I don't think so, the waves are actual shock waves which are a solution to the Riemann problem for the shallow water equations because they are nonlinear hyperb

I don't think so, the waves are actual shock waves which are a solution to the Riemann problem for the shallow water equations because they are nonlinear hyperbolic equations. You can find them even before you start introducing any numerical grid or discretization. See e.g. the classic exposition by Leveque: https://www.clawpack.org/riemann_book/html/Shallow_water.html https://www.clawpack.org/riemann_book/html/Shallow_water.htm...