Navier-Stokes vs lattice Boltzmann: will it change the landscape of CFD?


Navier-Stokes vs Boltzmann (image source: Wikipedia

For most people,  CFD is about continuity and Navier-Stokes equationsBut this is not always true.

One of the alternatives for CFD simulation is the lattice Boltzmann equation (LBE), where the fluid is treated as fictitious mesoscopic particles (not molecules). If you need something to make you sleepy, please read the short (and concise, and free) book:  A Practical Introduction to the Lattice Boltzmann Method.

But for commercial CFD code, most are based on Navier-Stokes equations, and differ in the numerical method: finite volume, or finite element, or a hybrid of both. Finite difference based CFD is hard to find in commercial codes.

When Exa hit the market with the first commercial LBE based CFD code, PowerFlow, about 15 years ago, not so much buzz was created in CFD market. Actually, the first a few releases got not-so-good reviews, partially due to the marketing and sales issues (over-promising). Of course, apparently, in recent years,  they got a lot of improvements in both solver and marketing. They also got a few big customers in the automotive industry.  But it is still not considered as the mainstream CFD software among CFD practitioners. In the academic circle, there have been several free, LBE based CFD solvers circulating around.

Now, Exa will not feel lonely in the commercial CFD market. A similar LBE based CFD solver, XFlow,  from Next Limit, has come. It may create some turbulence in the CFD market because :

  • Not N-S equations based. This differs it from major or mainstream CFD codes.
  • Mesh-less  (mesh-free).
  • Marketed by MSC. This gives it a significant exposure. (Why didn’t MSC acquire it?)

There are some obvious advantages of LBE approach:

  •  Intrinsic linear scalability in parallel computing, because the collisions are calculated locally.
  • Geometric complexity is not a challenge. This includes the solid moving and domain deformation.
  • Efficient inter-phase interaction handling for multiphase flow because phase interaction is inherently included in the particle collisions.

Of course, there are some apparent disadvantages of LBE approach:

  • Computationally expensive.
  • Turbulence modelling.
  • Inherently unsteady (transient) simulations only.

As for accuracy, the claim of better accuracy of LBE approach is only theoretically, and probably, correct. In reality, N-S equations approach is still the most reliable one, due to its maturity.  Anyway, the accuracy depends on 1). The physical problem; 2). The numerical implementation; 3). Models/correlation used. LBE approach itself will not give you more accurate results. It is up to the software implementation, and the user(usage).

Therefore,  it is too early to say the lattice Boltzmann will change the landscape of CFD market. LBE approach still needs time to prove itself, needs more validation cases. Some big players will still adopt the wait-and-see strategy as in any other industry. But it is possible that some will be considering whether they will invest in this area.

About shengwei

Dr. Ma Shengwei has spent last 20 years in numerical simulation, including writing CFD solver and applying numerical simulation in solving various real-world problems, including pollutant dispersion, sediment transport, heat transfer, membrane separation, water and waster treatment, centrifugal pump, natural ventilation, and separation systems.

You may get his detailed info on his expertise from Linkedin .


  1. “It may create some turbulence in the CFD market…”

    Hilarious– there aren’t too many CFD jokes or puns out there… thanks for adding another! Already a fan of your writing. Keep up the good work.

    It’s interesting that few people have heard of EXA- even die hard CFD fans seem unaware of LB for the most part. I do think the implementation of LB in EXA’s product and XFlow have gotten rock solid since EXA first promoted LB. These will, indeed, be some exciting times in the CFD world!

    You are correct that LB is inherently transient and unsteady. That doesn’t mean it can’t be used for steady state problems, though. You just have to wait for the model to reach a “pseudo steady-state” condition. That sounds ironically similar to watching a residuals plot go to zero in a RANS code 🙂

    Having said that, there will certainly be many cases where a RANS code will outperform an LB code for steady state problems. On the other hand, how long does it take to clean up the geometry and create a valid mesh for that RANS code? I’m really looking forward to exploring that business case.

    My gut says that initial implementation for XFlow will be as supplement to traditional CFD for many customers. So, you’ll use it for models that have a lot of transient/unsteady action, crappy-hard-to-mesh geometry, free surface needs, etc. In other words, the things traditional CFD codes aren’t particularly good at.

    BTW: I work for MSC and am involved in the XFlow launch here in North America. Here’s a super fast video overview:


    • Hi Jeff,
      thank you very much for your input, and the detailed explanation. LB approach definitely has been overlooked in CFD market in last decade.

      Yes, the users now have one more distinctive option.

      Jumping to MSC’s bed is a wise action because XFlow need greater exposure. And MSC need a stunning CFD solution. Best wishes for the marriage.

    • Hi Jeff

      Where are you launching the X-flow in USA? I’m aware of that X-flow is a Madrid-based company, but no much about it.

      Thanks for the information

  2. This looks like a great approach for complex interaction and “moving mesh” problems and poor CAD, as Jeff suggested.

    I come from a background using the NS codes ANSYS and OpenFoam in Formula One and have always been interested in the LB formulation that Exa were using, but never had the opportunity to test and validate it.

    As more customers are relying on the automated geometry cleaning and automated meshing without even looking into the details, which has a profound impact on the results, then this solution may indeed offer a more accurate approach.

    An interesting area of development and I am sure that we will continue to see this grow in the future.

    Best of luck to the XFlow team.

    Scott Beeton

    • Hi Scott, thanks for sharing your experience. LBE based CFD is seldom taught in classroom, especially in Engineering departments. For CFD researchers from physics background, LBE actually is more “native” for them.

      Another overlooked application for LBE is multiphase flow problems. N-S approach relies on too many contradictory assumptions to get the inter-phase terms.

      Anyway, LBE still need time to prove and to improve. This need efforts from both academic and commercial spheres. But unfortunately, most established CFD vendors have not invested heavily on this, due to the uncertain ROI in short term.

      The partnership between MSC and XFlow will force other CFD vendors to re-consider their technology investment strategy in LBE, at least, they may start to sow some seeds.

  3. LBE technique has evolved for last two decades and ventured into all possible applications which could otherwise be handled using N-S. Further, ongoing research is to use LBE methodology for problems which are beyond N-S capability. The Boltzmann equation is valid over all range of Knudsen numbers. However, LBE has demonstrated its usefulness in the continuum and slip flow regimes due to discrete nature of the solution method. The LBE simulation tool now is well matured for the flow through porous media, non-Newtonian flows and even multiphase flows. Hence, I see a very good future for the method in this commercial CFD world.

  4. ClaudTelos says

    Unfortunately MSC will kill this software for the rest of us.
    I have seen it the last 25 years with FEA.
    This is a VERY sad day for the ones that were awaiting LB to be available.
    I guess we have to wait longer now.

  5. Chainsaw says

    Well, as pointed out by the main article, there’s not only Xflow out there. There’s also Exa Powerflow which has been produced and tested for quite a lot of years now…

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