source: production/onslow_2006/report/computational_setup.tex @ 3390

To set up a model for the tsunami scenario, a study area is first 
determined. Preliminary investigations have indicated the point
at which the output from MOST is the input to ANUGA is
sufficient at the 100m bathymetric contour line\footnote{ 
Preliminary investigations indicate that MOST and ANUGA compare
well at the 100m contour line. In addition, the resolution for
the MOST modelling indicate that it can theoretically model 
tsunamis with a wavelength of 20-30km, and the wavelength of
the tsunami wave at the boundary is approximately 20km. A much
higher model resolution will be used in developing the probabilistic
models for further studies.}. Historical run-up heights are 
of the order of 10m and we would expect that a tsunami wave
would penetrate no higher for this scenario.
Current computation requirements define a coastline
extent of around 100km. Therefore, the study area of around 6300 km$^2$ 
covers approximately 100km of
coastline and extends offshore to the 100m contour line and inshore to 
approximately 10m elevation. 

The finite volume technique relies on the construction of a triangular mesh which covers the study region. This mesh can be altered to suit the needs of the scenario in question. The mesh can be refined in areas of interest, particularly in the coastal region where complex behaviour is likely to occur. In setting up the model, the user defines the area of the triangular cells in each region of interest\footnote{Note that the cell 
area will be the maximum cell area within the defined region and that each 
cell in the region does not necessarily have the same area.}.
The area should not be too small as to exceed realistic computational time, and not too great as to inadequately capture important behaviour. There are no gains in choosing the area to be less than the supporting data.
Figure \ref{fig:onslow_area} shows the study area and where further mesh refinement has been made. For each region, a maximum triangular cell area is defined and its associated lateral accuracy.
With these cell areas, the study area consists of 401939 triangles
in which water levels and momentums are tracked through time. The lateral accuracy refers to the distance at which we are confident in stating a region is inundated. Therefore we can only be confident in the calculated inundation extent in the Onslow town centre to within 30m.

\begin{figure}[hbt]

  \centerline{ \includegraphics[width=100mm, height=75mm]
             {../report_figures/onslow_resolution_zones.jpg}}

  \caption{Study area for Onslow scenario highlighting four regions of increased refinement.
Region 1: Surrounds Onslow town centre with a cell area of 500 m$^2$ (lateral accuracy 30m).
Region 2: Surrounds the coastal region with a cell area of 2500 m$^2$ (lateral accuracy 70m).
Region 3: Water depths to the 50m contour line (approximately) with a cell area of 20000 m$^2$ (lateral accuracy 200m).
Region 4: Water depths to the boundary (approximately 100m contour line) with a cell area of 100000 m$^2$ (lateral accuracy 445m).
}
  \label{fig:onslow_area}
\end{figure}

%\begin{figure}[hbt]
%
%  \centerline{ \includegraphics[width=100mm, height=75mm]
%              {../report_figures/mesh.jpg}}

%  \caption{Computational mesh for Onslow study area where the
%cell areas increase in resolution; 500 m$^2$, 2500 m$^2$, 20000 
%m$^2$ and 100000 m$^2$.}
%  \label{fig:mesh_onslow}
%\end{figure}

The final item to be addressed to complete the model setup is the 
definition of the boundary condition. As 
discussed in Section \ref{sec:tsunamiscenario}, a Mw 9 event provides
the tsunami source. The resultant tsunami wave is made up of a series
of waves with different amplitudes which is affected by the energy
and style of the event as well as the bathymetry whilst it travels
from its source to Onslow. The amplitude and velocity of each of these
waves are then provided to ANUGA as boundary conditions and propagated
inshore.
%To complete the model setup, we illustrate the
%tsunami wave from the earthquake source described
%in Section \ref{sec:tsunamiscenario} which is used as the boundary condition,
%as described in Section \ref{sec:methodology}. 
%MOST was used to initiate the event and propagate the wave in deep water. 
%ANUGA uses the MOST wave amplitude and velocity at
%the boundary (the 100m contour line as shown in Figure \ref{fig:onslow_area})
%and continues to propagate the wave in shallow water and onshore. 
%To illustrate the form of the tsunami wave, we show the 
%tsunami wave moving through the point locations shown in 
%Figure \ref{fig:MOSTsolution} as a surface showing the wave's
%amplitude as a function of its spatial location and time.
%This figure shows how the wave has been affected by the bathymetry in 
%arriving at these locations as the amplitude is variable. It is also
%important to note that the tsunami is made up of a series of
%waves with different amplitudes.

%\begin{figure}[hbt] 
% \centering 
% \begin{tabular}{cc} 
%\includegraphics[width=0.49\linewidth, height=50mm]{../report_figures/point_line_3d.png}& 
%\includegraphics[width=0.49\linewidth, height=50mm]{../report_figures/solution_surfaceMOST.png}\\ 
%(a) & (b) \\
%\end{tabular} 
% \caption{Point locations used to illustrate the form of the tsunami wave and the
%corresponding surface function.} 
% \label{fig:MOSTsolution} 
% \end{figure}