How can we simulate nebulae shapes computationally?
What are the governing equations or forces acting on nebulae? Is it suitable to just use Navier Stokes fluid dynamics and solar winds or is there also significant effects from gravity?
What causes the asymmetry and clumping seen in nebulae?
I am looking to recreate shapes similar to the following:
Nebulae are broadly going to be simulated using magnetohydrodynamics, rather than the Navier-Stokes equations. These modify the Euler equations to account for the interaction of the plasma and the magnetic field (mostly via a new pressure gradient): \begin{align} \frac{\partial \rho}{\partial t}&=-\nabla\cdot\rho\mathbf v \\ \frac{\partial\rho\mathbf v}{\partial t}&=-\nabla\cdot\left(\rho\mathbf v\mathbf v+(p+\frac12B^2)\mathbb I\right) -\mathbf B\mathbf B\\ \frac{\partial e}{\partial t}&=-\nabla\cdot\left(\left[e+p+B^2+\mathbf B\mathbf B\right]\cdot\mathbf v\right)\\ \frac{\partial\mathbf B}{\partial t}&=-\nabla\cdot\left(\mathbf v\mathbf B-\mathbf B\mathbf v\right) \end{align} where the $\mathbf a\mathbf b$ is a dyadic, $\rho e=p/(\gamma-1)$ with $\gamma$ the adiabatic index is the equation of state, $\mathbb I$ the identity matrix, and $\rho$ the mass density, all other variables take their normal meaning. We also have the further condition that $\nabla\cdot\mathbf B=0$. (NB: text overlap from here because I'm lazy)
These PDEs are commonly evolved using FDM or FVM schemes, though doing this in 3D is quite computationally intensive and requires some tricks in programming or stencil design to ensure the magnetic field divergence is actually zero (unfortunately, numerical instabilities exist to prevent this from happening naturally). It's also quite time consuming to actually write a (good) MHD solver (months and years time-scale), so it might be worth finding existing academic software for use with your own interests.
This area was not something I studied, but I do know that the FDM/FVM schemes are usually quite symmetric, so any asymmetric appearance in a simulation would have to be the result of (a) an asymmetric velocity profile or (b) an asymmetric density. Maybe also some sort of internal boundary. Flow instabilities probably could also generate asymmetry.
Nebula is a comprehensive term in astronomy used for any gas and dust object, lit up or seen in silhouette at any wavelength. It covers a wide range of densities, masses, sizes, and ongoing physical forces. A dense cloud, like a globule or a molecular cloud, will be in quasi-equilibrium between gravitational collapse, thermal pressure gradients, turbulent motion, and magnetic fields. The external pressure of the material surrounding the nebula is also important. It will have dense substructures, often unobserved, that may or may not have ongoing star formation. If stars are present, their luminous energy and ionizing effects need accounting. The photon field needs to be followed with ray tracing through all substructures. If heating is sufficient, perhaps by supernovae, the cloud will expand and run into pre-existing structures, one cause of strong asymmetries.
Doing this in detail is often difficult because stars can be obscured by so much dust that they are not visible and the density distributions and magnetic fields in 3D are unknown. The Eagle Nebula has all these problems and more. In general, except for simple symmetric nebulae like some planetary nebulae or supernovae, models are schematic and are updated as new information comes in.
