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I have to present a working 3D simulation of an arbitrary comet in a close proximity to the Sun or to the Jupiter. In specific, I want to simulate comets D/1993 F2 and C/2011 W3, using the theoretical model I have proposed in my recent reseach. My deadline is 1st April 2014.

As I see it now - I make my comet of tons of small particles, define the physics of these particles, define the external physics and just run the simulation for some period of time. I need to obtain both select data in numerical form, and a 3D visualisation of the whole process.

For now I do not have to do that in Minkowski space, just regular 3D space, albeit in spherical coordinates. Physics wise - thermodynamics, gravity, mechanical properties of materials, solar wind.

I've got:

  • Chunk of free time.

  • A Windows/Linux laptop. Might have an access to OS X workstation.

  • Solid knowledge of mathematics behind these physical phenomena (PDEs, integrals, series, complex functions).

  • A little bit of experience in coding - Turbo Pascal 7, C++, Delphi (order from most to less experience).

  • Budget of roughly 500 USD - for software, literature etc. I am qualified for student discounts.

  • I can not use existing solutions, as I have to define the mathematical model for physics according to my research.

I do not know where to start, and from what do I begin.

Edit according to the input from Ben. I have a developed mathematical model of a system comet-star, or comet-planet (it is simplified comet-sun case). I am looking on how I can make a 3D simulation of this model, with gathering specific data and the visual representation of the processes happening.

I hope this helps. If it is still to broad to be answered, feel free to specify more details.

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    $\begingroup$ Welcome to SciComp.SE! Your question is broad, and it would help if you could be more clear about what exactly you're looking for. Do you already have a model that you're now looking to solve numerically? Are you still developing the model? $\endgroup$ – Ben Jun 8 '13 at 22:51
  • $\begingroup$ Edited the main post according to your input, Ben. I hope this helps and I have gotten all the points correct and understandable. $\endgroup$ – user4515 Jun 8 '13 at 23:17
  • $\begingroup$ To clarify: you have a set of differential equations that, when integrated, reproduce the elliptic/parabolic/hyperbolic orbit of the comet? $\endgroup$ – J. M. Jun 9 '13 at 0:58
  • $\begingroup$ Basically, I have 3 sets of equations that describe external phenomena, 3 sets of equations that describe phenomena inside the comet and a set of equations that describe the orbital motion of the comet. What I want to simulate - comets destruction (and determining where it will be, and which of external phenomena will be main cause for that). Comets destruction is governed by equilibrium between external and internal phenomena. All these equations are in spherical coordinates, and 5 sets out of seven are PDEs that have to be integated during the calculation. $\endgroup$ – user4515 Jun 9 '13 at 6:54
  • $\begingroup$ For visualisation you could use glowscript or VPython. On the Glowscript page there is a gravitational/collisions simulation for hard spheres. $\endgroup$ – boyfarrell Jun 9 '13 at 10:03
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I would check out the field of "Smoothed-particle hydrodynamics", and its sister discipline, smoothed-particle mechanics. These approaches lend well to variable boundary conditions and integration of numerous mathematical models/forms. I imagine there are heat and mass flows within the system as well as external (possibly time varying) conditions imposed on them.

The chief downside is that they are computationally expensive, and depending on the phenomenon integrated, your time-scales may get painfully small. For example, incorporating surface tension on a fluid model we worked on shrunk time scales into the microseconds per step, this was ok for us because our particle count was in the hundreds, and time only needed to span a few seconds.

There are lots of packages out there that do these physics, and I can point you at one or more given some more specific information.

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  • $\begingroup$ Thanks for the input, the method is interesting and similar to what I need. Albeit my problem is, according to your method, that I have a time period of roughly 2 Julian years, in two different scenarios, and a laptop. It will be fun, I guess. $\endgroup$ – user4515 Jun 9 '13 at 20:03

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