Revisiting well-posed boundary conditions for the shallow water equations

• A general form of well-posed boundary conditions is derived for shallow water equations.
• Both the number and the type of boundary conditions are presented.
• The results are compared with a number of often used open boundary conditions.

We derive a general form of well-posed open boundary conditions for the two-dimensional shallow water equations by using the energy method. Both the number and the type of boundary conditions are presented for subcritical and supercritical flows on a general domain. The boundary conditions are also discussed for a rectangular domain. We compare the results with a number of often used open boundary conditions and show that they are a subset of the derived general form.