Lattice Boltzmann Method For Flow Research Articles

Implementation of Multi-GPU Based Lattice Boltzmann Method for Flow Through Porous Media

AbstractThe lattice Boltzmann method (LBM) can gain a great amount of performance benefit by taking advantage of graphics processing unit (GPU) computing, and thus, the GPU, or multi-GPU based LBM can be considered as a promising and competent candidate in the study of large-scale fluid flows. However, the multi-GPU based lattice Boltzmann algorithm has not been studied extensively, especially for simulations of flow in complex geometries. In this paper, through coupling with the message passing interface (MPI) technique, we present an implementation of multi-GPU based LBM for fluid flow through porous media as well as some optimization strategies based on the data structure and layout, which can apparently reduce memory access and completely hide the communication time consumption. Then the performance of the algorithm is tested on a one-node cluster equipped with four Tesla C1060 GPU cards where up to 1732 MFLUPS is achieved for the Poiseuille flow and a nearly linear speedup with the number of GPUs is also observed.

Lattice Boltzmann Models for Flow and Transport in Saturated Karst

Flow and transport simulation in karst aquifers remains a significant challenge for the ground water modeling community. Darcy's law-based models cannot simulate the inertial flows characteristic of many karst aquifers. Eddies in these flows can strongly affect solute transport. The simple two-region conduit/matrix paradigm is inadequate for many purposes because it considers only a capacitance rather than a physical domain. Relatively new lattice Boltzmann methods (LBMs) are capable of solving inertial flows and associated solute transport in geometrically complex domains involving karst conduits and heterogeneous matrix rock. LBMs for flow and transport in heterogeneous porous media, which are needed to make the models applicable to large-scale problems, are still under development. Here we explore aspects of these future LBMs, present simple examples illustrating some of the processes that can be simulated, and compare the results with available analytical solutions. Simulations are contrived to mimic simple capacitance-based two-region models involving conduit (mobile) and matrix (immobile) regions and are compared against the analytical solution. There is a high correlation between LBM simulations and the analytical solution for two different mobile region fractions. In more realistic conduit/matrix simulation, the breakthrough curve showed classic features and the two-region model fit slightly better than the advection-dispersion equation (ADE). An LBM-based anisotropic dispersion solver is applied to simulate breakthrough curves from a heterogeneous porous medium, which fit the ADE solution. Finally, breakthrough from a karst-like system consisting of a conduit with inertial regime flow in a heterogeneous aquifer is compared with the advection-dispersion and two-region analytical solutions.

Lattice Boltzmann method for flows in porous and homogenous fluid domains coupled at the interface by stress jump

AbstractA numerical method was developed for flows involving an interface between a homogenous fluid and a porous medium. The numerical method is based on the lattice Boltzmann method for incompressible flow. A generalized model, which includes Brinkman term, Forcheimmer term and nonlinear convective term, was used to govern the flow in the porous medium region. At the interface, a shear stress jump that includes the inertial effect was imposed for the lattice Boltzmann equation, together with a continuity of normal stress. The present method was implemented on three cases each of which has a porous medium partially occupying the flow region: channel flow, plug flow and lid‐driven cavity flow. The present results agree well with the analytical and/or the finite‐volume solutions. Copyright © 2008 John Wiley & Sons, Ltd.

Unified lattice Boltzmann method for flow in multiscale porous media.

In this paper, we develop a unified lattice Boltzmann method for flow in multiscale porous media. This model not only can simulate flow in porous systems of various length scales but also can simulate flow in porous systems where multiple length scales coexist. Simulations of unidirectional steady flow through homogeneous and heterogeneous porous media both recover Darcy's law when the effects of inertial forces and Brinkman correction may be negligible. Direct use of this model on the usual computational nodes, with zero resistance on void spaces and infinite resistance on solid walls, gives results that agree well with analytical solutions. Simulations performed on a fractured porous system show that the method presented here gives very good overall permeability values for the whole fractured system. A series of simulations is performed on a simplified fractured system. The results indicate that, when the ratio of the permeability of the rock matrix to the fracture permeability calculated by the cubic law is less than 10(-4), the effects of the rock matrix flow are negligible, and the discrete-fracture models that ignore such flow are plausible. When the ratio is larger than 10(-4), the matrix flow has significant effects on the fractured system, and the assumption that the matrix is impermeable does not hold. Therefore, the use of the cubic law to calculate the fracture permeability may cause a significant error. It is also indicated that the larger the ratio of the width of the porous matrix to that of the fracture, the more significant is the error caused by using the cubic law.