Continuum Mechanics Simulation; need some help with the math

[FireStorm000]

Hello all,
Background
I've been playing with computer simulations quite a bit recently, and wrote one that crudely simulates the formation of star systems. My first version was a conventional many body simulation with about 300 small bodies; it actually tends to come up with convincing star systems, either with one or two stars, and several smaller bodies orbiting. In that sense, it is successful.

Unfortunately, the computation cost scaling on an N-body simulation is only so-so, requiring n(n-1) calculations. Even with a negligibility condition, it becomes unmanageable very quickly (and I have a really fast computer...). It's just too many operations.

I've since gone back to the drawing board and decided to try a continuum mechanics approach, where I specify the state of matter at specific fixed intervals, and move mass between them. This way allows considerable optimizations over the N-body simulation, and is more able to be run on my graphics card, which is at least several hundred times more powerful than my CPU for single precision operations (~5TFlops vs ~20GFlops). Cost scaling for this approach appears to be linear for the gravity calculations, plus I can use a look-up table to speed things along.

Problem
While I can currently specify the properties of the gas at any given point, I'm not entirely certain how to move mass between points on the grid. I need something that respects both the bulk velocity of the gas, as well as having it respond to the pressure at adjacent points, and so forth. The most promising suggestion I've heard so far is to model my problem as an electronic one, with a grid of capacitors, and then solve with kirkov's laws. I like that idea, and it would be easy computationally, but I'm not entirely sure how to set up the parallels for current, voltage, etc. Any suggestions would be much appreciated.
-FireStorm-

 

[Chestermiller]

It might help to check out computational fluid dynamics software, which is geared to solving continuum fluid mechanics problems. You may have to modify the set up a little to include mutual gravitation..

 

[FireStorm000]

It might help to check out computational fluid dynamics software, which is geared to solving continuum fluid mechanics problems. You may have to modify the set up a little to include mutual gravitation..

I would absolutely love to see source code for such an application, but I'd be surprised if I could find one. I can find commercial stuff, but nothing I could get source code to or modify, much less incorporate into my own program or redistribute. If you know of an open source one, I'd certainly check it out.

 

[Chestermiller]

I would absolutely love to see source code for such an application, but I'd be surprised if I could find one. I can find commercial stuff, but nothing I could get source code to or modify, much less incorporate into my own program or redistribute. If you know of an open source one, I'd certainly check it out.

Try googling computational fluid dynamics. I'm sure that there are some cfd products out there where you can include some of your own source code.

 

[PJC01]

I would first like to commend you on your innovative approach to simulating star system formation. It is clear that you have put a lot of thought and effort into this project, and your results so far are impressive.

In terms of your current challenge with the continuum mechanics approach, it seems like you have already considered some potential solutions and are on the right track by looking at electronic models. However, as you mentioned, setting up the parallels for current, voltage, etc. may be a bit tricky.

One suggestion I have is to look into using a finite element method (FEM) for your simulation. This method is commonly used in engineering and physics for solving problems involving continuous media, such as fluid dynamics. It involves breaking down the system into smaller, finite elements and solving equations for each element, which can then be combined to get an overall solution.

In the case of your simulation, you could break down the gas into smaller elements and use FEM to solve for the movement of mass between these elements based on the bulk velocity and pressure at adjacent points. This approach may be more computationally efficient and could provide more accurate results compared to the electronic model.

Additionally, there are many software packages available that utilize FEM for simulations, so you may not have to start from scratch in terms of programming. I would suggest researching and experimenting with different FEM methods and software to find the best fit for your specific simulation.

I hope this suggestion helps and I wish you the best of luck with your simulation. Keep up the great work!