Here we simulate a radial dam break enclosed by a dry bathymetry ring. In the setup, a circular dam of slightly higher water level is placed at the centre of a square domain, surrounded by initially still water and a dry annular region. When the dam is released, a radially symmetric wave propagates outward, interacts with the dry ring, and reflects from the boundaries.

The model is based on the two-dimensional nonlinear shallow-water equations for the water depth \( h \), depth-averaged momenta and \( hu \), \( hv \), and the bathymetry \( z \). The computational domain is a \( 10 \times 10 m^2 \) square. A circular dam of radius \( R = 1m \) is centred in the middle of the domain; inside the dam the water depth is \( h = 1.1m \), while outside the dam it is initially \( h = 1.0m \). Additionally, a dry ring is imposed between radii \( 2R \) and \( 3R \): in this annulus the bathymetry is raised to \( z = 1.2m \) and the water depth is set to zero, producing an initially dry region that the wave must overtop. Everywhere else the bottom is flat with \( z = 0\). The initial conditions are as follows:

\begin{align*} h(x, y, 0) &= \begin{cases} 1.1 & \text{if } r \leq{} \frac{N}{10} \\ 0.0 & \text{if } 2\frac{N}{10} \leq{} r \leq{} 3\frac{N}{10} \\ 1.0 & \text{otherwise} \\ \end{cases}, \\ hu(x, y, 0) &= 0.0, \\ hv(x, y, 0) &= 0.0, \\ b(x, y) &= \begin{cases} 1.2 & \text{if } 2\frac{N}{10} \leq{} r \leq{} 3\frac{N}{10} \\ 0.0 & \text{otherwise} \\ \end{cases}, \end{align*}

where \( (x, y) \in [0, N] \times [0, N] \) in meters.