Parallelization of lattice Boltzmann method for incompressible flow computations

Abstract

Parallel computation of the two and threedimensional decaying homogeneous isotropic turbulence using the lattice Boltzmann method are presented. BGK type approximation for collision term in 9 velocity square lattice model is used. It is found that the lattice Boltzmann method is able to reproduce the dynamics of decaying turbulence and could be an alternative for solving the Navier-Stokes equations. The lattice Boltzmann method is parallelized by using domain decomposition and implemented on a distributed memory computer, Hitachi SR2201. It is found that vertical decomposition gives the highest speedup. In the case of horizontal decomposition the longer the number of lattice units in horizontal direction of each subdomain, the shorter the CPU time. Extension to three-dimension is carried out using 15 velocity cubic lattice model. Compared with the result of two-dimensional case, a higher speedup is obtained than in the three-dimensional simulation. Further investigation is needed on the accuracy and ef®ciency of cubic lattice BGK model. IntroductionComputational Fluid Dynamics (CFD) requires enormous CPU time and huge memory. Conventional single processor computer is very dif®cult to satisfy these demands. With the advent of reliable, high-performance massively parallel computers the range of CFD applications is dramatically increasing.There are two approaches in CFD. Conventional one is to solve the Navier-Stokes equations based on the continuum assumption. In the case of incompressible computations one has to solve the momentum equation together with the Poisson equation to satisfy divergence free condition. The second approach starts from the Boltzmann equation using the Lattice Gas Method. The Boltzmann equation can recover the Navier-Stokes equations by using the Chapman-Enskog expansion. The scheme is ideal for massively parallel computing because the updating of a node only involves its nearest neighbors.Boundary conditions are easy to implement. Therefore the code is simple and can be easily written in the form suitable for parallel processing.Among the lattice gas methods there exists the Lattice Gas Automata (LGA).LGA has fundamental dif®culty in simulating realistic¯uid¯ows obeying the Navier-Stokes equations. Beside its intrinsic noisy character which makes the computational accuracy dif®cult to achieve, it contains certain properties even in the¯uid limit. The lattice gas uid momentum equations cannot be reduced to the Navier-Stokes equations because of two fundamental problems. The ®rst is the non-Galilean invariance property due to the density dependence of the convection coef®cient. This limits the validity of the LGA method only a strict incompressible region. Second the pressure has an explicit and unphysical velocity dependence. To avoid some of these problems, several lattice Boltzmann (LB) models have been proposed. The main feature of the LB method is to replace the particle occupation variables n i (Boolean variables) by the single-particle distribution function (real variables) f i hn i i ...

Multiphase lattice Boltzmann simulations for porous media applications

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