Here we consider a dam-break–type shallow-water test in a channel with complex bathymetry, referred to as the Three Mounds Channel configuration. The purpose of this case is to study how an initially confined body of water propagates over an uneven bed and interacts with multiple isolated bottom obstacles, providing a benchmark for inundation patterns, flow separation, and wave–topography interaction in two dimensions.

The model again uses the nonlinear shallow-water equations in terms of the water depth \( h \), the depth-averaged momenta \( hu \) and \( hv \), and the bathymetry \( z \). The computational domain is a rectangular channel of size \( 30m \times 30m \). Initially, the left part of the domain \( x\leq 5m \) is filled with water of uniform depth \( h = 0.9m \), , while the remainder of the channel is dry. The bottom topography consists of three smooth, conical mounds defined by radial functions \( m_1 \), \( m_2 \) and \( m_3 \), centered at \( (15, 22.5) \), \( (15, 7.5) \) and \( (28, 15)\), respectively. The bed elevation is taken as the maximum of these contributions and zero, producing two moderate mounds near the center of the channel and a steeper one closer to the right boundary. At time \( t=0 \) the water is at rest, so all momenta are zero.

The three radial functions are given by:

\begin{align*} m_1 &= 1.0 - 0.10 \sqrt{(x - 15.0)^2 + (y - 22.5)^2} \\ m_2 &= 1.0 - 0.10 \sqrt{(x - 15.0)^2 + (y - 7.50)^2} \\ m_3 &= 2.8 - 0.28 \sqrt{(x - 28.0)^2 + (y - 15.0)^2} \end{align*}

The flooding is triggered by a dam break at \( t = 0 s \).

Taken from https://doi.org/10.48550/arXiv.1607.04547