Hi Guys. How do you comment the computational efficiency of the Lattice Boltzmann method even though anyone work on the LB methods said the method has very good parallel efficiency. This topic is limited to the efficiency comparison for unsteady state problems. The relaxation time of the LB-BGK model cannot be adjusted within a wide range due to the numerical accuracy and stability. This means the physical time step cannot be increased greatly when the mesh structure is given. On the contrary, the traditional CFD method, such as FEM, can allow for adjusted physical time steps even for a non-linear problem. Sometimes, the physical time step of the FEM method is several order magnitude higher than that by the LB-BGK method. Though the LB-BGK method can take less computational time to run a numerical step, the numerical step is much lower than the traditional CFD method. For validation, I compared a parallel LB code with the COMSOL software, which shows a much worse efficieny of the LB-BGK model than the COMSOL software when solving a single-phase reactive flow through some squares in an open channel. How about the computational efficiency of the LB method for the other physical problems, such as two-phase flow, or flow in more complex structures. Can the relaxation time of MRT method be adjusted within a wider range for a greater physical time step but to guarantee the numerical stability and accuracy? Any other method to overcome the problem? Thanks a lot.
Typical achievements of LBM are: Data pre-processing and mesh generation in a time that accounts for a small fraction of the total simulation only. Parallel data analysis, post-processing and evaluation. Fully resolved multi-phase flow with small droplets and bubbles. Fully resolved flow through complex geometries and porous media. Complex, coupled flow with heat transfer and chemical reactions.
It is easy to couple it with embedded particle methods, for sediment transport or other phenomena.
It involves only a very limited amount of floating points operations per computational node. It is particularly well suited for computations on a parallel architecture, even with a slow interconnection network.
They are weakly compressible by nature than FEM and CFX, but has a significant wall clock time advantage. It is competitive for incompressible transient problems, but asymptotically slower for steady-state Stokes flow because the asymptotic algorithmic complexity of LBM is not optimal compared to the multigrid solvers in the FEM and CFX code. The influence of the finite Mach number in LBM simulations of incompressible flow is easily underestimated.
One has to differentiate carefully between modeling errors, especially for complex fluids, discretization errors and implementational issues, which in the case of unstructured grids can have substantial influence on computational efficiency. Conducting truly efficient simulations requires the development of adaptive methods based on error estimates.
Dear Arjun，
Thanks for your insight answers. I really appreciate them. I still have two questions. Hope to discuss with you. Firstly, you comment that one of the LB advantages is LB method can easily couple flow with heat transfer and chemical reactions. In my opinion, LBM also need introduce other distribution functions and their evolution equations, such as so-called DDF model, to recover the energy equation, since the multi-speed model had bad numerical stability，accuracy and difficult numerical implementation for a high temperature variation. If the reaction takes place on the surface, the species boundary conditions should be treated carefully, such as with Kang's scheme. This boundary scheme implementation is much tedious than the bound-back scheme for the no-slip boundary condition of fluid flow. The surface node and the corner node in the structured mesh should be separately discussed. Therefore, the numerical coupling flowchart of LBM appears to be 1) solve flow; 2) solve energy equation; 3) treat the boundary conditions; 4) move to the next time step and repeat step 1). For comparison, FD and FV can couple all the equations to solve the matrix and easily adjust the physical time step. The advantage of the FD and FV will be highlighted when the physical problem is highly non-linear. In overall, I donot agree with your opinion about the coupling advantage of LBM. Secondly, I am very curious about how to differentiate carefully between modeling errors, discretization errors and implementational issues. Did you mention the theory error analyses of LBM? The numerical error of LBM is quite complex and even affected by the relaxation time, except the time step and the mesh space. Would you please to provide some insight paper about this issue, especially for the complex flow. I really appreciate your discussion and help.
Have a good day!
Qianghui
Dear Emad,
Thank you for your kind reply. I agree with the first and second advantage of LB as you comments. However, I am curious about the third one, which shows the implementation of boundary conditions on complex boundaries is simple. Do you just limited the boundary scheme to the bound-back scheme for the no-slip boundary conditions of the imcompressible fluid flow. Do you think the Neumann and Robin boundary conditions of heat and mass transfer are much simpler to implemented with LBM over the traditional CFD methods, such FV and FD. Why? Hope your reply!
Best,
Qianghui
I hope the following papers may help you to have an insight about coupling advantage of LBM.
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