LBM is described as a powerful tool in treating fluid flows.
We always hear about its advantages as a numerical method.
The question is what are the limitations of LBM when it comes to complex flows?
It isn't very straightforward to incorporate the non-sothermal flows, high Mach number flows in LBM settings.
The first complexity in fluid flow modeling will come to the picture when the free surface must be modeled. To solve this problem, one can use Thurey's approach. His method call LBM-VOF. Also, there are many other methods to solve the free surface problem. Still, I believe that Thurey's approach is more reliable and has relatively more minor complexity.
There are some other hurdles in the LBM, but all of them have their own solutions. For example, instability in high Reynolds number simulations. One of the best ways to overcome this problem is that the LBM implement in the MRT framework.
For a better understanding of LBM, I suggest the following book:
https://connect.kntu.ac.ir/civil-session/
Below are the list of limitations and scope of further developments in LBM for complex flows"
1. Spurious currents: Unwanted or ghost currents are generated near the interface of the two-phase system due to discretization error in the forcing scheme as well as non-galiliean invariance. Many works are done in order to reduce the spurious currents yet it is challenging in various applications. One way is to use sophisticated collision models e.g. MRT, CM-MRT, cumulative etc. while the other way is to develop appropriate discretization rules for the forcing schemes.
Please refer, Christophe Coreixas , Linlin Fei for CM-MRT and a well picture of why spurious currents and how a well-balanced LBM is done by modifying equilibrium states please refer Zhaoli Guo recently published article in Physics of Fluids. Moreover, an insight into the force disrectization errors can also be understood in this paper.
2. Coupling with physicochemical processes: Complex flows are not encapsulated in mutiphase flows. Thermal and Chemical processes are still need to be coupled for the near imitation of natural processes. E.g. in drying of porous media, we need to couple the fluid flow with a thermal diffusion-advection method to show the non-isothermal effects. However, the ooccurrencef spurious currents hinder the process. One may use another set of PDFs for thermal process or use straight forward temperature equation with entropy balance but in the end it is again a query of how good your model is in respect to noisy currents.
Please refer, Feifei Qin for proper understanding of entropic LBM, using multirange forcing scheme to suppress spurious currents and then coupling with thermal effects.
3. The enigma of porous media: Complex flows need a medium like porous media for example. The intricate geometry of a porous media of widest pore spaces to narrowest channel of meniscus invasion often comes with a hurdle. For example, the Haines jumps. Haines jumps occur when a near pore-space is suddenly invaded due to contact angle instability. However, the invasion is so rapid that accurate tracking of the meniscus as well as having a mesh independent lattice domain is a challenge. To know more about Haines jumps in drying please refer my works where we overcame the challenge of mesh dependence as well as showcase the effect of haines jumps to drying kinetics.
Below are the list of papers worh reading to understand more about LBM
Presentation Well-balanced lattice Boltzmann model for two-phase systems
Article Impact of collision models on the physical properties and th...
Article Study of non-isothermal liquid evaporation in synthetic micr...
Article Pore-scale physics of drying porous media revealed by Lattic...
Article Influence of thermal gradients on the invasion patterns duri...
Article Multiphysics flow simulations using D3Q19 lattice Boltzmann ...
This is an interesting section relating to the LBM that I also have a big consideration for now. Hoping some experts can share their great experiences for solving the interface between different fluid phases and fluid-air.
In my opinion, I consider that the high Pe number, in other words, the tau in ADE closes to 0.5, the stability is poor, the numerical error is large.
Overall, the limitations of using LBM depend on the model used.
Read the following article to better understand.
Article Dynamic behavior investigation of capillary rising at variou...
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