Implicit Function Theory Applications; Part 0
I developed analytical solutions for a couple of simple transient compressible fluid flow problems that include fluid-structure interactions. I think the problems and solutions might be candidates for standard problems / benchmarks / Method of Exact Solutions.
Implicit function theory is an important aspect of the analytical solutions. Getting the required implicit function theory results was proving to take more pages and space that the analytical solutions. I decided to document those results in these separate notes. The results needed for the analytical solutions are given in the latter part of the notes, beginning with Variable Fluid Control Volume.
I have uploaded a Table that is in landscape and that I don’t now how to get into a portrait layout-document. That Table is here and should open in a separate window.
There are tons and tons of algebra associated with this work; straightforward but tedious algebra. I have checked and re-checked but maybe haven’t cleared out all the errors. If you plan to use any of this material, let me know what is of interest and I’ll work with you to ensure that the equations are correct.
The PDF file is here and should open in a separate window.
Update February 26, 2011
A corrected version of Table 3 is here. There was a bug in the first column of the third row.
Update January 14, 2011
There’s a typo in Eq. (1.8). The X_sub i in the last line ( the bottom part of the bottom ) should be Y_sub i. That’s a strange kind of bug; a typo in a nemonic device.
In the Section, The Bridgman Method, I say:
I have uploaded the table as a PDF file and provided this URL link in my post: http://edaniel.files.wordpress.com/2011/01/testbridgmantable.pdf . You’ll have to copy-n-paste the link into your browser.
That is the same Table mentioned in the Post, and you don’t have to copy-n-paste the URL; it’ll open from the PDF.
Note that Eq. (1.33) can be written in terms of the square of the sound speed.
And in a few places following Tables of derivatives, I said that the entropy derivatives had not been reduced when in fact they are shown reduced form in the tables.
Let me know if you find any problems.
The Great Roads List ca. 1994 ( oops 1993)
Highway 28 in NC / SC has been discovered. Now known as Moonshiner 28. Road described here.
I’ve uploaded a historial copy of The Great Roads List from ca. 1994 1993. The Denizens of Doom ( DoD ) Internet Motorcycle Club maintained the list in the early days of The Web. Or, was that before the early days and we used text and e-mail? We used a 7-bit word and binary arithmetic to assign Member Numbers; I’ve forgotten mine. Route 28 was well-known among some Biker Trash even back then.
It’s a great ride !!
An Interesting and Important Discussion
Steve Fitzpatick is summarizing important aspects of radiative energy transport and its interaction with material in the Earth’s atmosphere, at Jeff Id’s tAV. I think many of these phenomena and processes are represented by parameterizations.
Analytical Sensitivity Analysis
Sensitivity Analysis [Hardcover]
A. Saltelli (Editor), K. Chan (Editor), E. M. Scott (Editor)
Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models [Hardcover]
A. Saltelli (Author), Stefano Tarantola (Author), Francesca Campolongo (Author),Marco Ratto (Author)
Uncertainty Modeling and Analysis in Engineering and the Sciences [Hardcover]
Bilal M. Ayyub (Author), George J. Klir (Author)
Sensitivity & Uncertainty Analysis, Volume 1: Theory[Hardcover]
Dan G. Cacuci (Author)
Sensitivity and Uncertainty Analysis, Volume II: Applications to Large-Scale Systems [Hardcover]
Dan G. Cacuci (Author), Mihaela Ionescu-Bujor (Author), Michael Navon (Author)
Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models [Hardcover]
A. Saltelli (Author), Stefano Tarantola (Author), Francesca Campolongo (Author),Marco Ratto (Author)
More on V&V and SQA at LANL for ASC and the NNSA
This previous post mentioned V&V and SQA at Los Alamos National Laboratory ( LANL ) within the framework of the Advanced Simulation & Computing ( ASC ) Program for the National Nuclear Security Administration ( NNSA )
Verification and Validation of scientific and engineering software seems to have become a very important part of scientific and engineering software at Los Alamos National Laboratory.
This section:
Typical Questions That V&V Can Answer…
Has this entry:
• “Models can be validated without data.”
Wrong! There is no validation without data because model validation must assess prediction accuracy relative to a physical reality. While code verification and calculation verification are concerned with the accuracy of the numerical implementation and convergence, respectively, validation activities focus on the adequacy of numerical simulations when applied to the description of reality, which requires experimental observations. We nevertheless recognize that the lack of test data can pose serious problems to model validation. Rigorously controlled expert elicitation techniques can provide information that is substituted to experimental testing in cases of severe lack of data and uncertainty.
Code-to-code comparisons are not Validation. Never have been, never will be.
More Sensitivity
I have carried out the sensitivity calculations discussed in this post for the equation discussed in this post and uploaded a file.
Special Pleading Continues
Professor Easterbrook continues the special pleading for exemption that is so common among software developers that have not yet properly addressed important IV&V and SQA issues. This latest version of Professor’s pleading includes the following aspects; (1) a Red Herring, (2) broad generalizations, and (3) appeal to authority.
Appeal to Authority ( His Own )
Professor Easterbrook has not yet cited any of the literature associated with IV&V and SQA for engineering and scientific software. Literature that has presented procedures and processes that have been widely accepted and proven successful. What more can you say about that? Self reference based on a position of authority always fails.
Red Herring
Professor Easterbrook is the only person who has suggested that IV&V and SQA procedures and processes that are applied to commercial software be applied to engineering and scientific software. The subject software is not generally developed fresh from scratch but instead has evolved over decades of time. The engineering community has developed procedures and processes that take into account this obvious and critically important aspect of real-world complex software. Easterbrook attempts to introduce a comparison of apples and zebras into the discussions.
Broad Generalizations
The activities Easterbrook describes are Standard Operating Procedures for every software project that I have experience with. Direct experience. It is not IV&V Lite; it’s plain and simple SOP. SOP is not IV&V and SQA; never has been, will never be.
Collaborative comparisons of software results, and more importantly collaborative comparisons with experimental data, have a very long history in engineering and science software. This software is almost always not commercial software. In my industry, this work started in the mid-1970s. In turbulence modeling the work started in the early 1980s with the (in)famous Stanford Olympics. Infamous because so many calculations got so many different wrong results by so many different ways, sometimes when using the same software; the same models, methods and software. Turbulence is a hard problem.
It is common in many industries for user groups to be formed around a single piece of software. These groups have members that number in the 10s to a few 100s. Importantly the groups focus on a single version of the software, the frozen production-grade version of the code. That’s a lot of eyes looking in detail into all aspects of a single piece of software. From how I understand Easterbrook, the same kind of effort in the GCM community is significantly diluted relative to this standard.
A Prediction
I predict that papers will be written by Professor Easterbrook, reviewed by friendly cohorts who are equally unaware of the literature which has presented the modern methods that are applicable to engineering and science software, published in only the proper peer-reviewed Scientific Journals, and be quoted in the next IPCC reports that the Climate Science GCM software is pure. However, as mentioned above, self reference based solely on a position of authority always fails.
Not Even Wrong
This Comment by John Mashey is simply wrong. Look around this site, and this one, and this one, and this one, and this one, and this one.
Coding Standards Finally Appear
Steve Easterbrook has provided a list of coding standards that are associated with some of the climate models. The first one is for the NASA / GISS ModelE model and code.
Professor Easterbrook states,
Two followup tasks I hope to get to soon – (1) analyze how much these different standards overlap/differ, and (2) measure how much the model codes adhere to the standards.
Here are a few leads relative to Task (2):
The first of these posts was written almost four years ago. The date on the NASA / GISS ModelE document is February 2010. I’m not hopeful that Better late than never will work out in this case. It’s very difficult to retro-fit coding standards to code that is several decades old.
Looks like we’re getting some Traction
This is interesting; Computational science: …Error. From Nature News, even. Comments allowed over there.
Old Science, New Science
Old Science:
Testable hypotheses Validated by Causality. Quality.
See Robert M. Pirsig, 1974.
New Science:
Plausible connections; Validation and Causality optional.
