CFD in Astrophysics: Exploring Interdisciplinary Boundaries

[HossamCFD]

Hi all,

I have a B.Sc. in Mechanical engineering, a M.Eng in aeronautical engineering and I am currently looking for a topic for my Ph.D. I've been working in "conventional" CFD (Computational Fluid Dynamics) for almost 4 years now and I really think it's time to move on beyond the Navier-Stokes equation. I've always been interested in astrophysics, cosmology, and relativity. and I was searching for some ideas to couple CFD (perhaps kinetic models, magnetohydrodynamics MHD, Boltzmann equ., or even Navier-Stokes) with one of these topics. I didn't really commit much of a time in searching of topics but I was wondering if some of the experienced people in Astrophysics and modern physics may share some thoughts with me.

I know that I seem like a refugee from the engineering camp seeking Asylum in the physics camp :) but I really believe that engineering and physics are very interdisciplinary that sometimes it's difficult to draw a solid line between them. I believe that I am lying somewhere in the boundary between them (if such boundary even exists)

 

[Astronuc]

It's a relatively new area.

See the TOC of this book:

Computational Methods for Astrophysical Fluid Flow, Vol. 199
Saas-Fee Advanced Course. Lecture Notes, 1997
Randall J. Leveque, O. Steiner and A. Gautschy
Springer-Verlag, 1998
Modern numerical techniques for compressible fluid flow, with special consideration given to astrophysical applications
http://www.cfd-online.com/Books/show_book.php?book_id=98


This is commonly referenced by I can't readily find a TOC.
Numerical Modeling in Applied Physics and Astrophysics
R. L. Bowers and J. R. Wilson
https://www.amazon.com/dp/0867201231/?tag=pfamazon01-20


See this TOC
Numerical methods in astrophysics: an introduction By Peter Bodenheimer
@taylorandfrancis - http://www.taylorandfrancis.com/sho...ng_cart/search/search.asp?search=Astrophysics


Maybe useful
A Primer on Eulerian Computational Fluid Dynamics for Astrophysics
http://arxiv.org/abs/astro-ph/0210611

That'll get one started.

 

[Wallace]

Have you ever looked at Numerical Relativity? Much of the gains that field has made in recent years has been by exploiting the CFD techniques developed by Scientists and Engineers working in completely different fields. It is kind of cool when you think that you literally are treating the fabric of the Universe (space-time) as a fluid, including shocks, waves etc and you get gravity out of that.

There is probably a steeper learning curve to get into Numerical Relativity as opposed to some other CFD relevant area of astrophysics, but to my mind the rewards could be greater. Literally only in the last year or two have additional fluids been put into Numerical GR codes (i.e. modelling stars falling into black holes using CFD for the star material as well as the background gravity), so there is a real pioneering spirit in the field.

 

[HossamCFD]

Thanks so much for your replies, I truly appreciate it.

well, it seems an overwhilmingly interesting topic. Of course it will be a major change of career for me and I am not sure yet whether I have the credentials to support a study in this field since I come from an engineering background. But I will definately consider it. I just need to know more about relativistic fluid dynamics in general as a field of study. I mean how mature is it comparing to mainstream CFD ? is there any open source or commercial code already developped ? what are the leading institutes concerned with that research ? in short, any info will be highly appreciated.

 

[Wallace]

By the sounds of things you have the credentials to make a very useful contribution, you just need to find the right institution/supervisor who will know how to channel you CFD technique knowledge into an astrophysical area. A lot of people in the areas you might be looking at are primarily astrophysics who know the physics, but learned the numerical techniques essentially by osmosis and example, rather than in a thorough way. Therefore there is likely to be improvements there for someone with a strong numerical modelling background, even if you don't (yet) know the physics so well, don't let that deter you!

As for codes, there are some standards (FLASH, GADGET-2, RAMSES among many others) but it really depends on the physical regime under study. The codes are constantly changing and adapting as differrent physics are included in different ways. I guess that is a fundamental difference compared to the way CFD might be treated in Engineering, where the 'rules' of the Universe are known, and the whole task is about accurate modelling. In astrophysics you are trying to solve both problems at once.

For institutions etc, if you give us idea of where you are in the world (and where you might be prepared to move to) that could help narrow things down a bit.

 

[HossamCFD]

That was really helpful. you got me with this contrasting between conventional CFD and astophysics. Indeed, consider turbulence modeling for instance, for more than 30 years no major theory has been developed, instead, all the efforts are in fine tuning the constants and refining the models for enhancing the accuracy. to the point that it became an almost 'saturated' field. multiphase and combustion CFD are not much different. It is really difficult to find a non trivial topic for potential contribution in 'Navier Stokes CFD'. It seems that it's time to move on !

As for where am I, well, I am egyptian and I got my B.Sc. from Egypt and M.Eng. from Malaysia. I don't think any of them is on the map of pioneering research in fundamental physics anyway. Therefore, I do not have any preferences in terms of the place to go. but I noticed that the Max Plank institut is one of the pioneering institutes in that field. I may be mistaken though.

 

[Astronuc]

Max Planck is one of the lead institutions.

See this - AMRA Adaptive Mesh Refinement for Astrophysics
http://people.sc.fsu.edu/~tomek/AMR/index.html

This has different references
Freshman Seminar on Computational Fluid Dynamics
http://www.amath.washington.edu/courses/freshman/

The problem of modeling the details of turbulence is one of modeling the chaoatic dynamics, especially if a second phase is present or one has time-dependent boundary conditions, e.g., fluid-structure interaction. Given the computational resources, cell/mesh size is a pretty significant issue, and so we often must be satisfied with a semi-emprical approach.

Astrophysics is much more complicated than ordinary CFD since the masses (and gravity field), pressures and temperatures are much, much greater, and we through in charges, currents, E&M fields, radiative transport, nuclear reactions in stars, so one must deal with a much larger set of highly non-linear PDE's.

 

[HossamCFD]

Thanks for the great info Astronuc,

Indeed, my master thesis was about modelling two phase turbulent spray and atomization characteristics, I was able to avoid using the famous semi emperical DPM (discrete phase model) by using an Eulerian-Eulerian two fluid model that describes each phase by a separate set of conservation equations. of course I had to rely on a statistical equation to describe the evolution of droplets in the second phase which in turn relied on emperical models for the break up time of the droplets :(. there is no way out of using semi emperical models unless you are going to use Direct Numerical Simulation (DNS). but then again, you will be solving a chaotic system by a deterministic approach which in itself a matter of debate.

speaking of Astophysics, I understand that there will be a huge amount of 'submodels' (not sure if this term is appropiate here) to account for the complex physics. I can also imagine that the dissipative effects will be totally neglected and that the Euler equations will be used as background rather than the viscous Navier-Stokes equations. or perhaps a kinetic model like the Boltzmann equation will be used.

 

[twofish-quant]

One area that would be very useful for you to look at from a taero-astro Ph.D. standpoint is shocks, combustion, and hypersonic flows. This is one area in which is a very, very hot topic in astrophysics where there would be some overlap with aeronautics. One other area is using parallel grid algorithms and GPGPU technology.

The one big difference between aeronautical CFD and astrophysical CFD, is that aeronautical CFD tends to have complex boundary conditions but simple internal dynamics (i.e. just navier-stokes with maybe turbulence). Astrophysical CFD tends to have simple boundary conditions, but very complex internal dynamics (i.e. lots of combustion, radiation energy transfers, shocks, etc. etc.)

 

[twofish-quant]

One thing that would really get attention is if you can think about how to apply things like grid/cloud computing or GPGPU to CFD. Most of the current algortithms are designed for single node vectorized CPU's, and trying to rethink CFD algorithms to see how one could or would apply massive parallel grids to it would be an interesting (and rather difficult) problem.

 

[twofish-quant]

No actually astrophysical models tend to be dissipative. You are dealing with extremely high Reynolds numbers so there is turbulence which generates viscous dissipation. What happens is that in a simulation is that the size of a single grid point is large enough so that the smoothing that you have to do in order to have a stable calculation introduces some dissipation. What you then do is to write the equations so that the energy that is dissipated by the artificial viscosity gets dumped into the material so that energy is conserved.

Also it's really tough to use kinetic models because all of the microphysics is happening at scales smaller than a grid cell.

 

[twofish-quant]

One other difference is that in every astrophysical calculation that I can think of, we don't have enough data to do any real "fine tuning" of parameters, and the goal is to understand "general behavior." A lot of astrophysical coding depends on making sure that the "basic rules of the universe" are obeyed (i.e. you are conserving energy and momentum) and then the details are filled in with models of various accuracy. What you are often asked for is "what is the important physics?" In some situations you put in a simpe hydro model because the physics you are interested in is elsewhere.

Also areas of astrophysics that are related to CFD are N-body simulations of interacting galaxies and early universe radiation models.

 

[HossamCFD]

Dear twofish-quant,
thanks for the great amount of ideas. Are you saying that the dissipative behaviour in astrophysical problems would arise only from artificial viscosity or that flow turbulence would contribute in the flow? I can imagine the role of numerical dissipation arising from the numerical algorithms, but when it comes to real turbulence I thought that would be totally neglected in most astrophysical problems even at huge Reynolds number. For instance, the common trend of treating hyperonic flows (assuming continuum not rarefied kinetic models) is by solving the Euler inviscid equations rather than Navier-Stokes and thus neglecting any viscous or turbulence dissipation since it is too small comparing to inertia. And of course hypersonic flows also have huge Reynolds number comparing to typical fluid flows.

 

[twofish-quant]

We have to distinguish between the model and what is being modeled. In the real star turbulence causes some of the energy of motion to be dumped into the material through turbulent processes. In the model, you have numerical dissipation, and by properly taking into account the energies involved you can use this numerical dissipation to simulate the effects of turbulence.

One thing that you need to remember is how bit the grid cells are. You typically have an object that is say 100 km wide, and you have 1000 grid cells, so each grid cell is 100 m, and to resolve any feature you need two or three grid cells, which means the smallest thing that you can see in the simulation is 300 meters. In a aero simulation, you can model the flows directly, but in astrophysics everything that happens in that 300 meter cell is unseen and you simulate those internal flows by assuming that the numerical viscosity dumps the right amount of energy into the material.

 

[twofish-quant]

The other thing is that I know nothing about the latest trends in aeronautic CFD, and I wouldn't be surprised that if you read the astrophysical literature you come up with something that can be done a lot better than it is. Which is good for you :-) :-)

The problem with astrophysical flows is that if you don't introduce any numerical dissipation then the simulation quickly becomes unstable. What is happening is that the simulation is trying to dump energy at scales that are much smaller than the grid size, it can't do it and so the one cell quickly becomes completely detached from another.

 

[HossamCFD]

I got your point now. thanks for the explanation. I was confused because in "conventional CFD", artificial viscosity and turbulent dissipation are two different things. like you pointed out, artificial viscosity basicaly arises from the numerical treatment of the non linear equations and tends to stabilize the simulation (although sometimes stability can compromise accuracy). sometimes we introduce extra amount of artificial viscosity only to stabilize the solution, though this would affect the accuracy. Turbulence on the other hand is regarded as a physical phenomena that is mostly treated by introducing a stress tensor to the statistically averaged equations. of course the problem is simpler in aeronautical CFD since we can construct realtively high resolution grids that enable us of using deterministic or semi deterministic approaches so that we can actually SOLVE turbulence rather than modelling it.

Actually, this is the first time for me to hear about combining both turbulence and numerical dissipation. That's why I love interdisciplinary discussions. Thanks again for that :)