Trying to (Simply) Simulate a Protoplanetary Disc

[ThePsion5]

Hi,
I'm a (very) amateur astrophysicist, and for the past couple of weeks I've been interested in creating a very rough web-based simulation of planetary formation. I've decided to limit the initial scope of this project as much as possible by starting with a VERY rudimentary simulation of a protoplanetary disc.

I know that I have little hope of understanding the math and writing/understanding algorithms to simulate things like fluid dynamics and gravitational instability, so instead I want to try and simulate a protoplanetary disc as a horizontal cross-section with density, temperature, and shear force attributes. I can then use these attributes to calculate a rough metric for stability per any radial section of the disc and from there work on simulating planet formation.

I THINK that this is possible - at least to the extent that it won't give wildly unrealistic or physically impossible results. But I'm not exactly sure where to start. I was hoping that someone could point me in the right direction (or a direction in general).

Thanks in advance!

EDIT: An example of where I might start is by writing an algorithm that will determine the average temperature of the disc at radius r given some basic info about its mass and density.

 

[lippyka]

The first step would be to calculate the total mass of the disc, M_disc. This can be done using the formula M_disc = 2*pi*rho*r_max^2, where rho is the average density and r_max is the maximum radius of the disc. Once the total mass is known, the temperature at any given radius can be calculated by assuming that the disc is in thermal equilibrium. The temperature at radius r can then be determined using the equation T(r) = (3/8)*(G*M_disc/k_B)*(1/r), where G is the gravitational constant, k_B is the Boltzmann constant, and M_disc is the total mass of the disc. From here, you can then use the temperature (and possibly other parameters like the shear force) to calculate a metric for stability per any radial section of the disc. Good luck!