Benchmarking and evaluating the accuracy of a lattice Boltzmann BGK scheme for multi-fluids 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.
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, ...
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.
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.
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.
Physical Review E, 2011
We conduct a comparative study to evaluate several lattice Boltzmann (LB) models for solving the near incompressible Navier-Stokes equations, including the lattice Boltzmann equation with the multiple-relaxationtime (MRT), the two-relaxation-time (TRT), the single-relaxation-time (SRT) collision models, and the entropic lattice Boltzmann equation (ELBE). The lid-driven square cavity flow in two dimensions is used as a benchmark test. Our results demonstrate that the ELBE does not improve the numerical stability of the SRT or the lattice Bhatnagar-Gross-Krook (LBGK) model. Our results also show that the MRT and TRT LB models are superior to the ELBE and LBGK models in terms of accuracy, stability, and computational efficiency and that the ELBE scheme is the most inferior among the LB models tested in this study, thus is unfit for carrying out numerical simulations in practice. Our study suggests that, to optimize the accuracy, stability, and efficiency in the MRT model, it requires at least three independently adjustable relaxation rates: one for the shear viscosity ν (or the Reynolds number Re), one for the bulk viscosity ζ , and one to satisfy the criterion imposed by the Dirichlet boundary conditions which are realized by the bounce-back-type boundary conditions. While the aforementioned LB models have existed for quite some time, there has never been a comprehensive comparative evaluation to quantitatively assess the efficacy of these LB models for solving problems in CFD. In this work, we intend to compare the LBGK, ELBE, MRT, and TRT models in terms of their accuracy, stability, and computational efficiency for solving the incompressible Navier-Stokes equations in two dimensions (2D). We use the lid-driven square cavity flow in 2D as a benchmark test.
Multi-Relaxation Time Lattice Boltzmann Simulation for Incompressible Fluid Flow
In this paper, multi-relaxation time of lattice Boltzmann method is used to compute the flow characteristics in the cavity located on a floor of horizontal channel. The results are compared with the conventional single-relaxation time lattice Boltzmann scheme and benchmark solution for such flow configuration. The multi-relaxation time lattice Boltzmann scheme demonstrated good agreement, which supports its validity in computing fluid flow problem.
Lattice Boltzmann method for fluid flows
Annual review of fluid mechanics, 1998
We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.
Viscous flow computations with the method of lattice Boltzmann equation
Progress in Aerospace Sciences, 2003
The method of lattice Boltzmann equation (LBE) is a kinetic-based approach for fluid flow computations. This method has been successfully applied to the multi-phase and multi-component flows. To extend the application of LBE to high Reynolds number incompressible flows, some critical issues need to be addressed, noticeably flexible spatial resolution, boundary treatments for curved solid wall, dispersion and mode of relaxation, and turbulence model. Recent developments in these aspects are highlighted in this paper. These efforts include the study of force evaluation methods, the development of multi-block methods which provide a means to satisfy different resolution requirement in the near wall region and the far field and reduce the memory requirement and computational time, the progress in constructing the second-order boundary condition for curved solid wall, and the analyses of the single-relaxation-time and multiple-relaxation-time models in LBE. These efforts have lead to successful applications of the LBE method to the simulation of incompressible laminar flows and demonstrated the potential of applying the LBE method to higher Reynolds flows. The progress in developing thermal and compressible LBE models and the applications of LBE method in multi-phase flows, multi-component flows, particulate suspensions, turbulent flow, and micro-flows are reviewed.
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