I just wonder why so many people use "SIMPLE"?

(1). I don't use it. (2). In CFD war, like real war, hundreds or even millions can be killed. (3). "use" simply says they are not "thinking". (4). I would say that if you are associating with the Imperial College school of thinking, then you are likely the user of the method. (5). It is only one of the method. (6). I am always puzzled by the many millions of people killed in war. Even in Korean war, ordinary farmers were sent to war to fight the bullets. If human being can not "think", they can easily die for no reasons (or funny reasons). (7). "SIMPLE" is one method I don't use in my codes.

I am sad at the evils of the Korean war.I am not able to understand how CFD is like a war and request Mr.Kim to elaborate which can be useful to newcomers into CFD like me.Also can know what is meant by the Imperial college school of thinking-Is it because SIMPLE was developed there?

Hi

I use "SIMPLE" too because its SIMPLE. My advisor too is a product of Imperial College. I think with older people retiring SIMPLE will retire with them.I am not underestimating it's power, It was used with fairly good success for over two decades, The reasons I am not sure, Good marketing or whatever. BTW the co-inventor of Simple Prof Patankar is alumni of our institute & Mech Engg Department, If you don't know.

Hope u found info interesting

Abhijit Tilak Aero Engg Dept IIT Bombay India.

I think I should have forwarded my query to Mr.John C.Chien.

(1). Most low speed incompressible flow formulation used in commercial cfd codes are of "SIMPLE" type or its variation. It's originally developed by researchers at Imperial College.(professors and PhD students) (2). CFD is "thinking-intensive" process. You can also by-pass it and use someone's code directly, and pretending that you are doing CFD. This is one of the source of war. (3). The war is very simple: it try to spread one man's idea to others who are not thinking. The idea could be the pride, the control of the business market, the elimination of a type of human being, the control of resources, etc... (4). If you are doing cfd research (why?), and your goal is to understand the nature (fluid mechanics), then you are away the cfd war. Otherwise, it is around you all the time.

Technically speaking, people use SIMPLE (or it's variants) because of efficiency. Since the pressure-velocity coupling is achieved through sequential iterations (Picard iterations), the formulation is implicit and thus a large time step can be used. There is no explicit CFL type restriction on the time step. Converging the pressure is the significant challenge in SIMPLE (or related methods). There has been a lot of applied math work (see SIAM journals) on numerical solution of Poisson equations (which govern the pressure). Acceleration schemes like CG, Multigrid and FFTs work well for these equations. Preconditioning techniques like ADI also work really well.

Consider the alternatives : i)fractional step methods : usually are based on explicit treatment of the advection terms and are not very efficient. Very few implicit formulations exist though they are specific to constant density flows (See papers by H. Choi). These methods have not been used much for variable density flows (include me in those who have). ii) pseudo-compressibility methods : Allow large time steps but are difficult to converge unless one has a good preconditioners. A comparison of these methods with projection method shows that these methods are more expensive even for incompressible flows. iii) Vortex schemes, spectral methods are more of less useless for complex geometries. Spectral or wavelet elements methods are good but are hard to develop and have been gaining prominence only recently.

A straight forward way of achieving pressure-velocity coupling is to use the Newton iterations. All governing equations are linearized and inverted all at once (as a part of a huge linear system). Technically, these methods have quadratic convergence if you have a good initial (guess) solution. However, the convergence becomes linear (or superlinear at best) if inexact (or approximate Jacobian) Newton methods are used. Also, since all variables are computed at once, the preconditioning becomes a big problem. If you were to compute each variable separately one after another (like in SIMPLE), you know something about the equation governing each variable and the variable behavior and this makes it easier to design preconditioners for computing each variable.

Historically, Spalding's group concentrated more on everyday engineering problems (like heat transfer, stratification and other mechanical/chemical industry problems). Hence, SIMPLE based methods became a natural choice for commercial codes. Most other methods were designed by Aerospace people (e.g. Roe scheme, Van Leer schemes, Potential and TSD equations) and have not become popular in engineering. Spectral and fractional schemes were mostly used in turbulence research and have never found their way into commercial codes (probably because of problems in including compressibility effects). Since SIMPLE is a pressure-based scheme, one can use it for incompressible or compressible flows by modifying (relatively easily) the pressure equation. This can be done without significant loss of efficiency unlike in codes based on full compressible NS equation (which become terrible at low speeds).

The PISO scheme however seems to be replacing SIMPLE (and variants) these days. It is also based on pressure and can be developed easily if you already have a SIMPLE code.

iii) Vortex schemes, spectral methods are more of less useless for complex geometries. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Quite the contrary. I remember in the early 80's finite-volume methods, including SIMPLE which I myself used for my master's thesis could basically handle rectangular geometries. It took many many generations, tens of thousands of (scientific) man years and quite a few iterations on different schemes for the finite volume people to come up with a half-decent solution strategy for simulation in complex geometries. Even today, with all the advances in automatic mesh generation, if this forum is any indication, mesh generation for even simple geometries is a difficult task (if we want accurate results and not just nice colors).

In contrast, in less than 10 man years I was able to develop the first ever vortex-boundary element method for simulating flow in complex 3D moving geometries; e.g. flow in an engine with moving pistons and valves. Of course, there is still alot to be done, but I wouldn't label vortex methods useless, especially when you consider that the first-second generation vortex methods can already solve problems that took finite-volume people over 20 years (requiring a large community of scientists) just to take a shot at.

Adrin Gharakhani

(1). Well, not everyone is well-informed about the leading edge development of various algorithms. (2). I have been working in the vorticity related formulation all the time, for all kind of low speed compressible and incompressible flows. (3). I think, one has to deal with the vorticity directly in the viscous flows.(instead of working directly on the momentum equations) Even in this case, I don't know much about what you are doing. I hope that through the forum, our readers can have a chance to learn your approaches in the future.

I followed the work related to vortex methods in the early 90s when I myself was working on them. I am a bit unfamiliar with the state of the art these days. There are a lot of questions in these methods.

i) How do you deal with scalar transport. Do you use Lagrangian methods like in monte-carlo simulations. The diffusion is not well closed here.

ii) How do you deal with compressible phenomena like shocks.

iii) Can you do LES with these methods. Information about spatial scales may not be immediately evident in these schemes.

iv) The geometry complexity of the flow geometry can make it hard to derive Greens functions in pure vortex methods. I suppose use of boundary elements can alleviate the problem a little.

Can you point me to some literature where I can find answers to these questions.

If what you claim about vortex schemes is true, why is it that most people do not use these methods. What is useful and convenient is determined by how many people use it rather than the claims made by the developers. My statement about vortex schemes was from a engineering applications point of view. From a scientific research point of view, I think that vortex schemes offer some advantages (symplectic nature in 2D Euler flows, meshless CFD). I had used them earlier to study statistical mechanics of vortex dynamics.

Hi Kalyan,

start with the book by G.-H. Cottet and P. D. Koumoutsakos titled "vortex methods"

hope it helps

regards Mayank Tyagi

From the book description, it seems that it deals mostly with incompressible flows. However, it seems to deal with DNS (and presumably LES). Perhaps it has a good explanation as to when a vortex method based simulation can be considered a DNS. If there are other papers that explain this, I would appreciate it if somebody pointed it out to me. Thanks.

Ok, let's start, again, by stressing one major major factor: tens of thousands of man years have been spent on traditional methods, whereas virtually hundreds and may be just a few thousands of man years might have been spent on vortex methods. This is a very important factor to remember. And given the fact that in such a short time vortex methods can solve certain problems even better than the "best" finite volume methods out there should be justification enough to take the method seriously. Of course the method needs lots of work, still, but even at this level it can be quite competitive.

I'll start by the example of flow over a 2D cylinder at Re=9500. Vortex methods produce the fine details of the vortex structures near the surface (and beyond) with spectral accuracy, using the minimal number of particles (collocation points). To date, I've yet to see any finite volume method do as good a job. As soon as you introduce adaptive gridding and all sorts of complex capabilities, finite volume methods lose their "efficiency". Nevertheless, show me a good 2D cylinder flow example.

This is a very important benchmark test. If the method cannot capture the details of the flow for such a "simple" geometry, then how can we take the results seriously for more complex cases. It is not difficult to add bells and whistles, but it is difficult to get accurate results. Any time we have to deal with massive flow separation vortex methods will win.

Now I'll answer some of the questions more directly:

i) How do you deal with scalar transport. Do you use Lagrangian methods like in monte-carlo simulations. The diffusion is not well closed here.

These are two different questions. You can, fundamentally, deal with scalar transport the same way you deal with vorticity. But more work is necessary in this direction. Check papers and results by Soteriou, or Knio or Ghoniem.

As for diffusion, random walk has been used for a while with some success, but there are new, advanced deterministic diffusion schemes which simulate diffusion very accurately. Check Vorticity Redistribution Method, Particle Strength Exchange Method, Diffusion Velocity Method in the papers. You can visit the projects section of http://www.Applied-Scientific.com to see results from a high-order Vorticity Redistribution Method. Or check out others at galcit.caltech.edu. These developments have renderred vortex methods quite accurate, especially as it relates to capturing separation, etc.

ii) How do you deal with compressible phenomena like shocks.

Some work is being carried out at a few institutions. For example, I know Prof. Leonard at Caltech is working on it. I'm working on it, only as a hobby, and not seriously. Low Mach. number compressibility effects are, however, handled alot better. I don't think vortex methods are necessarily the best approach for compressible flow, for reasons that are beyond the discussion here. But mainly, the concern is cost.

iii) Can you do LES with these methods. Information about spatial scales may not be immediately evident in these schemes.

Yes, you can. Check out recent JCP papers by Mansfield, et al for vortex based LES with dynamic Smag. models. I have just finished developing a standard Smag. LES based on the Vorticity Redistribution Method for diffusion. I will next develop a more advanced version.

From a physical point of view, vorticity is a better property to track/monitor in turbulent flow. Isn't it ironic that people solve velocity-pressure equations but their discussions of turbulence always revolves around vorticity? (for good reason). So, even in a grid-based approach, vorticity-velocity and not pressure-velocity should be the parameters to resolve. Also, check out JFM papers by Meneveau, et al. which show that modeling turbulence in a Lagrangian reference frame is more natural and more accurate than in Eulerian reference frame. Well, you combine Lagrangian and vorticity, and what do you get?

iv) The geometry complexity of the flow geometry can make it hard to derive Greens functions in pure vortex methods. I suppose use of boundary elements can alleviate the problem a little.

No need for special Green's functions. vortex-boundary element methods can handle all geometries.

>If what you claim about vortex schemes is true, why is it that most people do not use these methods. What is useful and convenient is determined by how many people use it rather than the claims made by the developers.

Strictly speaking, your reasoning is not correct. The old Beta vs. VHS example comes to mind immediately. Or Mac. vs PC's. There are historic reasons why many people are using the old methods. Vortex methods are relatively new and are relatively more complex than the traditional finite volume methods. Even the concept of vorticity is alien to many, although it is more powerful for understanding physics. Many people use the traditional methods because that is what is available to them, commercially. And nowadays not too many people do development work. Also, in the 80's the US gov't spent alot of money on developing grid-based technologies, and quite often it does not make (short-term) economic sense for them to shift direction or even to support something else in parallel. I repeat though, vortex methods have a long way to go to be all things to everyone. But, at present, they are perhaps the best tool for incompressible turbulent flow simulation.

Adrin Gharakhani

Point taken.

Still, much like in other methods, the vortex based methods need more work. I have seen some papers related to scalar transport and the work on diffusion is far from complete. If you were to simulate premixed flames (whose propagation is determined by diffusion and reaction rates), could you predict the laminar flame speed even for the simple case of planar propagation. I would very much like to see any work in this area.

Also, you say that compressibility is hard/expensive to handle in these methods. How then do you simulate IC engine combustion. There are significant compressibility effects (acoustics due to compression, near transonic velocities close the injectors, knocking etc.).

I visited the Applied-Scientific homepage and let me complement you on the progress you seem to have made in a short time. As interesting (and sometimes advantageous) as I think the vortex methods are, I would not try to oversell their ability in a general sense especially for combustion.

> Also, you say that compressibility is hard/expensive to handle in these methods. How then do you simulate IC engine combustion. There are significant compressibility effects (acoustics due to compression, near transonic velocities close the injectors, knocking etc.).

At least for IC engines, the flow is compressible, yet well within the low Mach number range. I have seen many Mach number contours for IC engines and they are all low. For now, I can simulate compression for cold flow IC engines, mainly because I haven't got around dealing with combustion yet - that's next generation. But vortex based low-Mach number reacting shear layers/jets/plumes (and even with radiation) have already been simulated with very good success. IF shocks are an issue in engines (hardly the case) then that means we'll have to enter the range that I think vortex methods may not be as effective.

(Note: I would be overselling vortex methods if I claimed that we can solve all ranges of problems, like finite volume people do )) - Also, note that I have just as much hands on experience with grid-based methods, so I know both sides of both stories)

Anyway, the world is full of problems where the ability to deal with low Mach number compressibility will be more than sufficient, and that's when vortex methods will be better than other methods.

As for the diffusion flame problem I'd love to work on it (and show that it can be done) if you can find some level of funding within your department or elsewhere )

Adrin Gharakhani

Adrin,

We have moved sufficiently away from the original topic of discussion. From my side, I would end by saying this.

It would be nice to get away from the grid-related issues and I would welcome any developments in this direction. But I expect the progress to be very slow for a couple of reasons. First, very few people are actively pursuing the vortex based Lagrangian methods. Other than Profs. Chorin and Ghoniem (and now you), I do not know many people who have tried to apply these methods to real (engineering type) problems). Second, I am not sure (with my limited exposure) whether accurate deterministic diffusion schemes can be developed. The Lagrangian PDF (monte-carlo type) community which is quite active in turbulent combustion has been at this problem for a long time. It is for this reason some people doubt the ability of PDF methods in capturing differential diffusion. I, however, wish you all the success if you are trying.

PS : I just got out of school couple of years ago and am definitely not in a position to influencing funding anywhere.

(1). I would concentrate on the positive side of the method and try to make it useful. (2). The reason is, it is hard to predict the future approach. DOS used to be very popular on PC, now, it is gone. (3). The problem with the current approach is: it is too slow. And I don't think the current finite-volume approach using the momentum equations is the right approach. I don't use it in my code. (4). So, five years ago, dot.com business was very popular, now you see many many failure and lay-off in dot.com business. (5). My feeling is: if the method is fast, there is alway a possibility to use it in the positive way. And even if it is inviscid, people are still using it on routine basis in a positive way. I would say that the speed of the method will determine the future of that method. Chemical reacting compressible flows? One billion dollars for five years is probably not enough to get it solved.

About the fractional step method, I must disagree with you.

I use a fractional step method called projection-2 scheme. For this category of projection scheme, the pressure term is not removed from the momentum equations (as it is with the original scheme proposed be Chorin). Therefore, the advection terme can be discretized implicitly and very large time steps used. Furthermore, the projection-2 scheme can be used to solve variable density flows. I have some references where two phase incompressible flows are solved with the projection-2 scheme.

P.S. As for the projection 1 scheme proposed by Chorin, the advection term must be discretized explicitly in order to have an accurate solution. If it discretized implicitly, the solution will be highly influenced by the time step (even if it is a permanent flow). Furthermore, the boundary conditions for speed must take into account the pressure term in order to get an accurate solution (this was proven by Leveque in 1981).

I do not see where we disagree. As I have indicated in my posting, I included myself in those who use an implicit fractional step method for modeling variable density flows (most times with CFL numbers between 5 and 10).

I have seen people use fractional step methods for variable density flows and I have seen implicit fractional step methods. I have not come across a numerical paper that claims to have used an implicit fractional step method (with large CFL) for modeling variable density flows.

If you have use implicit fractional step methods for variable density flows, I am afraid I have not seen your publications on the subject. I can always check if I have overlooked some subtle issues in developing my code (since my expertise in not scheme development) if you can send me your papers.

In a master thesis and other papers I have at my hand, the authors also use an explicit fractional step method for variable density flow.

But in my own thesis, I proposed a implicit fractional step method with incomplete splitting (projection-2 scheme). Unfortunatly, this latter scheme was not tested for variable density flow, but only proposed for other researchers. Nevertheless, the projection scheme I developped gave good results for constant density flow problems.

I you can read french, I will be glad to send you a copy of the relevant chapters of my thesis.

Regards.