Porous Convection model

[GeorgeR227]

Based off equations and constants given in lecture 4 of Solving PDEs on GPUs, this simulation is currently based off exercise 1, where the pressure update is done implicitly and the temperature done explicitly.

I've switched the use of the pseudo-transient method they use for a Poisson equation solve in order to retrieve the pressure based off temperature, such that the computed Darcy velocity is divergence-free (eqs 10 and 11 combined). This is I believe similar to what is being done in our vortices example.

More work currently needs to be done on the advection of the temperature as a result of the Darcy velocity since the velocity field is not constant over the space, as in the introductory advection-diffusion example , and the current Lie derivative scheme is not stable.

[GeorgeR227]

Porous_Convection_alt_cnsts.mp4

Basic results using the wedge-codif advection formulation (wrong for varying velocity fields), no top/bottom initial conditions and modified constants for better stability. While the full model is unstable, the above showcases that the physics themselves (with much weakened but still present advection) is generally correct. Notably the pressure field at the start is what is expected.

[jpfairbanks]

Latest result as 1/13/2025:

Porous_Convection.mp4