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Peano
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Peano
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We study the run-up of a solitary wave on a sloping beach using the nonlinear shallow-water equations in the ExaHyPE2 framework. This benchmark is based on the classical experiments and numerical studies of Li & Raichlen and Synolakis, who investigated non-breaking and breaking solitary-wave run-up on plane slopes. In our configuration, we reproduce the solitary-wave shape and initial velocity given in Li & Raichlen’s work, and use additional geometric parameters (such as the characteristic wave length) taken from their companion paper "Solitary wave runup on plane slopes".
The computational domain is two-dimensional with physical size \( 15m \times 15 m\) and an offset \([-5, 0] \) so that the beach toe and shoreline region are well resolved. The bathymetry describes a plane beach of constant slope \( \beta = 30^{\circ}\) connected to a constant-depth ocean of still-water depth \( h_0 = 1m \). For \( x < 0\) the slope is extended slightly landward; for \( 0 \leq x < x_0 = h_0/\tan{\beta}\) the beach rises linearly; for \( x \geq x_0 \) the bottom is flat at depth \( -h_0 \). On top of this background we superimpose a solitary wave of amplitude \( A = 0.5 m\). The wave crest is positioned one half characteristic length offshore from the foot of the slope, consistent with the setup in the reference papers. The depth field is set to \( h_0 + \eta(x) \) in the offshore region, equals the local water column over the sloping beach, and reverts to \( h_0 \) outside the characteristic wave region.
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