Multi-Relaxation Time Lattice Boltzmann Simulation for Incompressible Fluid Flow (original) (raw)
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Journal of Physics: Conference Series
Lattice Boltzmann Method (LBM) is the novel method for simulating fluid dynamics. Nowadays, the application of LBM ranges from the incompressible flow, flow in the porous medium, until microflows. The common collision model of LBM is the BGK with a constant single relaxation time τ . However, BGK suffers from numerical instabilities. These instabilities could be eliminated by implementing LBM with multiple relaxation time. Both of those scheme have implemented for incompressible 2 dimensions lid-driven cavity. The stability analysis has done by finding the maximum Reynolds number and velocity for converged simulations. The accuracy analysis is done by comparing the velocity profile with the benchmark results from Ghia, et al and calculating the net velocity flux. The tests concluded that LBM with MRT are more stable than BGK, and have a similar accuracy. The maximum Reynolds number that converges for BGK is 3200 and 7500 for MRT respectively.
Lattice Boltzmann Method and its Applications to Fluid Flow Problems
The main objective of this paper is to demonstrate the validity of lattice Boltzmann method (LBM) for different flows and phase transition process. For the present simulation D2Q9 model has been used. The soundness of LBM has been checked by implementing it on test problems including Plane Poiseuille flow, Planar Couette flow and Lid Driven Cavity flow. The results of these simulations show the capability of present incom-pressible LBM model in handling both steady and unsteady flows. Blood flow simulation has been performed using Casson's Rheology model and lastly, phase transition process has been simulated using Shan and Chen model. The results obtained for blood flow and phase transition process are in excellent agreement with the analytical results and the results present in literature.
Application of lattice Boltzmann method for incompressible viscous flows
Applied Mathematical Modelling, 2013
Because of the presence of corner eddies that change in number and pattern the lid-driven cavity problem has been found suitable to study various aspects of the performance of solution algorithms for incompressible viscous flows. It retains all the difficult flow physics and is characterized by a large primary eddy at the centre and secondary eddies located near the cavity corners. In this work, lid-driven cavity flow is simulated by lattice Boltzmann method with single-relaxation-time and it is compared with those by lattice Boltzmann method with multi-relaxation-time and finite difference method. The effects of the Reynolds number on the size, centre position and number of vortices are studied in detail together with the flow pattern in the cavity. The close agreement of the results bears testimony to the validity of this relatively new approach. However lattice Boltzmann method with multi-relaxation-time model is seen to remove the difficulties faces by the lattice Boltzmann method with single-relaxation-time at higher Reynolds numbers.
A Generalized Lattice Boltzmann Method for Three-Dimensional Incompressible Fluid Flow Simulation
Journal of Applied Fluid Mechanics, 2009
In this work, a 19-bit Incompressible Generalized Lattice Boltzmann (IGLB) method has been proposed for threedimensional incompressible fluid flow simulation, for the first time. Equilibrium moments in moment space are derived from an incompressible BGKLB method. The incompressible Navier-Stokes equations can be recovered through the Chapman-Enskog multi-scale expansion without artificial compressible effects. To compare the performance of proposed model, several benchmark problems (such as a cubic lid-driven cavity flow, flow over a backward-facing step, and a double shear flow) are solved and the results are compared with those of both 19-bit Incompressible BGK Lattice Boltzmann (IBGKLB) method and existing CFD simulations. It is shown that the stability and accuracy of the 19-bit IGLB method is better than those of the 19-bit IBGKLB method; in fact with the IGLB model we can increase the Reynolds number by factor of 2.5 and still get stable results. The proposed 3-D IGLB method is successfully expanded and applied to simulation of the 3-D incompressible buoyancy driven flows. The results of the 3-D steady-state natural convection in an air-filled differentially heated cubic cavity obtained by the extended model comply well with the existing data in literature. In addition, natural convection from a discrete heat source which is mounted flush with the bottom wall of a horizontal enclosure is simulated. The obtained results indicate that the proposed method is very convenient for simulation of thermally driven flow problems.
Applied and Computational Mechanics, 2018
The aim of this study is to investigate the effect of boundary conditions on the accuracy and stability of the numerical solution of fluid flows in the context of single relaxation time Lattice Boltzmann method (SRT-LBM). The fluid flows are simulated using regularized, no-slip, Zou-He and bounce back boundary conditions for straight surfaces in a lid driven cavity and the two-dimensional flow in a channel. The solutions for all types of the boundary conditions show good agreement with numerical references and exact solutions. The cavity pressure contours at low relaxation time show drastic perturbations for Zou-He boundary condition, whereas, the perturbation is ignorable for regularized boundary condition. At High Reynolds number, severe velocity gradients are major reason for numerical instabilities. Therefore, regularized boundary condition, which considers the velocity gradient in its calculation, has better numerical stability comparing the Zou-He boundary condition. Overall, ...
Analysis of Lattice-Boltzmann methods for internal flows
Computers & Fluids, 2011
The applicability of several Lattice-Boltzmann methods to wall-bounded turbulent flows is investigated. The various methods consist of the standard Bhatnagar-Gross-Krook (BGK) method with 19 (BGK19) and 27 (BGK27) discrete velocities, the multiple-relaxation-time (MRT) model with 19 discrete velocities and the cascaded Lattice-Boltzmann method (CLB). Based on the findings of turbulent channel flow it can be concluded that stability considerations, predicting the superiority of the advanced moment based schemes like the CLB and MRT method not necessarily hold for wall-bounded turbulent flows. Moreover, in some flow problems the simple BGK method with 19 discrete velocities delivers reasonable and stable results, where the other methods yield unphysical solutions.
The Lattice Boltzmann Method used for fluid flow modeling in hydraulic components
Linköping electronic conference proceedings, 2017
The Lattice-Boltzmann Method for the approximate solution of the Navier-Stokes equations has become an interesting alternative to classical finite volume based discretization methods. Because the flow domain is not meshed in the classical sense but only voxelized and geometrically complex boundaries can be introduced in an easy form by bounce-back or off-Lattice boundary conditions, the method lends itself very well to simulations of channel flows inside hydraulic components. In this paper, a flow problem in a single acting cylinder attached to a 3/2 directional spool valve is used as a benchmark problem. The Lattice-Boltzmann simulation is used to generate a reference solution for the pressure step response of the blocked cylinder with superimposed wave propagation. From this reference data set, a non-parametric frequency domain input-output model is extracted and compared with results from classical lumped parameter modeling.
LATTICE BOLTZMANN SIMULATION OF NON-NEWTONIAN FLUID FLOW IN A LID DRIVEN CAVITY
Lattice Boltzmann Method (LBM) is used to simulate the lid driven cavity flow to explore the mechanism of non-Newtonian fluid flow. The power law model is used to represent the class of non-Newtonian fluids (shear-thinning and shear-thickening fluids) by considering a range of 0.8 to 1.6. Investigation is carried out to study the influence of power law index and Reynolds number on the variation of velocity profiles and streamlines plots. Velocity profiles and the streamline patterns for various values of power law index at Reynolds numbers ranging 100 to 3200 are presented. Half way bounce back boundary conditions are employed in the numerical method. The LBM code is validated against the results taken from the published sources for flow in lid driven cavity and the results show fine agreement with established theory and the rheological behavior of the fluids
Procedia Engineering, 2013
Three-dimensional square cavity flows are simulated using multi-relaxation lattice Boltzmann method and graphic processing units. It was found that transition takes place between 1700 < Re < 2000. Parallel computations are conducted on a single node multi graphic processing unit (GPU) system, consisting of three nVIDIA M2070 or GTX560 devices using OpenMP. Results show that the speedup performance is strongly dependent on problem size and the precision adopted. For single precision computation with 240 3 grid density, about 159 times speedup can be obtained, while for double precision computation, this is slightly degraded to 112. Both are achieved with three Tesla M2070.
Application of Lattice Boltzmann Model to Simulate Different Test Cases in Two Dimensional Enclosure
International Journal of Engineering Applied Sciences and Technology
ASTRACT-Lattice Boltzmann Method have been advantageous in simulating complex boundary conditions and solving for fluid flow parameters by streaming and collision processes.This paper includes the study of three different test cases in a confined domain using the method of the Lattice Boltzmann model. 1. An SRT (Single Relaxation Time) approach in the Lattice Boltzmann model is used to simulate Lid Driven Cavity flow for different Reynolds Number (100, 400 and 1000) with a moment-based boundary condition is used for more accurate results. 2. A Thermal Lattice BGK (Bhatnagar-Gross-Krook) Model is developed for the Rayleigh Benard convection for both test cases-Horizontal and Vertical Temperature difference, considered separately for a Boussinesq incompressible fluid with different Rayleigh number. 3.The phase change problem governed by the heat-conduction equation is studied using the enthalpy based Lattice Boltzmann Model to provide a better understanding of the heat transport phenomenon.An approximate velocity scale is chosen to ensure that the simulations are within the incompressible regime.The simulated results demonstrate excellent agreement with the existing benchmark solution implicates the viability of this method for complex fluid flow problems.