GridapGeosciences

The goal of this repository is to showcase the suitability of the Gridap ecosystem of packages to solve geophysical flow problems. In this repo, you will find:

• [click here] A convergence study of Raviart-Thomas-DG mixed finite elements for the solution of a Darcy problem on the cubed sphere.

• [click here] A convergence study of grad-conforming finite elements for the solution of a Laplace-Beltrami problem on the cubed sphere.

• [click here] Numerical solution of the linear wave equation on the cubed sphere using a Strong-Stabilitity-Preserving Runge-Kutta explicit 2nd order method (SSPRK2) for time integration and Raviart-Thomas-DG mixed finite elements for spatial discretization.

• [click here] Numerical solution of the Nonlinear Rotating Shallow Water Equations on the cubed sphere using a fully implicit theta-method for time integration, full Newton nonlinear solves, and compatible mixed finite elements for spatial discretization.

• [click here] MPI-parallelization of all the above using GridapDistributed.jl and its satellite packages GridapPETSc.jl and GridapP4est.jl.

• [[click here]] More to come ...

<p align="center"> <img src="_readme/NSWE_48x48_1_trapezoidal_dt_480_tau_dtdiv2.gif"> Vorticity field for the Nonlinear Rotating Shallow Water Equations on the cubed sphere. Galewsky benchmark. </p>