Sounds like a classic CFD nightmare – heat diffusion, advection, phase change, turbulence… you’d start with the heat equation, add a source term for the magma, then couple it to a Navier‑Stokes solver for the fluid flow. You’d probably need a staggered grid or finite element mesh, then a predictor‑corrector scheme for pressure. In code, that’s a lot of matrix operations, a lot of time steps, and a lot of “why isn’t this stable?” moments. The thrill comes when the temperature spikes, the pressure gradient drives an eruption, and you can actually see the simulation explode in real time—just make sure your profiler is ready for a crash.