This is a classical test case for shallow-water solvers. Water flowing over a bump goes from subcritical through supercritical over the bump and back to subcritical. Figure 146 illustrates the stationary solution with a shock. Figure 147 gives the convergence with resolution. The analytical solution was obtained thanks to the SWASHES library [12].
This is meant to replicate the multilayer test case of [4, 5]. The vertical viscosity is set to ν=0.01 m^{2}/s and the Navier condition at the bottom is given by the Strickler relation
k(h,U)= |
| ||U|| |
with S=25 m^{1/3}/s, the Strickler coefficient, h the water depth and U the depth-averaged velocity.
The stationary solutions are summarised in the figures below. They can be compared to Figure 9 of [5] and Figure 8 of [4]. They agree more or less although our Strickler coefficient is lower (i.e. we need a larger explicit friction to match [4, 5]).
(a) (b) (c)