Numerical projects in GEF4510

Collection of the numerical projects done for the course "Atmosphere and Oceans on Computers" (GEF4510) at the University of Oslo. The projects revolve around the fundamental methods used for solving the partial differential equations (versions of the Navier-Stokes equations for fluid flow) governing the physics of the atmosphere and oceans. Project 1 is about the diffusion equation applied to vertical diffusive mixing in the atmosphere and the oceanic boundary layer. Project 2 considers the advection equation on a passve temperature tracer and focuses on developing flux correction methods (in particular MPDATA) to minimize numerical diffusion. Projects 3 solves the shallow water equations applied to a storm surge problem using both analytical and numerical methods. Project 4 studies the nonlinear shallow water equations and solves them using the method of characteristics while also employing a flux relaxation scheme to deal with open boundary conditions.