one-dimensional reaction-diffusion with very simple kinetics, diffusion (two reactions, constant diffusivity, uniform grid)
two-dimensional reaction-diffusion with very simple reaction kinetics, diffusion (two reactions, constant diffusivity, uniform grid)
one-dimensional advection-diffusion
viscous Burger's equation
one-dimensional, compressible Navier-Stokes equations for a pure, calorically perfect gas
one-dimensional, compressible Navier-Stokes equations for a multi-component, chemically reacting mixture
two-dimensional, incompressible Navier-Stokes equations for a lid-driven cavity flow (this will require a special Method to be done with the current time governor abstraction)