A Once in a Generation Opportunity to Honor 3 CFD Giants

If you are reading this blog, you most likely know what CFD is. You also probably have a favorite CFD solver or method, and know a few names associated with various algorithms, techniques, schemes, Riemann solvers...With the proliferation of CFD in many industries, the number of worldwide CFD users and developers is at least in the order of tens of thousands (one of the CFD groups on linkedin.com has more than 17,000 members).

The CFD community is a very diverse one. If a CFD History is written by people from different disciplines, you will likely get dramatically different versions. I googled "CFD History", and the top hit was Cincinnati Fire Department History, perhaps indicating no CFDer has seriously attempted to write a CFD History. This is not at all surprising since "CFD History" is so tightly related to how one learned CFD, which text book one read, and what literature one followed. My version of "CFD History" is presented next, from an aerospace engineer's perspective.

I discovered CFD during my last year in college, and was immediately fascinated. My favorite courses were Mathematics, Physics, Aerodynamics and Programming, but my undergraduate major was solid rockets, which did not use my skills that much. I started looking for a different field to pursue my graduate degree. A professor recommended CFD, and I knew right away that's what I wanted to do. During my senior design, I switched to CFD and was advised by Academician Zhang Hanxin. The first ever CFD paper I read was an AIAA conference paper authored by Professor Bob MacCormack, who solved the shock boundary layer interaction problem using his own famous method. The first CFD book I studied was Computational Fluid Mechanics and Heat Transfer, by Anderson, Tannehill and Pletcher. The first scheme I published a journal paper on is the total variation diminishing (TVD) scheme, introduced to me by Professor Zhang. The TVD and high-resolution method related literature opened my eyes to many wonderful works (of art) by pioneers of compressible flow CFD including Boris, Chakravarthy, Godunov, Harten, Jameson, Lax, Osher, Roe, van Leer, Yee, ... who laid the foundation of modern shock-capturing methods.

For a graduate student studying CFD, the people mentioned in the last paragraph were like rock-stars.   They are all giants in CFD. I consider myself very fortunate to have met nearly all of them (except Harten and Lax), and become colleagues and friends with them over the years.

As mentioned in my previous blog, three of the CFD giants, Jameson, Roe and van Leer, will be honored in a symposium (JRV symposium), Four Decades of CFD: Looking Back and Moving Forward, to be held in San Diego on June 22-23, 2013. The objectives of the symposium are:

• To provide an open and impartial forum for evaluating the current status of CFD
• To learn from the past and chart the future of CFD in the coming decades

The three giants (or JRV) have not only made path-breaking contributions themselves, but also educated generations of CFDers, who are shaping CFD today. The symposium is open to participants from all over the world. A special invitation is extended to all former students of JRV by the organizing committee. Please come and share your fond memory. This is a once in a generation opportunity to honor all three giants together.

JRV Symposium web site:
  http://zjwang.com/JRV.html

I recommend a very funny Wine-Snob's Guide to Flux Functions from UM:
  http://aerospace.engin.umich.edu/cfd/pubs/other/wine.pdf

Random thoughts (about CFD, etc) on the Christmas Day of 2012

Merry Christmas!

It has been quite an eventful year with my recent job change from Iowa State University (ISU) to the University of Kansas (KU). Many of my colleagues and friends were very surprised (or even shocked) that I would even consider moving to the "dark side" (by being the chairperson of an academic department). I fully agree that something like this would have been unfathomable only two years ago. I have always enjoyed research and teaching as a college professor, and would have been extremely happy doing both for the rest of my life. The person who was the most responsible for this change was Dr. Rich Wlezien, my previous boss and the Vance and Arlene Coffman Endowed Department Chair in Aerospace Engineering at ISU. Rich tapped me to be his Associate Chair for Research and the Director of Graduate Education (or DOGE at ISU) around late 2010. Since I did not volunteer for the position, I agreed to give it a try to see whether the job would distract me from my regular research and teaching. Serving in this role revealed to me a bigger picture of the Department than what I would normally see. With the Graduate Studies Committee, we were able to reform the graduate program in several areas. Earlier, these reforms had been considered beneficial to the entire Department, but not pushed through due to resistance from multiple directions. With extensive discussions and consensus building, the reformed graduate policies received nearly unanimous faculty support. Events like this showed me that a positive impact can be made to an academic environment not only through teaching and research, but also through service, including being a Department administrator. Another person who was also responsible for the change was Dr. Charlie Zheng, my fellow CFDer and colleague at KU, who convinced me to take a look at the opportunity. A heartfelt thank you to both Rich and Charlie.

I have found that both ISU and KU are great places to work. Both aerospace programs are nationally ranked, and have produced very prominent national leaders such as Thornton "T" A. Wilson (ISU alum and former CEO and Chairman of the Board of Boeing), Vance Coffman (ISU alum and former CEO and Chairman of the Board of Lockheed Martin), and Alan Mulally (KU alum and current CEO of Ford). ISU has been known for its CFD program since the 1980s, and its faculty (Tannehill, Pleacher and Anderson) authored one of the most popular CFD text books. ISU has a much larger faculty, has graduated much more students, and ranks higher than KU. KU is known internationally for its aircraft and engine design education. Over the years, KU students have won many AIAA student aircraft and engine design competitions, ranking KU near the top (if not at the top) of all international aerospace programs. KUAE is poised to grow rapidly in the next few years due to the University's strategic plan to grow the engineering faculty by 30% and the number of students by 50%. I hope to strengthen KUAE's research profile so that it will one day rank as high as ISU. Although we loved living in Ames, Lawrence does have the better climate, downtown and variety of restaurants!

I heard a rumor that I changed job because CFD is dead, or my research has hit a big obstacle. I can forcefully state that neither is true. In fact, I intend to continue my CFD research and education in the foreseeable future. I brought nearly my entire group from ISU to KU, and we are working very hard on tackling some of the challenges in high-order adaptive CFD methods (see my previous blog for sample topics). Now and then, we look for talented and hard-working students or postdocs to join our team. If you are motivated and enjoy math, programming and fluid dynamics, you are welcome to apply to KUAE. On CFD education, we are considering to establish a graduate CFD certificate at KUAE, hopefully in the Fall 2013. Do visit KUAE (http://www.ae.engr.ku.edu/) often for updates.

After more than three decades of development, CFD has undoubtedly established itself as a critical tool in the design process of many industries. I am not sure of the market size of commercial CFD software products, but won't be surprised if it is in the order of billions of dollars/year. Constant improvements have been made to these products, which are increasingly more efficient, accurate, robust, and easier to use. There are also many web sites and blogs dedicated to CFD. The fact that these sites and blogs are being visited is a good sign that CFD is well and receiving a lot of attention. I particularly like "Another Fine Mesh", maintained by John Chawner of Pointwise. I just wonder how John manages to run his company and still find time to do the blogs on a weekly basis. 


Almost all CFD commercial software has benefited from research carried out in the "golden age" of CFD, generally considered to be the 1980es, by many well-known CFDers. If we do a survey about the top CFD giants in the world, who have made the most far-reaching impact, I am very confident that the names of Antony Jameson, Phil Roe and Bram van Leer would stand out. In order to celebrate their seminal contrbutions in CFD, an international symposium in their honor is being organized, with support from AFOSR. More information will be posted in the near future with a link from this blog.

BTW, the 2nd International Workshop on High-Order CFD Methods will be held in Germany. See this web site for more info: http://www.dlr.de/as/desktopdefault.aspx/tabid-8170/13999_read-35550/   

Finally, what happened to the often dreamed "push button" CFD tool, which is supposed to give you accurate CFD solutions by pushing a few buttons? Is such a tool going to appear one day, or is it still desired? Let me know your thoughts.

Last but not least, have a great 2013!

A Very Successful Workshop

This blog is so overdue, since the Workshop concluded nearly six months ago! But better late than never. So here I am, giving you an much delayed update.

After several years of planning, the 1st International Workshop on High-Order CFD Methods was successfully held in Nashville, Tennessee, on January 7 and 8, 2012, just before the 50^th Aerospace Sciences Meeting. Over 70 participants from all over the world across the research spectrum of academia, government labs and private industry attended the Workshop. Many interesting results were presented. The major findings from the Workshop include:

1.     For problems with smooth solutions and geometries, high-order methods are able to demonstrate high-order accuracy with h and p-refinement. High-order methods demonstrated better performance than the 2^nd-order finite volume method for both steady and unsteady problems based on error vs. cost.

2.     For problems with non-smooth solutions or geometries, high-order methods cannot achieve high-order accuracy as expected. They are comparable to low order methods in performance.

3.     Solution based hp-adaptations have been shown to be very effective in minimizing the computational cost to achieve a given level of accuracy.

4.     For RANS simulations, high-order methods are still not as robust as low order methods in converging to the steady state solution. It is believed that this behavior is related to non-smoothness introduced in the turbulence models.

If you are interested in doing research on high order methods, the following pacing items may interest you:

1.     High-order mesh generation

2.     Solution based hp-adaptations

3.  Scalable, low memory efficient time integrators for RANS and hybrid RANS/LES approaches

4.     Robust, accuracy-preserving and parameter-free shock capturing

Some of the abstracts of the workshop are contained here:

http://www.public.iastate.edu/~zjw/hiocfd/abstracts/HOW_abstracts.htm

The next workshop will be held in Cologne, Germany next summer. Check the workshop 

web site for updated information.

On a personal note, I will join University of Kansas as the Spahr Professor and Chair of Aerospace Engineering in August 2012. It was a difficult decision, but I do look forward to the new challenges ahead.

High-Order CFD Workshop

Merry Christmas and Happy New Year!

Hello again after a long silence. The last few months were quite hectic. In addition to our daily activities, we had several prominent visitors to aerospace engineering, including a three-star general, a NASA astronaut, a top Boeing executive. In fact, the general was interested in seeing some CFD. I therefore got to shake his hand. I also had the pleasure of visiting South America for the first time, as a matter of fact, the largest country there - Brazil. I really enjoyed Brazil and will definitely visit again. Here is a photo of Sao Paulo.

Oh yes, another big event in town was the the biggest upset in ISU's football history - we beat Oklahoma State!

Now back to CFD...

The 1st International Workshop on High Order CFD Methods will be held in Nashville on Jan. 7 and 8, 2012. Many types of high-order methods will be covered by researchers from all over the world. We will have two full days of actions. See the following agenda for details:

 http://zjw.public.iastate.edu/hiocfd/HOW_agenda.pdf 

Here is a bit of history regarding the Workshop. I became a member of the Fluid Dynamics Technical Committee of AIAA in 2006-2007, and then started to chair the CFD Algorithm Discussion Group (DG) until 2010, when Dr. H.T. Huynh of NASA Glenn took over.  The charter of the DG has been:

To coordinate research and promote discussion for the improvement of CFD algorithms with a particular focus on:

       i.     High-order spatial discretization

       ii.     Error estimate, grid adaptation and methods capable of handling bad grids

       iii.     Efficient time marching/iterative solution methods for unsteady flow

       iv. Benchmark and challenge problems for above methods

Many leading CFD pioneers and experts including Jameson, Roe and van Leer participated in various discussions. The workshop idea came from one of the many discussions, and was also shared by the ADIGMA project in Europe. A strong support has been provided by AFOSR and DLR of Germany. Through several years of hard work, the DG has achieved two major milestones:

1. Identified three pacing items based on a survey and numerous discussions - discontinuity capturing, hp-adaptations and low storage efficient solver. Details are given in the following presentation.

http://zjw.public.iastate.edu/zjw_FDTC_2009.pdf 

2. The planning of the high-order workshop.

Let's hope we will have a very successful Workshop in Nashville!

Why is the order of accuracy important?

Most of the commercial CFD codes are 1st or 2nd order accurate. This is largely due to the robustness offered by these low order methods.  First order methods can be used to compute a steady-state solution reliably and quickly on almost any mesh. For many industrial applications, getting a solution with the correct order of magnitude may be good enough to provide some guidance for product designs. In such cases, low order CFD codes obviously serve a useful purpose.

If the accuracy of a solution is important (e.g. the lift coefficient of a Boeing airliner), first order methods are usually too crude. In theory, one can always refine the mesh enough times to obtain the desired solution accuracy. But mesh refinement is a very inefficient means for low order methods to reach an accuracy threshold. High order (OOA > 2) methods are much more efficient with mesh refinement. Here is why.

Assume that doubling the number of cells in each direction in space (3D) and time increases the computational cost by a factor of 16, i.e., 2^4. For a 1st order scheme, however, the solution error is only reduced by a factor of 2. For a 2nd order scheme, the error is reduced by a factor of 4, while for a 4th order scheme the error is reduced by a factor of 16. Now you see why mesh refinement is much more efficient in reducing the error for a high order method. In fact, a 4th order method on a mesh of 1 million cells may produce a more accurate solution than a 1st order method on a mesh of a billion cells! In computational aeroacoustics (CAA), high-order methods have been used almost exclusively for wave propagation problems because of the stringent accuracy requirement.

Why, then, aren't all the commercial codes 4th order accurate? The quick answer is that it is very difficult to develop robust and efficient high-order methods for unstructured meshes!


How about structured meshes? It is relatively straightforward to develop high-order methods on structured meshes. However, the structured meshes must be smooth enough to achieve the high-order accuracy. Otherwise, the actucal OOA may be only 2nd order or even 1st order.

Given that almost all commercial codes use unstructured meshes, the ultimate solution appears to be adaptive high-order methods capable of handling unstructured meshes.See the following Workshop for the latest development:
http://zjwang.com/hiocfd.html

Mystery surrounding order of accuracy in CFD...

Just came back from a trip to Beijing, where I gave two lectures in a Workshop, one on high-order CFD methods, and the other on the quadrature method of moment for multiphase flows. On the last day, I got to see the beautiful Great Wall at Mu Tian Yu. See the top picture for a magnificent view! Personally I believe this is a better tourist attraction than the more famous Great Wall at Ba Da Lin because it is less crowded. I am now paying a price for the trip: I am still recovering from the jet lag.

In the Workshop at Beijing as well as in many other technical conferences, I often heard people talking about and making mistakes on order of accuracy (OOA) in CFD. As often as it is mentioned, there appears to be as much confusion about it too. There are two major mistakes regarding OOA:

1. If a flow solver produces a more accurate solution than another, it must posses  higher order accuracy. 
2. The OOA is the same as the order of the polynomial approximating the (unknown) solution.

I still remember an incident in an AIAA conference (maybe at Reno). A guy believed like a religion that the OOA is the same as the order of the reconstructed solution polynomial in a finite volume scheme. In fact, he accused the finite volume community of lying about the accuracy of their favorite schemes. You cannot help feeling bad for the guy with such a strong (but wrong) conviction. The truth is that the OOA of a finite volume scheme with a degree p solution polynomial is (p+1).

Let's define OOA. A scheme is pth order if the solution error is proportional to (dx)^p, where dx is the mesh size, i.e.,

Error = C(dx)^p,

where C is a constant depending on the particular scheme. Or equivalently,

log(Error) = p*log(dx) + log(C).

In other words, p is the slope of the dx-Error plot in a log-log scale. Strictly speaking, OOA has nothing to do with the magnitude of the solution error, but only related to the rate of error reduction with mesh refinement, i.e., the slope.

How do you actually measure the OOA? If you know the exact solution, you need only perform two simulations: one on a coarse mesh, and the other on a fine mesh with half the mesh size of the coarse mesh. With a simple derivation, you can obtain the order p from

Error_(dx)/Error_(dx/2) = 2^p, or p = log_2[Error_(dx)/Error_(dx/2)]

where Error_(dx) is the error on the coarse mesh, and  Error_(dx/2) the error on the fine mesh.

More later on high-order methods...

Undergraduate CFD Education

CFD has become an indispensable design tool in many industries, especially in aerospace, automobile, micro-electronics, mechanical and chemical industries. The yearly worldwide revenue in CFD software is estimated to be in the hundreds of millions of dollars. In many industries, undergraduate students with CFD skills are highly sought after.

Iowa State University has been a pioneer in CFD research and education for over 4 decades. One of the most popular CFD text books was written by ISU faculty (Tannehill, Anderson and Pletcher). ISU's aerospace engineering education has always a strong emphasis on CFD fundamentals and computer programming. A basic CFD course has been taught as a senior elective for many decades, and has been a very popular one.

There is another paradigm in CFD education, maybe to reduce the cost at the undergraduate level. In this paradigm, students are taught how to use a particular commercial CFD software. The course is then centered around one CFD tool. The students learn "push button" CFD without having to learn how to program any computer languages. This paradigm has even been adopted by some PhD programs. In fact, I was told by a friend in the industry that he interviewed a PhD in CFD, who does not know what the Navier-Stokes equations are!   

I would like to know whether our way of teaching CFD is out of dated. Do leave a comment if you have an opinion. In addition, do you have a preference on which language should be taught, Fortran, c, C++, ...?