Hi Dear All,
I am new user to LBM community. I want to study different LBM models and especially do comparison between LBM models and Gas kinetic schemes. They both originated from kinetic schemes, but still need to verify some hidden features between these different approchaes.
My fisrt question as a bigginer to all LBM users is.
Can the single-relaxation-time and multi-relaxation-time LBM methods are two different methods, we have SRT model so why we need MRT models. Can any one gives some comments such as computational time, accuracy and stability are different for SRT and MRT models.
I want to know that MRT model take less or more computational time compared to SRT.
I hope i will find the detail answer from this forum.
Best Regards
Yuan Chao Mei
the MRT models offer more freedom in the choice of the relaxation parameters. Therefore it allows for example to integrate more physics in the model (you can add a bulk viscosity which is absent in the SRT case). You also have an enhanced stability by removing the “ghost modes” (see Dellar).
On the other hand you have to pay some computational power (the authors using the MRT schemes are saying that you lose 30% performance with the MRT compared to the SRT).
Anyway it is a difficult task to answer to the question “which model is the best”. In my opinion it will depend on lots of parameters like the physical problem that you are trying to solve, the boundary conditions you use, …
additionally to the advantage of more physics in your system, the MRT is more accurate when bounce-back boundary conditions are required. I have met Li-Shi Luo recently, who is a strict opponent of SRT. There have been interesting conference contributions, where many researchers claim that SRT cannot do the job, which MRT can do. However, it strongly depends on the kind of your problem.
As a rule of thumb, here is a list of advantages of MRT:
whenever you want to simulate compressible flows, MRT offers more possibilities (as Orestis has said)
incorporating bounce-back boundary conditions (e.g. porous media), MRT can be much more reliable
increasing the stability of the simulations in high Re simulations (i.e. high Ma and/or small viscosity) usually causes problems, but MRT has some stability advantages here
There is an issue with MRT, I have not fully understood. As far as I know one cannot include the Guo forcing term. Please correct me, if this information is not correct.
The expression proposed by Guo for a body force term is only valid for the SRT model. As Guo demonstrated in his work when only one relaxation time is considered in the collision operator the body force expression must be tau dependent. The following paper briefly explains how to incorporate body forces in MRT models:
P. Lallemand and L.-S. Luo, Theory of the lattice Boltzmann method: Acoustic and thermal properties in two and three dimensions, Phys. Rev. E 68(3):036706 (2003).
I have never studied in depth how to include body forces in MRT however, I believe that the correct expression for the body force should be equal to that of Guo but without the (1-1/(2*tau)) prefactor. Please, correct if I am wrong…
Regarding the SRT vs. MRT question I totally agree with the two previous answers. MRT really improves the SRT in some points (as previously pointed out) however most of the times those improvements are not really necessary for you so using SRT is just fine. It really depends on what problem you intend to study.
[quote=I have never studied in depth how to include body forces in MRT however, I believe that the correct expression for the body force should be equal to that of Guo but without the (1-1/(2*tau)) prefactor. Please, correct if I am wrong…][/quote]
It should depend on the parameters of MRT model, all omegas, somehow. Soon, I will do analysis for proper incorporation and let you know if you are interested.