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## Building background knowledge for high level math-physics

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### #1elix  Members

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Posted 20 December 2013 - 10:20 AM

Hi

I use physics in my studies but I can't go further, lack of my math-physics knowledge hold me back. I have a Bs. degree on Computer Science and MS. degree on Game Technologies but still I don't understand the language used in siggraph papers. Implementing physical rules is not my problem, there are so many theorems, different mathematical terms etc. I can't understand what they are trying to tell. Many times when I look at the code I understand how that does the magic but I still don't understand the things mentioned in the related description part.

I will tell about my current problem to make clear my position;

Currently I am working on fluid dynamics. Here is Jos Stam's paper,  unlike the other papers it explains the things quite clear, although it doesn't dive into all details. I have understood all the parts but I couldn't comprehend the process of making velocity vector field mass conserving. In a sample implementation here is the comment of the project() method which is responsible for that task:

* Use project() to make the velocity a mass conserving,
* incompressible field. Achieved through a Hodge
* decomposition. First we calculate the divergence field
* of our velocity using the mean finite differnce approach,
* and apply the linear solver to compute the Poisson
* equation and obtain a "height" field. Now we subtract
* the gradient of this field to obtain our mass conserving
* velocity field.

I want to understand such things when I see. I don't want to give up but it seems that searching for the terms that I am not familiar through google and wikipedia doesn't work. I asked if there are some video tutorials , but these topics... you know. Then I accepted that I need to reserve more time and build some background first. There are some courses in ocw. I am planning to check them for now.(I have basic background on linear algebra, differential eqns, numerical analysis)

Now, what kind of roadmap would you suggest?

Edited by elix, 20 December 2013 - 02:54 PM.

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Posted 20 December 2013 - 09:56 PM

If you want to understand fluid dynamics, then I suggest picking up an introductory book on it. The math is a different matter, IMHO. I don't pretend to understand why Hodge decomposition works for this, so I can't help you there.

This paper is actually very interesting. As an mechanical engineer, I have a decent understanding of fluid dynamics and the Navier-Stokes equations. After reading this paper, it's interesting that they don't exactly follow the Navier-Stokes equations because of the problems when dealing with nonlinear partial differential equations. I always wondered how games handle fluids because real CFD is even hard to set up so it runs right in a proper solver, let alone program a solver that runs in real-time.

Edited by cadjunkie, 20 December 2013 - 09:57 PM.

### #3elix  Members

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Posted 22 December 2013 - 11:22 AM

Yes, as mentioned in the paper for computer simulations the emphasis is on stability and speed. Physical accuracy is secondary, visually satisfactory results are enough.

I want to make an application about an art form called 'ebru'. It is something like this. I had already an implementation of this traditional fluid simulation by copying algorithms but as you see ebru is a little bit different, I need to comprehend the details and manipulate according to my needs.

I've understood somethings about the divergence field by checking the code, I think I can not be that patient and start with somethings experimental

Thanks.

Edited by elix, 22 December 2013 - 11:23 AM.

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Posted 23 December 2013 - 11:43 AM

Wow...that's some pretty intense artwork. That would be awesome if you could make something like that. It might actually be worth starting from the base concepts of Navier-Stokes to figure out how Stam's code works. I would recommend "Fundamentals of Fluid Mechanics" by Munson as a good introductory text for learning about the different pieces of Navier-Stokes. For math concepts, I would familiarize myself with differential equations, particularly the Poisson equation.

FWIW, I think Stam's code will work for you. The thing he warns about are large diffusion rates, which you won't have because it seems that ebru art uses high viscosity fluids. I think you'll have to get or empirically determine viscosity and density values for the fluid medium and the oils (or whatever the colored fluid is) that make things visually correct.

### #5elix  Members

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Posted 24 December 2013 - 07:11 AM

At first I also thought that Stam's method would work but as you dive into details it differs so much. I am aware that building a very successful implementation is difficult. For now my aim is to come up with something works. I can share the results here.

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