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current state of Lattice Boltzmann method?Dear experts in lattice Boltzmann method,
I am wondering if you can provide some insights to the latest state of lattice boltzmann method. Pros and Cons of LBM compared to traditional CFD solving N-S equations. Or, point to me papers in this area will be highly appreciated. I have seen some discussions on LBM (actually about XFlow) on this forum, but, it does not seem conclusive. Pei-Ying |

Lattice boltzmann methods are evolving.
LBM has few drawbacks major of them are: 1. Explicit procedure 2. Confined to cartesian type (box type) meshes. There are attempts to create unstructured grid versions and there attempts to create implicit versions. The multirelaxation IBM somehow reduce the time stepping limit of explicit methods but still a lot to be done. Future for them looks to be good and in some cases they can replace traditional CFD. I personally have lots of crazy ideas about IBM and in coming days will be trying them out slowly. But as it goes with research outcome is not guaranteed. But if they work out, they will remove all the major headaches that i listed above. BUT it is a big IF. |

Hi, Arjun,
Thanks for the reply! I am mainly interested in low Re flow, but, multi-components with surface tension. It looks like LBM will be the ideal method to use. I am really curious why LBM has not been taking off. Pei-Ying |

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1-It is not so popular as there are few people working/knowing LB than standard NS equation 2-This was mentioned above: 1. Explicit procedure 2. Confined to cartesian type (box type) meshes. as drawbacks by Arjun. However, the explicit and LOCAL property is a pro, as the populations f_i inside the collision term Q(fi) is computed at time t, and thus no need to mesure it outside, and thereby local property, which is good for parallelization. LBM is indeed confined to cartesian type "(box type) meshes", but again, it is another approach. In fact, the LBM is a probability-based fluid dynamics, which goes back to the math roots of PDE. There are several tricks/models to deal with off-cartesian nodes when it comes to boundaries. Again, the method has not taken off as people still use the same way of thinking as when dealing with NS-based CFD. Still you see LBM with finite different schemes, which goes against the main LB idea as seen/cite here: this paper: http://www.sciencedirect.com/science...78475412001966 (also you can downloaded/read on http://www.scribd.com/doc/132100792/...ion-approaches) As you can see, it is people and not the method who has the problem. LBM came "late" to the CFD world, and it takes times, actually it will take to people to die, so the new generation will hopefully take on this method. Good luck :) |

Copy that. The restriction to cartesian grids is not such a major drawback as one would expect from a finite volume perspective.
There are formulations for the wall boundary conditions that allow an arbitrary shape and position of the boundary regardless of the position of the collision center. In my opinion, this turns the con into a pro. Arbitrarily complex geometries can be meshed with minimum effort, the boundary formulation takes care of the rest. |

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the issue is not whether it could be applied to finite volume / finite difference types methods and thus break the shackles of cartesian type only, the issue is that when it is aplied in finite volume finite difference frame work, the constraits on time stepping are too limiting, limiting enough to make it useless for practical purposes. Having said it, professor Tsutahara did introduce negative viscosity approach that removes that limit on viscosity. But after having implemented that myself, i do not see much gain on time per time step as compared to finite volume approaches like starccm or fluent has. Having even said this much, I would still be working on finite volume lattice boltzmann and will see if it could be made useful for some difficult problems compared to starccm or fluent. So I do have hopes for it. |

The domain for the LBM is not steady-state simulations with a RANS turbulence model. The conventional computational methods are better suited for this kind of simulation and have been perfected over the last few decades.
The LBM has potential for direct turbulence simulation methods like LES and DNS aswell as computational aeroacoustics where a small time step size is required anyway. Another domain for the LBM are finite Knudsen number flows. The nonequilibrium effects can directly be incorporated in the computational method, which is not possible with any conventional CFD method. So I dont like this kind of argument "which method is better". The LBM has definite shortcomings for some applications but also has some advantages for other applications like the two mentioned above. |

Hi,
I recently played with Palabos (open source LBM). The requirements for RAM is significant. Although it should be quite efficient with parallel runs, but, it seemed take quite a longer time to run when compared with traditional NS solver. I compared Palabos against OpenFOAM. For industrial problems, I did not see Palabos has any advantage over OpenFOAM. Of course, I do not have enough knowledge in LBM. So, the conclusion I reached may not be a sound one. So, I am curious if there are any commercial companies rely on LBM for their designs. Pei-Ying |

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Before you get into that, I suggest you to take a step back and see the big picture. I suggest you not to drawn in measurements here and there. There is a FUNDAMENTAL thing that unites numerical and experimental works, which can be comparable in a comun domain: Dimensionless numbers!!Not sure if you refer to the work of Kataoka and Tsutahara contruction. In that paper, their lattice Boltzmann construction is based on FDS. I recall a later paper from some chinese people testing Kataoka and Tsutahara contruction with differents FDS and to be honest, each FDS gave different results. A nightmare as it tend to drawn in those schemes. Anyway, it is up to you. Just want to remind you that the main LB idea, which is cited in this paper: http://www.sciencedirect.com/science...78475412001966 (also you can downloaded/read on http://www.scribd.com/doc/132100792/...ion-approaches) Good luck :) |

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while a comparison between some of the two most popular LBM is found here http://www.scribd.com/doc/132100792/...ion-approaches Quote:
This is seen in table 1 on this paper: http://www.sciencedirect.com/science...78475412001966 So if the standard has to be reduced in 3D to be feasable, then high-order LBM have to be reduced even more, so the DNS based on the LBM is by far no cheap. Quote:
:) |

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Good luck and please, keep posting your experiences :) PS: There is a paper on http://pre.aps.org/abstract/PRE/v88/i1/e013314 where Palabos performance is tested with another code and an ideal approach. |

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Also I would not be surprised that someone got different results from different schemes given the fact that this is purely advection equation we are talking about it, I would not be surprised if other lbms also show dependence on them. My personal experience so far is that I got same results with UTOPIA and Second Order Upwind scheme but first order upwind simply killed the results. This was only tested for 1 two dimensional vortex shedding case. As I play more with it I would be able to understand how this is behaving and thus would be in better position to make proper conclusion. Also is it possible for you to point me to that paper where this dependency is shown, I could talk with Tsutahara-san (and he has been great help so far to me), so I would ask him what he thinks could be the issue. Also for me LBM is just another hobby so I do not see finding time for it in next two months, after that lets see how things develop. Needless to say I am interested in seeing if LBM could be used in general framework other than Cartesian meshes. |

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As far as the higher order methods for rarefied flows are concerned: Yes, they may be computationally expensive. But compared to the other methods for rarefied flows in complex geometries, they are cheap. In analogy: If you need DNS data of a turbulent flow, you would not run a RANS simulation just because it is computationally cheaper. |

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I suggest you to see table 1 in this paper: http://www.sciencedirect.com/science...78475412001966 (which is also found to be donwlodable on here http://www.scribd.com/doc/132100792/On-pressure-and-corner-boundary-conditions-with-two-lattice-Boltzmann-construction-approaches where comparison between some LB models and lattice sets. For instance, since turbulence is a 3D phenomena, the "ideal" lattice sets would be DdQ3^d with d=3, i.e. D3Q27 (based on the nomenclature found in that paper above). Note in table 1, in that aforementioend paper, that that lattice set gives the same matched moments for D2Q9 (H_(3)^9) as for D3Q27 (H_(3)^27). However, since D3Q27 is considered too computational expensive, the D2Q19 (H_(2-3)^19) or the D2Q15 (H_(2-3)^15) can be chosen as alternatives. These last four lattice sets LB models are reduced from the D3Q27. Note that these aforementioned four lattice set LB models have issues to match the energy flux term Q_(alpha, beta, beta). That is, they are worse than D3Q27. So the statement standard reduced means standard = low-order, as opposite to high-order, while the term reduced is already explained. I do NOT recall a singel simulation of a high-order LB model with a full (oppostite to reduced) lattice set, to determine how cheap it is compared to NS. That model would have at least, for 3D, D3Q125. That is a lot!! Let us wait the brave one who does it :) |

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I issue of the off-Cartesian nodes when dealing with boundaries and conservation laws was "resolved" in http://www.sciencedirect.com/science...78437105009696, which is cited as [9] on http://www.scribd.com/doc/132100792/...ion-approaches. I don't have the paper/link of the chinese people trying to test the "Kato-oka Tsutahara" construciton with different FDS, just recall it was published in a the journal of Chinese academy or similar some where in the 2000's decade. It is not a big deal, but I guess you can find those papers following the cited works of Kato-oka Tsutahara's paper. This is read in the above second linked-paper (page 33): "It should be pointed out that with the use of interpolations, the exact matching of the conservation laws is not guarantee and/or the locality is lost for many existing schemes [37,9]. Hence, the main LB idea is compromised with interpolations". Althought the first linked paper above solves the conservation laws issue, it destoyes the locality, unfortunately. If you use non-Cartesian, you might have issues with conservation laws missmatch and/or the lack of locality, which is against the main LB idea. Every method has its own philosophy, which is resumed on:http://www.scribd.com/doc/132100792/On-pressure-and-corner-boundary-conditions-with-two-lattice-Boltzmann-construction-approaches . Good luck :) |

Comparing a "full" (or at least higher order in terms of Kn) LBM with a conventional NS-solver is like comparing apples to squirrels.
In 3 dimensions, already a D3Q27 lattice is capable of simulating the Burnett-Equations. You would not compare a Burnett solver to a NS solver, complain that it is slower and use the NS solver for simulations of rarefied flows for this reason. |

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Do you have any paper claiming that the D3Q27 lattice is capable of simulating the Burnett-Equations? I'm sure you won't have it ;) Please, I strongly suggest you to read/study the paper downloable from http://www.scribd.com/doc/132100792/...ion-approaches The D3Q27 matches the same moments as the D2Q9, but on 3D, and still so, none of them can even reach the full N-S equations!! Again, please, read the above paper and see table 1 in that paper too. Low-order LB models are DdQ3^d in full lattice sets, and they are still NOT complete Galilean invariant, i.e., they do NOT match the full N-S equations. High-order LB can match the full N-S equation, with the potential to go beyond N-S equations, but the lattice set would have to be DdQq^d, where q>3, e.g. q=5,7,9,11, etc. I think you are confused about what it is the capability of the LBM for low-order (q=3) and high-order LBM (q>3). By the way: Do you know of any paper where Burnett equation is derived from the LB equation via moment method (and not via the Chapman-Enskog)?:) |

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