<%namespace name="tools" file="tools.tex"/>

\subsection{1D dam break test}
The 1D dam break test is a classic test to varify whether the advection scheme is momentum conservative or not. The upstream water level is set to 1m, and the downstream water level respectively 0m and 0.1m for the dry and wet bed cases. The initial velocities are set to zero and the release of the water is instantaneous. 

The dry bed case was first studied by \citet{Ritter1892} and later by \citet{StellingDuinmeijer2003}. The analytic solutions are based on \citet{Chanson2006} and \citet{Kroon2009}. The results shown are with a grid size of 0.1m, no friction and after 5 seconds. The surfbeat (hydrostatic) as well as the non-hydrostatic results are shown. XBeach non-hydrostatic uses another advection scheme. The difficult part to correctly reproduce is the tip of the shock wave, where deviations with the analytical solutions are often found.

${tools.image('DamBreak/', '01_DamBreak1Ddrybed.eps', 'The results of the 1D dam break test with dry bed after 5 seconds.')}
${tools.image('DamBreak/', '02_DamBreak1Dwetbed.eps', 'The results of the 1D dam break test with wet bed (h=0.1m) after 5 seconds.')}

%%\subsection{2D dam break test}

%%The 2D dam break test is a 2D version of the classic 1D dam break test, and carried out as a laboratory flooding experiment \citet{StellingDuinmeijer2003}. The difference with the 1D test is that there is now a limited opening of 0.4m wide, through which the water can flow. This creates a 2D wave pattern which tests whether the model can correctly reproduce the 2D flow propagation. The upstream water level is set to 0.6m, and the downstream water level respectively 0m and 0.05m for the dry and wet bed cases.  The initial velocities are set to zero and the release of the water is instantaneous (in the experiment however a gate is opened with 16 cm/s). The results shown are with a grid size of 0.1m and a manning friction coefficient of $n=0.012 m^{-1/3}s$.

%%The difficult part is to correctly reproduce the correct propagation speed and flow pattern around the opening. Because the original data was not available the XBeach results are plotted over the figures of the original paper. For both the dry and wet bed cases two figures are given, one with the position of the water front for multiple timesteps shown for half the domain and one with the water levels at four wave gauges along the symmetry axis.

%% {tools.image('DamBreak/', '03_DamBreak2Ddrybed.eps', 'The results of the 2D dam break test with dry bed, front position at $t=1,2,3,4 s$ along the symmetry axis. Shown are the experimental results (black), numerical results by \citet{StellingDuinmeijer2003} (dashed), XBeach SurfBeat results (red dots) and XBeach Non-Hydrostatic results (blue dots). All numerical results using $n=0.012 m^{-1/3}s$.')}
%% {tools.image('DamBreak/', '04_DamBreak2Ddrybed.eps', 'The results of the 2D dam break test with dry bed, water levels at wave gauges along the symmetry axis. Gauge 00 is at x=-1m from the opening, Gauge 01 at x=1m from the opening, Gauge 02 at x=6m from the opening and Gauge 03 at x=9m from the opening. Shown are the experimental results (red line), the blue and green lines the numerical results by \citet{StellingDuinmeijer2003} with $n=0.012m^{-1/3}s$ (blue line) and $n=0.01m^{-1/3}s$ (green line) respectively, XBeach SurfBeat (black) and XBeach Non-Hydrostatic (cyan), both with $n=0.012 m^{-1/3}s$.')}

%% {tools.image('DamBreak/', '05_DamBreak2Dwetbed.eps', 'The results of the 2D dam break test with wet bed (h=0.05m), front position at $t=1,2,3,4 s$ along the symmetry axis. Shown are the experimental results (black), the numerical results by \citet{StellingDuinmeijer2003} (dashed), the XBeach SurfBeat results (red dots) and the XBeach Non-Hydrostatic results (blue dots). All numerical results using $n=0.012 m^{-1/3}s$.')}
%% {tools.image('DamBreak/', '06_DamBreak2Dwetbed.eps', 'The results of the 2D dam break test with wet bed (h=0.05m), water levels at wave gauges along the symmetry axis. Gauge 00 is at x=-1m from the opening, Gauge 01 at x=1m from the opening, Gauge 02 at x=6m from the opening and Gauge 03 at x=9m from the opening. Shown are the experimental results (red), the numerical results by \citet{StellingDuinmeijer2003} with $n=0.012m^{-1/3}s$ (blue) and $n=0.01m^{-1/3}s$ (green) respectively, XBeach SurfBeat (black) and XBeach Non-Hydrostatic (cyan), both with $n=0.012 m^{-1/3}s$.')}