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Jonas Holdeman May 8, 2007 12:36

This is in response to Jonas Larson's message on the main forum. I registered a long time ago and have not submitted anything. My first problem was how to enter text and equations. I use LaTeX regularly, and have things which could be used in LaTeX form, but don't know how much of that is transferable to HTML.

Please don't anyone be offended, but just browsing around, what I have seen is more like a dictionary rather that an encyclopedia. Are there any parts I have not seen that read more like from a book or journal article?

My area of interest is the divergence-free finite element method. I suppose this might fit in the numerics section on methods for solving the NSE. But what I would have to say involves a lot of background, the type of stuff I do not see. Jonas Larson implied that one might consider "publishing" to the Wiki. Is anyone submitting cutting edge material?

Could the CFD-Wiki be like a handbook that one could go to to find out about something and how to do it?

jasond May 8, 2007 16:36

Re: Confused
Well, I'm not offended, but I disagree with characterizing the wiki as more like a dictionary rather that an encyclopedia. I think that this same thing can be said about Wikipedia (albeit with many added issues, including the whole "neutral point of view" thing and the endless flamewars), so I'm sure that this is not something that we could ever settle here. In my opinion, it is more important to think about what the wiki aims to be rather than what it currently is - and that is something like you last sentence. I don't think the aim is to be like a journal or a book (but that is just my opinion).

In previous discussions of the "new research" issue, I recall that the consensus was that truly new material did not belong in the wiki. What exactly do you mean by background material that you do not see? If it truly is background material, and it truly is CFD material, then I am pretty sure the contribution would be welcome.

Jonas Larsson May 8, 2007 16:48

Re: Confused
Here comes a few ansers:

1. LaTeX - CFD-Wiki uses normal text that you can cut-and paste from your latex documents. Some special wiki markups are needed to create headings, links, lists etc. To see how others have written their pages just click the "Edit" link to look at the source. For equations CFD-Wiki uses LaTeX syntax. A pure LaTeX text needs to be reworked so that the text parts use normal text together with wiki markups for headings etc. LaTeX equations can hopefully be used directly. Hence, a latex text needs to be modified with wiki markups, but you can use the text and the equations directly.

2. Encyclopedia or book - That is a good question. A wiki is something of both. The basic layout of a wiki with pages identified only by their name makes it directly usable as an encyclopedia. To build a larger book you have to create a set of pages and link them together with a table of content, cross references and links that make it easy to navigate. We have started on this, but so far we haven't finished any "book". The turbulence section contains a lot of text, but needs to get a better structure and indexing. We have many sections that are starting to get large, but most of them need a better structure to make them easier to navigate. In the turbulence modeling section I have started to add a table-of-content structure, see for example this model. I wouldn't worry too much about this "book" issue though. It is better to start adding things and once we have more material in CFD-Wiki we can start to look at the best way of organizing it into specific chapters or "books".

3. Publishing - First let me emphasize one thing. CFD-Wiki is not the place to publish new things. All material in CFD-Wiki should be "verifable", in the sence that is should already be an established and published truth. CFD-Wiki is not a scientific publication. I wouldn't recommend you to put completely new things in CFD-Wiki. Instead we should use CFD-Wiki to document things already published and which are already common knowledge in the scientific community. For example, you should not place a brand new turbulence model in CFD-Wiki and include some new results with it, instead you can place the models that you are already familiar with and which others have already used and for which there are already many papers.

You mentioned that CFD-Wiki could be something of a "handbook". That is not a bad idea. I would like CFD-Wiki to be the best place to go to when you need information about a particular discretization scheme, a particular turbulence model, a certain application area or whatever you are interested in that is related to CFD.

I hope that I answered some of your questions. Thanks for your interest in CFD-Wiki!

Jonas Holdeman May 10, 2007 01:15

Re: Confused
Jason and Jonas:

Let me explain how something can be old and new at the seme time, and demand a careful explanation. In 1936, the year before I was born, Leray introduced the Helmholtz decomposition of the incompressible NSE. This resulted in a pressure-free governing equation for the velocity, and an equation for the pressure as a function of the velocity. Application of this idea had to wait for a world war and the development of functional analysis. With functional analysis, the pressure-free velocity equation became the starting point for existance proofs in 2D and 3D, and uniqueness proofs in 2D. This approach is regarded as good, solid mathematics, but mathematicans continue to regard this as a mathematical trick (according to Vivette Girault -- personal communication). This is the first mathematical mindset.

Engineers and others have problems with boundary conditions for "pressure-driven" flows when there is no pressure. Then there is the derivation NSE from first principles, i.e. applying Newton's law to the forces, including pressure, acting on a small volume of fluid. This is the first engineering mindset. But these have an elegant explanation.

In the mid-1980s, there was a lively interest in divergence-free methods because they offered the prospect of decoupling the pressure, resulting in smaller systems to solve. But this approach was eventually abandoned as unworkable, although they were only a few steps away from the solution. However, they all used Lagrange finite elements, another mathematical mindset.

Earlier, there was a lot of work on developing Hermite elements for shell calculations. These elements have a scalar, and components of the gradient (and perhaps higher derivatives) as degrees-of-freedom. These can be twisted a little to make the DOFs the scalar stream function and the components of the divergence-free velocity. Taking the curl of this SF element yields a divergence-free velocity element. And there you have it.

If you expand the velocity in terms of a divergence-free basis, the result is necessarily divergence-free. Using the Galerkin method with divergence-free weight functions, the pressure gradient decouples because of orthogonality of the gradient and the curl of the stream function as guaranteed by the Helmholtz decomposition.

So there you have it. It could have been done 20 years ago but for those mindsets. A simple, elegant method for solving the NSE, where only the nonlinearity of the convection term remains. There is no LBB condition, even when recovering the pressure from the velocity, and no question about pressure BCs. Oh, pressure-driven flows: there the flow is determined by a boundary condition on the sream function. And the first-principle derivation of the pressure-gradient term? Well pressure disturbances in an incompressible fluid propagate at infinite speed, so any attempt to establish a dynamic pressure gradient fails because the gradient is instantly equilibrated, so there can't be a pressure term, but I have over-simplified this.

For non-rectangular elements one needs Hermite geometry elements for parametric mapping which preserves the solenoidal property, for reasons I will not explain here. And one can easily extend the method to non-cartesian orthogonal coordinate systems (polar, axisymmetric, etc).

For 3D there is no shell-element shortcut, and one must go back to the prematurely-aborted approach of the 1980s. This is new.

So for 2D, all the pieces of the puzzle are in the published literature, and just need to be put together. So is this new stuff or old stuff? And with this I can calculate, in principle, any test problem anyone else can. But interesting problems can take days to calculate using Matlab on my old desktop PC, and the old version I have gives memory errors in the sparse solver.

But I have no collaborators and no one to talk to. I have to do both the theory and programming by myself. And papers take at least two years from submission to publication. And I don't have a lot of years left.

Back to the Wiki... just browsing around, I have not seen description of the NSE decomposition, details of FE implementation, etc., so all of this must be explained. Look at questions repeatedly asked in the main forum, how do I write a CFD code? What pressure BC do I use? Oh, and aren't there any smaller fonts for mathematical equations? And doesn't the very concept of the wiki provide peer review of sorts?

I have been writing a book, a handbook of divergence-free methods. That is where my ideas are kept.

Jonas Larsson May 10, 2007 04:10

Re: Confused
Thanks for the explanation. About using CFD-Wiki to publish new concepts and new ways of doing things. I would not recommend you to do that. As I said before CFD-Wiki is not the place to present new theories in, although parts of the theories might have been published earlier. Trying to use a wiki to publish new things has often created problems in other wikis.

Some people have a favourite theory which they advocate and market in a wiki, then other people have other ideas and other theories and they get irritated and change back the wiki pages again. This has a tendency to create change-and-change-back wars and irritation in wikis. CFD-Wiki does not have any formal review process. The reviewing is done by other users that disagree with something they read. This works for some things, but it doesn't work well to sort out which theories and which methods that are best and should be described.

That said, please don't hesitate to add information to CFD-Wiki, but please only add theories and methods that have already been published and are accepted by the scientific community. Also make sure that you name sections and pages so that the names clearly show what they are about. For example, a theory about divergence free finite element methods should not be presented as the "Numerical CFD Method" or something, since it is a method that is not very frequently used today.

francisco Saldarriaga May 21, 2007 07:18

Re: Confused
Hi Jonas and Jonas: The history summary of Mr. Holdeman (36) is illustrative to me worth further inquire. In my thought process I have gaps to follow it up. As an engineer, I've been interested on solving the NSE with Fluent for particular geometries to incorporate solutions into manufacturing processes. How can I obtain further explanations from Mr. Holdeman to aid in documenting the wiki? handbook/reference/ me it doesn't matter what is is called.

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