Solving Moist Rayleigh Benard convection with Dedalus

The code solves the Moist Rayligih-Benard equations introduced by Pauluis and Schumacher (2010).. The corresponding equations are: $$\frac{D {\mathbf U}}{DT} = -\nu \Delta {\mathbf U} - \nabla p + B \mathbf{k}$$ $$\frac{D M}{DT} = - \nu \Delta M$$ $$\frac{D D}{DT} = - \nu \Delta D$$ $$\nabla \cdot {\mathbf U} =0$$ $$B = \mathrm{max}(M,D-N^2z).$$ The equations are solved on a two or three-dimensional domain. The boundary conditions used are periodic in the horizontal directions and rigid lid at $z=0$ and $z=1$. More specifically, the default boundary conditions are $$\mathbf{U}(z=0) =0 $$ $$\mathbf{U}(z=1) =0 $$ $$M(z=0) = 0$$ $$M(z=1) = -1$$ $$D(z=0) = 0 $$ $$D(1=1) = -1 + N^2.$$ While other choices for the boundary conditions are possible, these correspond to the ones from Pauluis and Schumacher (2010).

The repository here contains four pieces of code:

• MRBC_2D.py and MRBC_3D.py implement the MRBC problem in Dedalus.
• launch_MRBC_2D.ipynb and launch_MRBC_3D.ipynb are Jupyter Notebooks that organize the computate directory and create the slurm scripts.
• Read_MRBC_2D.ipynb and Read_MRBC_3D.ipynb are short Jupyer Notebooks that read the output files