MiMSEM

A parallel framework for solving geophysical flow problems at both planetary and non-hydrostatic scales using mixed mimetic spectral elements. The code is based on spatial and temporal discretisations that preserve the exact balance of energy exchanges for an improved representation of dynamical processes.

Includes solvers (and test configurations) for:

The 2D advection equation with explicit time integration
- solid body rotation (on the sphere)
- deformational flow (on the sphere)
The rotating shallow water equations with semi-implicit time integration
- Wilkinson2 steady flow (on the sphere)
- Rossby-Haurwitz wave (on the sphere)
- Barotropic instability (Galewsky) (on the sphere)
The 3D compressible Euler equations with horizontally explicit/vertically implicit time integration
- Baroclinic instability (on the sphere)
- Non-hydrostatic gravity wave (on the sphere)
- Warm bubble (doubly periodic planar)

Supports geometric configurations for:

Doubly periodic box (3D)
Cubed-sphere (2D/3D)

Optional stabilisation/forcing terms include:

Biharmonic viscosity for horizontal momentum and temperature equations
Energetically consistent variational upwinding for potential vorticity (in the horizontal) and potential temperature (in the vertical)
Held-Suarez forcing of temperature and lower atmosphere Rayleigh friction

How to run the baroclinic instability test case on the sphere

Install the dependencies (C++, Python3, OpenBLAS, MPI, PETSc)
Clone the repository
Run the set up script: ./scr/Setup.py <polynomial_degree> <number_of_elements_per_dimension> <number_of_processors> where
- polynomial_degree is the polynomial order of the $L^2$ basis functions in the horizontal
- number_of_elements_per_dimension is the number of elements in each dimension on each of the six faces of the cubed sphere
- number_of_processors is the number of cores to run the code on. Note that this must be $6n^2$ for integer n, ie: 6, 24, 54, 96, etc, and number_of_elements_per_dimension must fit evenly into n
Build the code: cd eul/; make mimsem
Run the code: mpirun -np <number_of_processors> ./mimsem <start_dump>, where 0 indicates starting from the analytic initial condition rather than a start dump
Plot an image: ../scr/WriteImage_NorthHemi.py <file_path> <field_name> <plot_contours> <vertical_level> <dump_time>

Picture Gallery

_{Baroclinic instability on the sphere, day 9: surface level Exner pressure, and potential temperature and vertical voricity component at z=1.5km}

_{Baroclinic instability on the sphere, day 11: surface level Exner pressure, and potential temperature and vertical voricity component at z=1.5km}

_{Global simulation with Held-Suarez forcing at day 40, surface level Exner pressure, potential temperature at z = 2.36km and vertical vorticity component at z = 3.14km}

_{Vorticity field at days 5, 6 and 7 for the Galewsky test case for the rotating shallow water on the sphere using energetically balanced upwinding of potential vorticity and and energetically balanced IMEX time splitting without dissipation.}

_{Potential temperature for the 3D rising bubble test case in planar geometry without dissipation and with energetically consistent variational upwinding at times 200s (left) and 400s (right)}