[lumaca96]

Hi,


during my class on CFD I have studied numerical methods for Euler equations using the book of LeVeque "Numerical Methods for Conservation Laws". This book has been written in the 90'; on the internet, looking for numerical methods, I can find other books/papers from those years.

Is there any paper/book which gives an overview of what happened in the community of numerical methods in the last 30 years? For example, I know that there exists a lot of methods Riemann solver free, such as the Kurganov and Tadmor scheme (early 2000s) which is used in openFOAM, some kinetic schemes (actually I do not know if they are still used, since they are more diffusive than classical Riemann solver based methods) and so on...

Finally, is there any reference that sums up the methods used in CFD today, possibly with examples of applications?

Best regards,
Luca

[aerosayan]

I like this video since it shows some portions of the history of CFD and it's presented by Dr Roe.


https://youtu.be/uaH91P665PI


It's a simple presentation with not much detailed info, but it may be helpful.

[lumaca96]

Originally Posted by aerosayan

I like this video since it shows some portions of the history of CFD and it's presented by Dr Roe.


https://youtu.be/uaH91P665PI


It's a simple presentation with not much detailed info, but it may be helpful.

Very interesting video, thank you. He also cites this paper
https://ntrs.nasa.gov/api/citations/20140003093/downloads/20140003093.pdf

which talks about the future of CFD.


However, I am still looking for some reference that expalains what happened during the last 30 years.



Luca

[sbaffini]

As of today, there are two books that, in my opinion, are very close to a state of the art implementation of general CFD solvers, which are those by Blazek and Moukhalled et al.

But, they are mostly focused on what a modern CFD solver can do, they don't analyze any single new scheme that recently came out of academia.

For those there are journal articles, yet I'm not aware of any specific review. But, for example, when I had to implement my own solver, a classical google search kind of returned all the recent developments.

[lumaca96]

Originally Posted by sbaffini

As of today, there are two books that, in my opinion, are very close to a state of the art implementation of general CFD solvers, which are those by Blazek and Moukhalled et al.

But, they are mostly focused on what a modern CFD solver can do, they don't analyze any single new scheme that recently came out of academia.

Thank you for the advice.

For those there are journal articles, yet I'm not aware of any specific review. But, for example, when I had to implement my own solver, a classical google search kind of returned all the recent developments.

I would have liked to know if a "general" review exists, in order to avoid to miss something in the whole picture. However, thank you for the help

Luca

[FMDenaro]

Originally Posted by lumaca96

Thank you for the advice.

I would have liked to know if a "general" review exists, in order to avoid to miss something in the whole picture. However, thank you for the help

Luca

Often, also the reviews are published on relevant journals rather then on textbooks.

Some volumes of Annual review of Fluid Mechanics illustrate recent methodologies but I can suggest also JCP, TCFD, IJNMF ...
I think you need to focus better on the field of fluid mechanics you are interested for CFD applications.

[lumaca96]

Originally Posted by FMDenaro

Often, also the reviews are published on relevant journals rather then on textbooks.

Some volumes of Annual review of Fluid Mechanics illustrate recent methodologies but I can suggest also JCP, TCFD, IJNMF ...
I think you need to focus better on the field of fluid mechanics you are interested for CFD applications.

Actually I am not interested in something specific, I am looking for something to read during this annoying quarantine. However, it seems that the two textbooks reccomended by sbaffini are a good starting point.

Thank you for your help
Luca

[sbaffini]

If we focus on unstructured, cell-centered like approaches, a possible landscape is the following one:

1) Classical 1st-2nd order FV solvers (covered in the books I mentioned)

2) Higher order FV solvers with K-Exact reconstructions, where the classical linear reconstruction in cells is extended to higher order Taylor approximations. There are also some extensions to non-classical reconstructions (e.g., based on Radial Basis Functions, etc.)

3) Flux reconstruction (FR) or correction procedure via reconstruction (CPR), which is a whole framework within which some already know methods (Spectral Volume, Spectral Difference, Discontinuous Galerkin, etc) and new ones can be formalized. This is mostly used for higher order approaches.

What all of these have in common, however, is that they need convective and diffusive fluxes at faces between cells.

For diffusive fluxes, at least in the classical FV case, there hasn't been much development, and the books I mentioned pretty much cover everything you need. I don't know much for the higher order extensions.

For the convective ones, you still have a Riemann problem to solve, even if you pretend you don't. It's just that, for scalars, you have less constraints.

On this front, besides the Roe scheme (there has been some progress on real gases, positivity preserving, etc.), there are the AUSM ones (that have seen a lot of development), but there are no very novel, already accepted, ideas in this field that I know of. Mostly fixing previous deficiencies.

Residual distribution schemes are something that has gained momentum at certain point, but I know nothing about them (not even where they fit in the picture I'm giving you)

A novel approach (not related to the fluxes but overall), that I like a lot for a number of reasons, has been put forward in the classical FV context by Nishikawa, and it involves using cell gradients as independent variables.

Roe has also pushed forward some new ideas recently https://www.researchgate.net/publica...ly_a_Good_Idea

But reading journal papers is really your only option here, if you want to be updated on every aspect.

[andy_]

Originally Posted by lumaca96

Finally, is there any reference that sums up the methods used in CFD today, possibly with examples of applications?

A 30 year old CFD text book will only be missing a few minor refinements in terms of the methods used in well developed software today to solve real engineering problems. In terms of fundamentals CFD became pretty well sorted in the 70s and 80s with the majority of useful work since being more development rather than research. Dotting the Is and crossing the Ts was how it was expressed to me in a discussion in the early 90s about what to do about the rapidly disappearing funding for basic CFD research (needed to look to more applied or specialised projects).

Mind you in the FEM structures field this had happened a decade or so earlier. In the late 70s I wanted my company to keep me on a full wage to do a PhD because I had no wish to return to being a relatively impoverished student. I was working in the stress office at the time which was still developing their own internal FE software. No problem in principle but the last internal PhD research project they had funded had been 10 years earlier. Although funding a fair sized development group internally they considered linear stress analysis to be sufficiently well researched by that time and were only prepared to fund research in one or two nonlinear aspects like crack propagation.

I enquired in a couple of departments that were developing internal CFD software and both had existing projects with university involvement and were happy to fund PhD projects. A year or two later the company axed their own internal stress analysis code in favour of adding what they wanted into commercial codes. The internal CFD group I moved to continued growing during the 80s and then declined in the 90s in favour of more involvement with external CFD codes. CFD related areas that did grow during the 90s were CAA and LES due to affordable computers becoming just about fast enough to perform useful engineering simulations in a few areas.

[lumaca96]

Your post is really appreciated. You have given a good overview I guess: at least a good starting point.

Originally Posted by sbaffini

A novel approach (not related to the fluxes but overall), that I like a lot for a number of reasons, has been put forward in the classical FV context by Nishikawa, and it involves using cell gradients as independent variables.

This approach seems to be very promising, am I right? I have read something about it this afternoon and if I have understood correctly it is capable of dealing with very rough and highly distorted meshes, while classical methods present oscillations in the solution when the mesh is not regular enough. This property should be very interesting. Am I missing something?

[lumaca96]

Originally Posted by andy_

A 30 year old CFD text book will only be missing a few minor refinements in terms of the methods used in well developed software today to solve real engineering problems. In terms of fundamentals CFD became pretty well sorted in the 70s and 80s with the majority of useful work since being more development rather than research.

I see! Thank you for having shared your experience. You all have helped me to have a more general idea of what is going on right now.

Yesterday night I have read the titles of the papers on the Annual Review: there are some "Recent developments in ..." papers, which talk about development in new turbulence modelling, combustion processes and so on.

During my MSc thesis I have worked with a particle method (SPH): in this field research is still at the beginning (e.g. there is no general way of imposing inflow/outflow boundary conditions) and I was wondering if there is research on the basics also in the mesh-based methods community. As said above, your answers have clarified my doubts.

Thank you,
Luca

[sbaffini]

Originally Posted by lumaca96

Your post is really appreciated. You have given a good overview I guess: at least a good starting point.

This approach seems to be very promising, am I right? I have read something about it this afternoon and if I have understood correctly it is capable of dealing with very rough and highly distorted meshes, while classical methods present oscillations in the solution when the mesh is not regular enough. This property should be very interesting. Am I missing something?

Well, there is more, see for example here:

http://ossanworld.com/hiroakinishikawa/fohsm/index.html

[lumaca96]

Originally Posted by sbaffini

Well, there is more, see for example here:

http://ossanworld.com/hiroakinishikawa/fohsm/index.html

Actually I already knew this website: the author have shared a lot of educational codes and I am currently studying how to work with unstructured grids through its code EDU2D-CCFV-EULER-EXPLCT (http://ossanworld.com/cfdbooks/cfdcodes.html).


I believed the author was Katate Masatsuka, now I discover that this is actually a pen-name for Hiroaki Nishikawa

[arjun]

Originally Posted by lumaca96

Your post is really appreciated. You have given a good overview I guess: at least a good starting point.

This approach seems to be very promising, am I right? I have read something about it this afternoon and if I have understood correctly it is capable of dealing with very rough and highly distorted meshes, while classical methods present oscillations in the solution when the mesh is not regular enough. This property should be very interesting. Am I missing something?

Modern CFD solvers could handle this without resorting to anything new IMO. For example here with Wildkatze I do all the time such thing and I am sure Fluent and Starccm are also doing the same for years.

For higher order solvers making gradients as solver variables might be worth the efforts, but for normal CFD it does not bring much to the table.

[lumaca96]

Originally Posted by arjun

Modern CFD solvers could handle this without resorting to anything new IMO. For example here with Wildkatze I do all the time such thing and I am sure Fluent and Starccm are also doing the same for years.

During my courses professors have always told us about the importance of a regular mesh, without distorted elements and so on. Where is the truth? I mean, if modern CFD solvers can handle with distorted grids, why is important to verify skewness, smoothness, aspect ratio?



Thank you

[arjun]

Originally Posted by lumaca96

During my courses professors have always told us about the importance of a regular mesh, without distorted elements and so on. Where is the truth? I mean, if modern CFD solvers can handle with distorted grids, why is important to verify skewness, smoothness, aspect ratio?



Thank you

Mainly because in old times things were not as stable and in modern times probably you are using openfoam and in order to have stable solution you need best of the meshes. (Though i think openfoam might have improved too.).

Another reason might be that this is always been taught so most people just believes it as gospel.

We are making progress, I believe, so things are slowly improving.

I attach you an image for a calculation i just did to show to you, for a delibrately created bad skew and aspect ration mesh. (3D, all tetra). I ran with K-W turbulence model and solver has absolutely no issues running it and giving me acceptable result.

(hopefully the image is clear enough).

[lumaca96]

Originally Posted by arjun

Mainly because in old times things were not as stable and in modern times probably you are using openfoam and in order to have stable solution you need best of the meshes. (Though i think openfoam might have improved too.).
Another reason might be that this is always been taught so most people just believes it as gospel.

We are making progress, I believe, so things are slowly improving.

I attach you an image for a calculation i just did to show to you, for a delibrately created bad skew and aspect ration mesh. (3D, all tetra). I ran with K-W turbulence model and solver has absolutely no issues running it and giving me acceptable result.

(hopefully the image is clear enough).

Are you sure that the solution is accurate and results acceptable, or is it only a matter of sensations? However, I am not such an expert to judge your simulation, so I have to believe

[aerosayan]

Originally Posted by arjun

Mainly because in old times things were not as stable and in modern times probably you are using openfoam and in order to have stable solution you need best of the meshes. (Though i think openfoam might have improved too.).

Another reason might be that this is always been taught so most people just believes it as gospel.

We are making progress, I believe, so things are slowly improving.

I attach you an image for a calculation i just did to show to you, for a delibrately created bad skew and aspect ration mesh. (3D, all tetra). I ran with K-W turbulence model and solver has absolutely no issues running it and giving me acceptable result.

(hopefully the image is clear enough).

Wow! How did that work?
Do you have any reference paper we could see or is it closed-source proprietary technology?

[andy_]

Originally Posted by lumaca96

During my courses professors have always told us about the importance of a regular mesh, without distorted elements and so on. Where is the truth? I mean, if modern CFD solvers can handle with distorted grids, why is important to verify skewness, smoothness, aspect ratio?

The truth is straightforward if you wish to get a handle on the marketing that dominates a great deal of CFD activity these days. Consider the relative performance of CFD methods at simulating problems of genuine current engineering interest. This is the acid test in determining where high value lies. Academic value in the sense of creating publications about interesting methods but where the cons outweigh the pros when it comes to real engineering simulations is useful but at a lower level.

Methods that can only predict square boxes, cannot handle realistic boundary conditions, require too much computer resources, do not rapidly increase accuracy with grid refinement, etc... are not particularly useful for engineering. For example, how well does the particle method you studied for your MSc do in this respect? Has the assessment changed since the late 70s when my old industrial CFD group considered and discarded this type of method for the main flow? (remained considered and at a low level funded for aspects related to combustion).

This is not a cynical view but one born of decades of watching what methods became adopted, which did not and trying to figure out why. The largest factor driving the development of CFD has almost certainly the decreasing cost of computing. This doesn't so much lead to the invention of new methods but more the adoption and development of established methods that used to require too much computing resource to be of much practical use. Your particle method perhaps?

Looking forward over the next few years to see what development are likely to be useful for engineering simulations rather than the mass production of academic publications I would lean more towards areas like grid adaptation rather than fancier ways of discretising pdes. The reasoning being that current weakness in this area is leading to high costs in engineers time messing about with grids. This might also make a case for particle-type methods with their lower gridding requirements but can they now deliver when it comes to the practical side of engineering simulations?

[arjun]

Originally Posted by aerosayan

Wow! How did that work?
Do you have any reference paper we could see or is it closed-source proprietary technology?

I am not allowed to say much because of company issues. But what i write next matters for stability and accuracy (heart of all this).

Originally Posted by lumaca96

Are you sure that the solution is accurate and results acceptable, or is it only a matter of sensations? However, I am not such an expert to judge your simulation, so I have to believe

The worst case scenario here is first order solution. If the solution is not accurate enough then it is not stable too mostly.

The way finite volume works is that you have to construct the values at face from left and right. If these two values do not match then the residuals do not go down. If they do not match over some delta then solver diverges. So accuracy is very much tied to stability.

It took me 10 years to learn this.

Another thing with gauss integration is that if you provide good values at face then accuracy is very high even with very bad meshes. This you can test with benchmarking with exact solutions (I was surprised when i learned this!)