Oscillation in a symmetrical paraboloid

This example implements the classic Thacker oscillating lake test: a planar free surface oscillating inside a parabolic bowl. The setup provides an exact, time-dependent solution to the nonlinear shallow-water equations and is widely used to validate shallow-water solvers, especially in the presence of moving shorelines and wetting–drying fronts.

The parameter choices in this implementation (paraboloid shape, water depth, oscillation frequency) follow the “planar surface in a paraboloid” case from the SWASHES collection of analytic shallow-water solutions (Delestre et al., 2013), originally introduced by Thacker (1981).

The paraboloid of revolution is defined as:

\begin{eqnarray*} b(x, y) = h_0 \left(1 - \sqrt{x^2 + y^2} \right) - 0.1 \end{eqnarray*}

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