less working memory in low Reynolds number flows. Our tests showed that the algorithm is less efficient in multiphase flows. To overcome this problem, further extension and the moments-only formulation was derived, inspired by the Multi-Relaxation Time (MRT) approach for single component multiphase flows.

Mechanistic Study of Fines Migration in Porous Media Using Lattice Boltzmann Method Coupled With Rigid Body Physics Engine

AbstractThis paper presents a pore-scale model proposed for numerical simulation of fines migration in porous media. The model simulates the behavior of spherical particles with different radii in flow by coupling lattice Boltzmann method (LBM) as a computational fluid dynamics (CFD) solver for the simulation of the fluid flow with a rigid body physics engine responsible for the simulation of the particulate transports. To achieve this, the basic LBM algorithm was extended to treat the curved particle boundaries, and a fluid-particle force interaction was implemented in order to account for the exerted force acting on the particles by the fluid and subsequent particulate movements. The accuracy and reliability of the proposed numerical model were successfully validated by simulating Poiseuille flow and Stokes flow and comparing the simulation results with those of the analytical solution. Thereafter, it was employed to simulate the migration of fine particles through synthetic 2D porous media. The simulation results were also presented to investigate the influence of fines migration on the porosity and permeability of the medium, and more interestingly on the hydraulic tortuosity as a criterion for changes in preferential flow path. As will be shown, the developed numerical method is able to successfully capture major retention mechanisms responsible for fines migration associated formation damage including external cake formation by the large particles, internal cake formation by the small particles, pore plugging, and surface deposition. This work provides a framework for further investigations regarding pore-scale phenomena associated with fines migration in the porous media.

High‐performance SIMD implementation of the lattice‐Boltzmann method on the Xeon Phi processor

SummaryWe present a high‐performance implementation of the lattice‐Boltzmann method (LBM) on the Knights Landing generation of Xeon Phi. The Knights Landing architecture includes 16GB of high‐speed memory (MCDRAM) with a reported bandwidth of over 400 GB/s, and a subset of the AVX‐512 single instruction multiple data (SIMD) instruction set. We explain five critical implementation aspects for high performance on this architecture: (1) the choice of appropriate LBM algorithm, (2) suitable data layout, (3) vectorization of the computation, (4) data prefetching, and (5) running our LBM simulations exclusively from the MCDRAM. The effects of these implementation aspects on the computational performance are demonstrated with the lattice‐Boltzmann scheme involving the D3Q19 discrete velocity set and the TRT collision operator. In our benchmark simulations of fluid flow through porous media, using double‐precision floating‐point arithmetic, the observed performance exceeds 960 million fluid lattice site updates per second.

A distributed parallel multiple-relaxation-time lattice Boltzmann method on general-purpose graphics processing units for the rapid and scalable computation of absolute permeability from high-resolution 3D micro-CT images

Digital rock physics (DRP) is a rapidly evolving technology targeting fast turnaround times for repeatable core analysis and multi-physics simulation of rock properties. We develop and validate a rapid and scalable distributed-parallel single-phase pore-scale flow simulator for permeability estimation on real 3D pore-scale micro-CT images using a novel variant of the lattice Boltzmann method (LBM). The LBM code implementation is designed to take maximum advantage of distributed computing on multiple general-purpose graphics processing units (GPGPUs). We describe and extensively test the distributed parallel implementation of an innovative LBM algorithm for simulating flow in pore-scale media based on the multiple-relaxation-time (MRT) model that utilizes a precise treatment of body force. While the individual components of the resulting simulator can be separately found in various references, our novel contributions are (1) the integration of all of the mathematical and high-performance computing components together with a highly optimized code implementation and (2) the delivery of quantitative results with the simulator in terms of robustness, accuracy, and computational efficiency for a variety of flow geometries including various types of real rock images. We report on extensive validations of the simulator in terms of accuracy and provide near-ideal distributed parallel scalability results on large pore-scale image volumes that were largely computationally inaccessible prior to our implementation. We validate the accuracy of the MRT-LBM simulator on model geometries with analytical solutions. Permeability estimation results are then provided on large 3D binary microstructures including a sphere pack and rocks from various sandstone and carbonate formations. We quantify the scalability behavior of the distributed parallel implementation of MRT-LBM as a function of model type/size and the number of utilized GPGPUs for a panoply of permeability estimation problems.

Research on the calculation method of convection effects on three-dimensional dendritic growth based on LBM

By coupling the phase field model of dendrite growth with the Lattice Boltzmann method (LBM), a Phase field LBM model (PF-LBM) that can simulate 3D dendrite non-isothermal growing from the under-cooled melt of a pure substance in forced flow has been established. Taking high-purity succinonitrile (SCN) as an example, the effects of flow on 3D dendritic growth were studied. The calculation efficiency of LBM and SOLA algorithm was compared under the same condition. The results show that, with the PF-LBM model, the effects of forced flow on 3D dendrite growth morphology and the dendrite asymmetric growth can be quantitatively modeled in large scale, and the dendrite growth is consistent with the crystallization theory. The LBM algorithm overcomes the weakness of a large amount of calculation and slow computation speed that exists in the traditional algorithm, and it achieves a speedup of 11.7 when the calculation region size is 2003.

A novel Lattice Boltzmann method for the dynamics of rigid particles suspended in a viscoelastic medium

We suggest a novel numerical algorithm based on the lattice Boltzmann method (LBM) to investigate particulate systems in which solid particles are suspended in a viscoelastic medium. In this model, polymer solution is described by the viscoelastic fluid based on the advection-diffusion LBM model, and it is coupled with the smoothed profile method (SPM) which describes the motion of rigid particles. To validate the present algorithm, we test three benchmark problems (two-dimensional simulation); viscoelastic flow past a cylinder, a single particle migration in a viscoelastic Couette flow, and dynamics of two particles in a viscoelastic Couette flow. Simulation results are carefully analyzed, and they are compared with previous simulation results implemented by finite element method (FEM) and finite volume method (FVM). In all test results, hydrodynamic properties and the motion of the particles induced by viscoelasticity are correctly captured, and they qualitatively as well as quantitatively correspond to previous reports. We conclude that both viscoelasticity and multi-body hydrodynamic interactions can be well incorporated in this new LBM algorithm. The present study has its significance as a first report, which strictly solves the flow behavior of solid particles immersed in a viscoelastic medium on the LBM framework.

Numerical modeling of slippage and adsorption effects on gas transport in shale formations using the lattice Boltzmann method

Shale formations consist of numerous nanoscale pores within a range of 2 nm–50 nm; the shale gas flow within this size range under typical shale reservoir pressure and temperature will fall into the slip flow or the transitional flow regime 0.001 < Kn < 10. Besides nano-pores in shale, there exist a number of mesoscopic and macroscopic pores with size larger than 50 nm, and many micrometer fractures. Natural gas, mainly methane, flows through nanoscale pores, mesoscale, and macroscopic pores or fractures during the production period. Gas slippage described by the Klinkenberg effect reduces viscous drag near the pore walls and influences permeability. In shale, the majority of gas molecules are adsorbed in kerogen that is considered to be organic source rocks. Within nano-pores and meso-pores, Darcy's law cannot effectively describe this type of transport phenomena due to its continuum assumption. Alternatively, the kinetic-based lattice Boltzmann method (LBM) becomes a strong candidate for simulating an organic-rich shale reservoir that contains a large number of nano-pores. In this paper, we present a multiple-relaxation-time (generalized) LBM, which is considered to be one of the most efficient LBM models. For gas flow in a confined system, its molecular mean free path is corrected depending on the size of the confined system and the distance of the gas molecules from the pore walls. Gas slippage on pore walls is captured with a combined bounce-back specular reflection boundary condition. In addition, adsorbed gas in shale has a significant influence on gas transport in shale gas production. Here, we propose to incorporate inter-molecular and adsorptive forces into the generalized LBM algorithm to capture gas adsorptions in organic nano-pores. Therefore, this approach is able to simulate gas flow with adsorption effect. Many factors are believed to control the flow mechanisms in these types of pores, including the pore size distribution, the specific surface area, and the adsorptive feature of the pore walls. The simulation results agree well with the existing data for high Knudsen flows between 2D parallel plates. Accounting for the adsorption and slippage effects, flow phenomena are investigated by varying different controlling factors in both simple and complex structures. The permeability of methane is also determined for complex porous geometries.

Lattice-Boltzmann simulation of microscale CH4 flow in porous rock subject to force-induced deformation

Accurate knowledge of the influence of rock deformation on the permeability of fluid flow is of great significance to a variety of engineering applications, such as simultaneous extraction of coal and gas, oil/gas exploitation, CO 2 geological sequestration, and underground water conservation. Based on the CT representation of pore structures of sandstones, a LBM (Lattice Boltzmann Method) for simulating CH 4 flow in pore spaces at microscale levels and a parallel LBM algorithm for largesize porous models are developed in this paper. The properties of CH 4 flow in porous sandstones and the effects of pore structure are investigated using LBM. The simulation is validated by comparing the results with the measured data. In addition, we incorporate LBM and FEM to probe the deformation of microstructures due to applied triaxial forces and its influence on the properties of CH 4 flow. It is shown that the proposed method is capable of visually and quantitatively describing the characteristics of microstructure, spatial distribution of flow velocity of CH 4 , permeability, and the influences of deformation of pore spaces on these quantities as well. It is shown that there is a good consistency between LBM simulation and experimental measurement in terms of the permeability of sandstone with various porosities.

A combined Lattice-Boltzmann method for the simulation of two-phase flows in microchannel

A new Lattice-Boltzmann method (LBM) is developed for the simulation of two-phase microflows. In this method, the phase separation is realized using Latva-Kokko redistribution scheme while the interfacial tension stress is computed according to Shan & Chen's expression. Introducing a redistribution step after the particle collision in Shan & Chen's LBM improves the algorithm stability and enforces a constant interface thickness independent of the interfacial tension. As a result, it provides independent control of the interfacial tension with little sensitivity to the viscosity. The interface curvature is easier to obtain in comparison to usual continuum surface force (CSF) and the spurious currents can be kept as low as in the color-field method. This hybrid LBM algorithm is validated by simulating a droplet deformation between two shearing plates and its capabilities demonstrated by experiments in the case of bubble generation in a T-junction microchannel using air/ethanol as the working system.

A modular lattice boltzmann solver for GPU computing processors

During the past two decades, the lattice Boltzmann method (LBM) has been increasingly acknowledged as a valuable alternative to classical numerical techniques (e.g. finite elements, finite volumes, etc.) in fluid dynamics. A distinguishing feature of LBM is undoubtedly its highly parallelizable data structure. In this work we present a general parallel LBM framework for graphic processing units (GPUs) characterized by a high degree of modularity and memory efficiency, still preserving very good computational performance. After recalling the essential programming principles of the CUDA C language for GPUs, the details of the implementation will be provided. The data structure here presented takes into account the intrinsic properties of the Gauss-Hermite quadrature rules (on which the LBM is based) to guarantee a unique and flexible framework for two- and three-dimensional problems. In addition, a careful implementation of a memory efficient formulation of the LBM algorithm has allowed to limit the high memory consumption that typically affects this computational method. Numerical examples in two and three dimensions illustrate the reliability and the performance of the code.

The numerical solution of the transient heat conduction problem using the lattice Boltzmann method

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

CUDA based lattice Boltzmann method: Algorithm design and program optimization

Lattice Boltzmann method (LBM) has become a powerful tool in modeling and simulating fluid flows for its fully parallelism, easy implementation, and simple code, and thus, LBM is quite suitable for large-scale computation of fluid flows on graphic processing unit (GPU) due to these advantages. In this paper, we implement the LBM algorithm on GPU using CUDA, and simulate 2D cavity flow, 2D flow around a cylinder and 3D cavity flow. The role of memory access optimization and other optimization technologies in programming and the performance of programs are analyzed in detail. The results show that our algorithm gives satisfactory acceleration, and confirm that LBM is very compatible with GPU for large-scale parallel computation.

Lattice Boltzmann method for solving the bioheat equation

In this work, we develop the lattice Boltzmann method (LBM) as a potential solver for the bioheat problems. The accuracy of the present LBM algorithm is validated through comparison with the analytical solution and the finite element simulation. The results show that the LBM can give a precise prediction of the temperature distribution, and it is efficient to deal with the space- and time-dependent heat source, which are often encountered in the treatment planning of tumor hyperthermia.