This page puts together the different test cases that I wrote to progress towards the computation of steady states of the Navier-Stokes equation with a free surface. The final result is below in the code free_surface_navier_stokes.m.

    Tests and validations in 1D:

    Tests and validations in 2D:

    With a free surface and a velocity potential for the flow:

    With a free surface and Navier-Stokes for the flow