Hey there! I wonder if there is any Boundary Element Method CFD commercial code? (I don't mean panel methods). The answer should definitely be "no", however... Also, anyone there doing any work on BEM for viscous (steady-state and/or transient) fluid flows? My regards Mikhail

YOU CAN CONTACT DR. P.K. BANERJEE AT THE STATE UNIVERSITY OF NEW YORK AT BUFFALO, DEPARTMENT OF CIVIL ENGINEERING. HE HAS A COMMERCIAL BEM CODE CALLED GPBEST , WHICH CAN DEAL WITH CFD PROBLEMS. You can go to the civil engg web site there to find out more about Dr. banerjee. Incidentaly, he is the person who gave the name BEM. The URL is http://www.civil.buffalo.edu/ . ELSE YOU CAN ALSO CONTACT DR. GARY DARGUSH THERE TOO. HE HAS WORKED ON DEVELOPING THAT CODE. His email is gdargush@eng.buffalo.edu.

Hope it helps.

Anindya Sengupta (Texas Tech University)

Thank you for your response. I'm myself in Department of Civil Engineering at SUNY (Buffalo), working with Dr.Gary Dargush and doing BEM CFD, not commercial codes. As for GPBEST, it's a general BEM code for structural analysis, structural dynamics, acoustics, geomechanics, thermomechanics (see www.gpbest.com for more details), but not for fluid dynamics. You are right when saying that they worked on CFD, but were not able to extend it to the commercial level due to many reasons. The most important seems to be tremendeous difficulty to develop reasonably good BEM technique. It's a real struggle... Thanks, Mikhail

As you are already aware, it is a real struggle to develop a competitive BEM-based CFD tool.

The advantage of BEM over other methods, at least for solving the Laplace (and certain Poisson) equations is that there is no need to discretise the domain interior. In 3D, this means discretizing the surface of the body, which is necessary anyway to define the geometry. This leads to significant savings in problem setup time, disk space, and in certain cases even CPU time.

Unfortunately, for real CFD problems BEM loses its edge because it still requires volumetric meshing (in 3D), and on top of that it is significantly slower than finite volume methods. I suppose, the problem with computational speed could be over-looked if the method could provide superior results, but it doesn't.

Adrin Gharakhani

Yep, I completely agree with you when you talk about BEM CFD inefficiency. Discretization only the surface of the domain, at least for linear problems, is the well-known advantage of BEM formulations. For CFD it's not the case. That's true. But, in my opinion, we disregard another bright side of the BEM, namely accuracy. Consider the simplest problem of transient heat diffusion with the following boundary (T=1 at x=0 and T=0 at x=1) and initial (T=0 at time=0) conditions. When applying conventional BEM formulation with the time-dependent kernels, numerical error is rather high, say 12% for temperature and hundreds %s for flux. Of course, I'm talking about initial time steps. The errors remain on the same level no matter how small time steps are used. Also, the same errors occur for finite-difference- and finite element methods. I would say, as long as we are unable to solve the problems like this with high level accuracy (say with 6-7 correct digits), BEM would be not a primary tool for numerical analysis.

The bottom line would be the following. The real advantage of the BEM for non-linear problems (especially for CFD) should be the accuracy. The tool for CFD may be quite inefficient in terms of CPU time, memory etc, but extremely accurate. Think of electronic microscope -- it's very expensive, time consuming, but guess why people use them. Regards

(1). The electron microscope can magnify a small area many thousand times I guess. (2). Are you suggesting that this BEM CFD method has the same property. If that is the case, it would be ideal for the study of a turbulent sublayer region. Am I missing something? (3). The electron microscope is not more accurate than an ordinary camera. For five dollars, you can get a camera with film loaded, ready for 27 frames of pictures. Can the electron microscope take a family picture? I think the difficulty lies in the difference between the Navier-Stokes equations and the Laplace equation.

Maybe comparison with an electronic microscope is not good enough, but I was trying to say that there is a strong need in very accurate numerical technique for the NS equations. CFD people are solving highly nonlinear set of equations that are extremely sensitive to even a round-off errors for some cases. Definitely, FDM and/or FEM approaches are not the best to model fluid flows, though for some cases they're quite good.

>That's true. But, in my opinion, we disregard another bright side of the BEM, namely accuracy

...

>When applying conventional BEM formulation with the time-dependent kernels, numerical error is rather high

My original argument was precisely this: IF BEM were to produce more accurate results then people might consider it. Yet, thus far I haven't seen any convincing results to this effect. In fact, in your argument above you are agreeing with me, that BEM is not any more accurate than conventional methods even for solving the transient heat problem. (I have difficulty believing this though, since the heat kernel is the exact solution - how much more accurate can you get )

Adrin Gharakhani

>... solving the transient heat problem. (I have difficulty believing this though, since the heat kernel is the exact solution - how much more accurate can you get

I'd refer you to page 226, chapter 8.8 of the book "BOUNDARY ELEMENT METHODS IN ENGINEERING" by P.K.Banerjee. Either, it's quite easy to implement to see how bad results are... The reason is the flux is infinite at t->0, and x=0.

BTW no numerical method is capable of properly solving this simple problem. Regards

I 'd like to add a few comments on the discussion on BEM-CFD. Together with Prof. Skerget I'm working on a development of CFD-BEM based solver at the University of Maribor, Slovenia. As other responses clearified, the original BEM with boundary only mesh doesn't work for highly convective flows, even if you use Dual or Multiple Reciprocity approximations of the domain integrals. The domain discretisation is unavoidable and its consequence is a high CPU time for computations. However, the use of special Diffusion-convection fundamental solutions locally in small elements (subdomains) seems to work extremely well, as convergence and accurate results of BEM even for higher Ra or Re values (let's say 10^7 for 400 element mesh natural convection in a cavity problem) can be obtained without any additional techniques (upwind). In such cases, the resulting system matrices have a large sparsity and can be effectively solved by iterative methods. Of course there are some still unresolved problems, as the speed-up of the nonlinear iteration process and comparatively larger number of unknowns as in FEM, but the results are very promising. Two of our articles will appear shorty in Int.J. num.meth. engineering and Int.J.num. meth.Fluids, where all the additional data is available. Also, we succeeded in implementing BEM for Non-newtonian fluid flow and we are currently developing the k-epsilon turbulence model for BEM. But as Mikhail said, it's a real struggle till you get close to promising results with BEM. Bye, Matjaz

i think you fellas missed the point of the question that initiated this thread. is there any commercial bem cfd codes? yes or no. if not end the thread and start a new one to talk about your research. it is my understanding (mostly from reading/talking to others about bem that it's main lacking is it's inability to deal with singularities/discontinuities-wrt thermo-structural analysis) i don't know if this dificulty is observed when applying the numerical method to viscous flows. i noticed that the problem matjaz solved was an incompressible. i like to know is his code can solve a wedge in mach 3 flow (ie can it handle shocks?)?

OK, we missed the point. Since there is no (to my knowledge) commercial BEM-CFD code available, we were tempted by the opportunity to discuss a few major research options in BEM-CFD. My answer to Clifford on his question on capturing shocks: NO. Explanation: BEM in CFD is only recently becoming a reality (with work of Dargush and our group in Maribor, perhaps also some others?), so we first have to develop really efficient codes for incompressible flows and then move on to compressible ones. Bye , Matjaz