Lattice Boltzmann Method Implementation Research Articles

Numerical analysis of the axisymmetric lattice Boltzmann method for steady and oscillatory flows in periodic geometries

Compared to more typical computational fluid dynamics techniques, the lattice Boltzmann method (LBM) is relatively new and unexplored. In recent years, axisymmetric LBM formulations, which can simulate flow in rotationally symmetric 3D geometries, have been published. Here we verify a novel axisymmetric LBM implementation using numerical criteria. Hagen–Poiseuille and Womersley flow are considered within a straight tube where analytic solutions are available. With this, we establish sufficient accuracy of the approximated flow and study the effects of changing simulation parameters (e.g. Reynolds number, Womersley number) and spatial/temporal parameters (e.g. relaxation time, mesh nodes, time steps). Furthermore, steady and oscillatory flows within a periodically-varying, longitudinally asymmetric geometry are considered. Analytic solutions are not available in these cases; however, the validity of the axisymmetric LBM for curved boundaries is ensured through convergence, mesh independence and qualitative observations. Guaranteeing reasonable flow field determination for the aformentioned geometry is relevant to a larger problem where particulate suspension is pumped back and forth through a membrane of axisymmetric micropores. In these circumstances, experiments have induced directed particle transport even though there is no net flow of the carrier fluid. Hence, our work aims to improve current numerical simulations of these flow problems to better understand the factors that facilitate particle transport.

Reduced kinetic model of polyatomic gases

Kinetic models of polyatomic gas typically account for the internal degrees of freedom at the level of the two-particle distribution function. However, close to the hydrodynamic limit, the internal (rotational) degrees of freedom tend to be well represented just by rotational kinetic energy density. We account for the rotational energy by augmenting the ellipsoidal statistical Bhatnagar–Gross–Krook (ES–BGK) model, an extension of the BGK model, at the level of the single-particle distribution function with an advection–diffusion–relaxation equation for the rotational energy. This reduced model respects the$H$theorem and recovers the compressible hydrodynamics for polyatomic gases as its macroscopic limit. As required for a polyatomic gas model, this extension of the ES–BGK model not only has the correct specific heat ratio but also allows for three independent tunable transport coefficients: thermal conductivity, shear viscosity and bulk viscosity. We illustrate the effectiveness of the model via a lattice Boltzmann method implementation.

Phase Change Materials Energy Storage Enhancement Schemes and Implementing the Lattice Boltzmann Method for Simulations: A Review

Utilizing phase change materials (PCMs) is one of the most effective methods of storing thermal energy and is gaining popularity in renewable energy systems. In order to analyze PCM performance, various numerical methods have been deployed to study the transient behaviour during phase changes. PCMs’ low thermal conductivity prevents their use as pure PCMs in industrial applications. There are various efficient methods of enhancing PCM thermal conductivity, which are addressed in this article. On the other hand, the lattice Boltzmann method (LBM) is very inclusive in the numerical simulation of complex fluid flows, thermal transport, and chemical interactions because of its ability to simply represent various complex physical phenomena, suitability for parallel programming, and easy coding and implementation. Many numerical studies have been conducted on PCMs using the LBM. This study aims to review these studies and categorize them in a way so that one may thoroughly understand the LBM’s capabilities in the simulation of PCM-related investigations. First, PCM characteristics and applications are presented, then the LBM implementation in PCM problems is addressed. Afterward, the fabrication and types of PCMs are mentioned. Next, the improvement of thermal energy storage methods of PCMs is stated. Furthermore, governing equations are reviewed. Lastly, the opportunities and challenges of the LBM in PCMs are discussed.

Esoteric Pull and Esoteric Push: Two Simple In-Place Streaming Schemes for the Lattice Boltzmann Method on GPUs

I present two novel thread-safe in-place streaming schemes for the lattice Boltzmann method (LBM) on graphics processing units (GPUs), termed Esoteric Pull and Esoteric Push, that result in the LBM only requiring one copy of the density distribution functions (DDFs) instead of two, greatly reducing memory demand. These build upon the idea of the existing Esoteric Twist scheme, to stream half of the DDFs at the end of one stream-collide kernel and the remaining half at the beginning of the next, and offer the same beneficial properties over the AA-Pattern scheme—reduced memory bandwidth due to implicit bounce-back boundaries and the possibility of swapping pointers between even and odd time steps. However, the streaming directions are chosen in a way that allows the algorithm to be implemented in about one tenth the amount of code, as two simple loops, and is compatible with all velocity sets and suitable for automatic code-generation. The performance of the new streaming schemes is slightly increased over Esoteric Twist due to better memory coalescence. Benchmarks across a large variety of GPUs and CPUs show that for most dedicated GPUs, performance differs only insignificantly from the One-Step Pull scheme; however, for integrated GPUs and CPUs, performance is significantly improved. The two proposed algorithms greatly facilitate modifying existing code to in-place streaming, even with extensions already in place, such as demonstrated here for the Free Surface LBM implementation FluidX3D. Their simplicity, together with their ideal performance characteristics, may enable more widespread adoption of in-place streaming across LBM GPU codes.

A decoupled and stabilized lattice Boltzmann method for multiphase flow with large density ratio at high Reynolds and Weber numbers

A decoupled lattice Boltzmann method (LBM) with improved numerical stability is developed from the conventional multiple relaxation time (MRT) model by eliminating the second-order mutual effects of viscosity modes. The dependency between relaxation times and viscosity is decoupled to remove the O(u3) errors in the original model, and thus a stabilization strategy is proposed by adjusting relaxation times without changing the local viscosity under the mass and momentum conservations. This new model still stays in the conventional MRT framework and keeps the advantages of simplicity and efficiency of LBM implementation. The decoupled MRT is demonstrated to be valid for high-speed flow with Galilean invariance. Moreover, the pseudopotential model is employed in this paper to present the improvement of numerical stability in simulating the large-density-ratio multiphase flows at high Reynolds (Re) and Weber (We) numbers. Droplet collision is achieved at density ratio 1153, Re = 34474 and We = 28212. Droplet splashing is achieved at density ratio 6637, Re = 34474 (and 71928) and We = 30538 (and 259). Droplet impacting on dry wall is achieved at density ratio 5720, Re = 11462 (and 22982) and We = 13573 (and 166). All collision regimes are simulated by the decoupled MRT from low Re (We) to high Re (We).

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

In this paper, lattice Boltzmann simulation for unsteady shock wave/boundary layer interaction in a shock tube is presented. This kind of problem, which contains the typical characteristics of supersonic viscous flows with shock wave and boundary layer, has rarely been well validated in the lattice Boltzmann community. This leads to few application of lattice Boltzmann method in supersonic flows with boundary layer. Some problems related to numerical dissipation and stability are exposed when simulating shock wave/boundary layer interaction using the conventional compressible lattice Boltzmann approach. The implementations of lattice Boltzmann for this kind of flow are investigated. As a novel problem for the lattice Boltzmann method, three main issues need to be addressed carefully, i.e., lattice Boltzmann model, solving scheme, and boundary treatment. For the first issue, a double-distribution-function compressible lattice Boltzmann model, in which the lattice velocity is studied for the stability in the simulation, is employed since we have demonstrated its feasibility in supersonic viscous flow previously. For the solving scheme, various space discretization methods are tested to enhance numerical performance. Meanwhile, the boundary treatment for the ghost layer is studied. The simulation result by the improved lattice Boltzmann implementation agrees well with the results through Navier–Stokes equations and gas-kinetic scheme reported in previous literatures. This work probes the numerical implementations of lattice Boltzmann method for unsteady shock wave/boundary layer interaction, providing important theoretical support for lattice Boltzmann application in supersonic viscous flows with shock wave and boundary layer.

Modeling of Dynamic Rock–Fluid Interaction Using Coupled 3-D Discrete Element and Lattice Boltzmann Methods

Scour of rock is a challenging and interesting problem that combines rock mechanics and hydraulics of turbulent flow. On a practical level, rock erosion is a critical issue facing many of the world’s dams at which excessive scour of the dam foundation or spillway can compromise the stability of the dam resulting in significant remediation costs, if not direct personal property damage or even loss of life. This interaction between the blocky rock mass and water is analyzed by directly modeling the solid and fluid phases—the individual polyhedral blocks are modeled using the discrete element method (DEM) while water is modeled using the lattice Boltzmann method (LBM). The LBM mesh is entirely independent of the DEM discretization, making it possible to refine the LBM mesh such that transient and varied fluid pressures acting on the rock surfaces are directly modeled. This provides the capability to investigate the effect of water pressure inside the fractured rock mass, along potential sliding planes, and can be extended to rock falls and slides into standing bodies of water such as lakes and reservoirs. Results show that the coupled DEM–LBM implementation is able to accurately capture the interaction between polyhedral rock blocks and fluid by analytically solving for the solid volume fraction in the coupling computations using convex optimization and simplex integration; however, further performance improvements are necessary to simulate realistic, field-scale problems. Particularly, adaptive mesh refinement and multigrid methods implemented in a parallel computing environment will be essential for capturing the highly computationally intensive and multiscale nature of rock–fluid interaction.

Multi‐GPU solution to the lattice Boltzmann method: An application in multiscale digital rock simulation for shale formation

SummaryCharacterization of rock properties is vital in producing oil and gas from shale reservoirs in an economically viable fashion. The nano‐pore structure and ultralow permeability in shale reservoirs present challenges to the traditional experimental characterization methods. Digital rock physics for the estimation of rock properties, especially for shale reservoirs, has become a powerful tool that greatly complements to lab experiments by combining advance imaging techniques with numerical simulations. The lattice Boltzmann method (LBM) is a well‐applied numerical method to simulate the fluid flow in pore structures at multiple length scales. Usually, the LBM simulation is resource intense because of its computation complexity and is facing great numerical challenges in extremely large‐cale computation. In this paper, we propose a multi‐GPU parallel implementation of 3D LBM on a hybrid high‐performance computing cluster to perform large‐scale simulations in reconstructed digital rocks. The program provides multiscale solution, pore scale and representative elementary volume (REV) scale based on the resolution of digital rock images. Optimization strategies are applied on partitioning simulation domain, improving data communication efficiency and maximizing CUDA occupancy. When running on a cluster of 32 GPUs, the proposed parallel implementation achieves a speedup of 1074x comparing to the in‐house sequential program.

A new GPU implementation for lattice-Boltzmann simulations on sparse geometries

We describe a high-performance implementation of the lattice Boltzmann method (LBM) for sparse 3D geometries on graphic processors (GPU). The main contribution of this work is a data layout that allows minimising the number of redundant memory transactions during the propagation step of LBM. We show that, by using a uniform mesh of small three-dimensional tiles and a careful data placement, it is possible to utilise more than 70% of maximum theoretical GPU memory bandwidth for D3Q19 lattice and double precision numbers. The performance of our implementation is thoroughly examined and compared with other GPU implementations of LBM. The proposed method performs the best for sparse geometries with good spatial locality.

Simulation of thermal flows by lattice Boltzmann method on the CUDA computational platform

Originating from lattice gas automata theory, the lattice Boltzmann method (LBM) is an interesting alternative to the solving of Navier-Stokes equations. In contrast to isothermal simulations, for a while thermal flow simulations were challenging for LBM. Thermal flow simulations are important task in various fields of research. Despite a large amount of work and research the dynamics of thermally induced flows are still highly demanded. Motivation of this work is development of computational tool for simulation of the dynamics of thermal flows. To this purpose, we developed LES-LBM solver accelerated by the Graphics Processing Unit (GPU) on the CUDA computational platform, integrating LBM with Large Eddy Simulation (LES). Simplicity of coding is usually an appealing feature of the LBM. Conventional implementations of LBM suffer from high memory consumption and poor computational performance. The main advantage of the solvers based on GPU is their ability to perform significantly more floating point operations per unit time (FLOPS) than a Central Processing Unit (CPU) and a good scalability of explicit parallel algorithms. LES-LBM code was tested on the NVIDIA GeForce GTX 1050 ti and NVIDIA TESLA K80 GPUs.

Direct numerical simulation of turbulent pipe flow using the lattice Boltzmann method

In this paper, we present a first direct numerical simulation (DNS) of a turbulent pipe flow using the mesoscopic lattice Boltzmann method (LBM) on both a D3Q19 lattice grid and a D3Q27 lattice grid. DNS of turbulent pipe flows using LBM has never been reported previously, perhaps due to inaccuracy and numerical stability associated with the previous implementations of LBM in the presence of a curved solid surface. In fact, it was even speculated that the D3Q19 lattice might be inappropriate as a DNS tool for turbulent pipe flows. In this paper, we show, through careful implementation, accurate turbulent statistics can be obtained using both D3Q19 and D3Q27 lattice grids. In the simulation with D3Q19 lattice, a few problems related to the numerical stability of the simulation are exposed. Discussions and solutions for those problems are provided. The simulation with D3Q27 lattice, on the other hand, is found to be more stable than its D3Q19 counterpart. The resulting turbulent flow statistics at a friction Reynolds number of Reτ=180 are compared systematically with both published experimental and other DNS results based on solving the Navier–Stokes equations. The comparisons cover the mean-flow profile, the r.m.s. velocity and vorticity profiles, the mean and r.m.s. pressure profiles, the velocity skewness and flatness, and spatial correlations and energy spectra of velocity and vorticity. Overall, we conclude that both D3Q19 and D3Q27 simulations yield accurate turbulent flow statistics. The use of the D3Q27 lattice is shown to suppress the weak secondary flow pattern in the mean flow due to numerical artifacts.

FULL GPU Implementation of Lattice-Boltzmann Methods with Immersed Boundary Conditions for Fast Fluid Simulations

Lattice Boltzmann Method (LBM) has shown great potential in fluid simulations, but performance issues and difficulties to manage complex boundary conditions have hindered a wider application. The upcoming of Graphic Processing Units (GPU) Computing offered a possible solution for the performance issue, and methods like the Immersed Boundary (IB) algorithm proved to be a flexible solution to boundaries. Unfortunately, the implicit IB algorithm makes the LBM implementation in GPU a non-trivial task. This work presents a fully parallel GPU implementation of LBM in combination with IB. The fluid-boundary interaction is implemented via GPU kernels, using execution configurations and data structures specifically designed to accelerate each code execution. Simulations were validated against experimental and analytical data showing good agreement and improving the computational time. Substantial reductions of calculation rates were achieved, lowering down the required time to execute the same model in a CPU to about two magnitude orders.

Verification of two-dimensional LBM-DEM coupling approach and its application in modeling episodic sand production in borehole

The lattice Boltzmann method (LBM) is implemented in the Particle Flow Code (PFC) as a pore-scale CFD module and coupled with the particulate discrete element assemblage in PFC using an immersed boundary scheme. The implementation of LBM and LBM-PFC coupling is validated with the analytical solutions in a couple of hydrodynamics and fluid-particle interaction problems, i.e., the accuracy of LBM as a CFD solver is verified by solving channel flow driven by a pressure gradient for which the closed-form solution is also derived; the accuracy of LBM-PFC coupling is validated by solving flow across a cylinder, Taylor-Couette flow, Kármán vortex street, and fluid flow through a cylinder array. To demonstrate potential applications of this coupling code, a perforation cavity subjected to axial fluid flush is then tested, showing that the collapse and reconstruction of sand arch in the perforation cavity can be reproduced in this coupling system. The developed system is ready for exploring more complicated physical issues involved in sand production.

Thermal link-wise artificial compressibility method: GPU implementation and validation of a double-population model

The link-wise artificial compressibility method (LW-ACM) is a novel formulation of the artificial compressibility method for the incompressible Navier–Stokes equations showing strong analogies with the lattice Boltzmann method (LBM). The LW-ACM operates on regular Cartesian meshes and is therefore well-suited for massively parallel processors such as graphics processing units (GPUs). In this work, we describe the GPU implementation of a three-dimensional thermal flow solver based on a double-population LW-ACM model. Focusing on large scale simulations of the differentially heated cubic cavity, we compare the present method to hybrid approaches based on either multiple-relaxation-time LBM (MRT-LBM) or LW-ACM, where the energy equation is solved through finite differences on a compact stencil. Since thermal LW-ACM requires only the storing of fluid density and velocity in addition to temperature, both double-population thermal LW-ACM and hybrid thermal LW-ACM reduce the memory requirements by a factor of 4.4 compared to a D3Q19 hybrid thermal LBM implementation following a two-grid approach. Using a single graphics card featuring 6GiB11Instead of the widespread but ambiguous GB and KB notations, we use the notations of the International System of Quantities, namely 1GiB=230B, 1KiB=210B, and 1kB=103B. of memory, we were able to perform single-precision computations on meshes containing up to 5363 nodes, i.e. about 154 million nodes. We show that all three methods are comparable both in terms of accuracy and performance on recent GPUs. For Rayleigh numbers ranging from 104 to 106, the thermal fluxes as well as the flow features are in similar good agreement with reference values from the literature.

On the Use of a Many-core Processor for Computational Fluid Dynamics Simulations

Abstract The increased availability of modern embedded many-core architectures supporting floating- point operations in hardware makes them interesting targets in traditional high performance computing areas as well. In this paper, the Lattice Boltzmann Method (LBM) from the domain of Computational Fluid Dynamics (CFD) is evaluated on Adapteva's Epiphany many-core architecture. Although the LBM implementation shows very good scalability and high floating-point efficiency in the lattice computations, current Epiphany hardware does not provide adequate amounts of either local memory or external memory bandwidth to provide a good foundation for simulation of the large problems commonly encountered in real CFD applications.

High-performance implementations and large-scale validation of the link-wise artificial compressibility method

The link-wise artificial compressibility method (LW-ACM) is a recent formulation of the artificial compressibility method for solving the incompressible Navier–Stokes equations. Two implementations of the LW-ACM in three dimensions on CUDA enabled GPUs are described. The first one is a modified version of a state-of-the-art CUDA implementation of the lattice Boltzmann method (LBM), showing that an existing GPU LBM solver might easily be adapted to LW-ACM. The second one follows a novel approach, which leads to a performance increase of up to 1.8× compared to the LBM implementation considered here, while reducing the memory requirements by a factor of 5.25. Large-scale simulations of the lid-driven cubic cavity at Reynolds number Re=2000 were performed for both LW-ACM and LBM. Comparison of the simulation results against spectral elements reference data shows that LW-ACM performs almost as well as multiple-relaxation-time LBM in terms of accuracy.

GPU accelerated lattice Boltzmann simulation for rotational turbulence

In this work, we numerically study decaying isotropic turbulence in periodic cubes with frame rotation using the lattice Boltzmann method (LBM) and present the results of rotation effects on turbulence. The implementation of LBM is on a GPU (Graphic Processing Unit) platform using CUDA (Compute Unified Device Architecture). Through the accelerated GPU-LBM simulation, we look into various effects of frame rotation on turbulence. It has been observed that rotation slows down the decay of kinetic energy and enstrophy. Rotation also breaks isotropy and induces vortex tubes in the direction of frame rotation. Characteristics related to velocity and its derivatives have been studied with and without rotation. Without rotation, the kinetic energy and enstrophy decay follow −10/7 and −17/7 scaling respectively whereas in the presence of rotation with the relatively small Rossby number (large rotation intensity), the energy decay slows down to −5/21 scaling when the initial isotropic turbulence energy spectrum is scaled to k4. These scalings with and without rotation are in quantitative agreements with the predictions from Kolmogorov hypotheses respectively. The skewness and kurtosis are seen more fluctuating in rotational turbulence, which agrees with the results from NS-based computation. Using this accelerated and validated GPU-LBM computation tool, we are further studying the inverse energy transfer behavior with and without rotation aiming to quantify the effects of rotation on the inverse energy transfer to reveal underlying physics of a particular stage of the turbulence development. The results will be presented in near future.

Numerical simulation of the collision of two microdroplets with a pseudopotential multiple-relaxation-time lattice Boltzmann model

Collisions of two equally sized liquid microdroplets in gaseous phase are numerically studied by the lattice Boltzmann method (LBM). The multiphase formulation adopted is a pseudopotential model with improved treatment of the equation of state and force incorporation which is then coupled with the multiple-relaxation-time scheme. That allows a detailed investigation into microdroplet collisions characterized by high-density ratios as well as by relevant inertial effects. Simulations related to a wide range of flow parameters (e.g. Weber and Reynolds numbers) are reported, in order to embrace all the collisional regimes presented in previous experimental studies. From surface tension-driven coalescence (both inertial and viscous coalescence have been examined) to catastrophic break-up with the formation of children microdroplets, the simulations demonstrate that the LBM correctly reproduces the collision dynamics and the final outcomes in almost all the regimes. Different break-up mechanisms like end-pinching and capillary wave-induced break-up have been observed. Finally, the initial stages of the inertia-dominated head-on collision process have been studied, showing once more the effectiveness and reliability of this multiphase LBM implementation.

Scalable lattice Boltzmann solvers for CUDA GPU clusters

The lattice Boltzmann method (LBM) is an innovative and promising approach in computational fluid dynamics. From an algorithmic standpoint it reduces to a regular data parallel procedure and is therefore well-suited to high performance computations. Numerous works report efficient implementations of the LBM for the GPU, but very few mention multi-GPU versions and even fewer GPU cluster implementations. Yet, to be of practical interest, GPU LBM solvers need to be able to perform large scale simulations. In the present contribution, we describe an efficient LBM implementation for CUDA GPU clusters. Our solver consists of a set of MPI communication routines and a CUDA kernel specifically designed to handle three-dimensional partitioning of the computation domain. Performance measurement were carried out on a small cluster. We show that the results are satisfying, both in terms of data throughput and parallelisation efficiency.

Analysis of conduction–radiation heat transfer during phase change process of semitransparent materials using lattice Boltzmann method

This article deals with the analysis of solidification of a 2-D semitransparent material using the lattice Boltzmann method (LBM). Both conduction and radiation terms in governing energy equation were computed using the LBM. First, the LBM formulation regarding conduction component was validated and the results analyzed. Next, the results involving phase change or radiation term in the LBM were compared with the finite volume method (FVM). The results show good accuracy and less time consumption during LBM implementation. Finally, temperature distribution, the location of solid-liquid front, mushy zone thickness and the effects of heat transfer parameters were studied.