source: production/onslow_2006/report/computational_setup.tex @ 3404

To set up a model for the tsunami scenario, a study area is first 
determined. Preliminary investigations have indicated that the
output from MOST should be input to ANUGA 
at the 100m water depth\footnote{ 
Preliminary investigations indicate that MOST and ANUGA compare
well at a water depth of 100 m. In addition, the resolution for
the MOST modelling indicate that it can theoretically model a
tsunami wave with a wavelength of 20-30 km. The wavelength of
the tsunami wave at the boundary in this scenario is approximately 20 km. A much
higher model resolution will be used in developing the probabilistic
models for further studies so that tsunami waves with shorter wavelengths
can be captured.}. Historical run-up heights are 
of the order of 10 m and we would expect that a tsunami wave
would penetrate no higher for this scenario, hence we have
bounded our study region at 10m elevation.
Current computation requirements define a coastline
extent of around 100 km. Therefore, the study area of around 6300 km$^2$ 
covers approximately 100 km 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 cell areas should not be too small as this will cause unrealisticly long computational time, 
and not too great as this may 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 with regions of difference cell areas. The total number
of cells is 401939. 
Lateral accuracy refers to the distance at which we are confident in stating a region is inundated. 
Figure \ref{fig:onslow_area} shows the maximum triangular cell area and lateral accuracy for each region. 
Therefore we can only be confident in the calculated inundation extent in the Onslow town centre to within 30 m.


\begin{figure}[hbt]

  \centerline{ \includegraphics[scale=0.15]{../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 30 m).
Region 2: Surrounds the coastal region with a cell area of 2500 m$^2$ (lateral accuracy 70 m).
Region 3: Water depths to the 50m contour line (approximately) with a cell area of 20000 m$^2$ (lateral accuracy 200 m).
Region 4: Water depths to the boundary (approximately 100m contour line) with a cell area of 100000 m$^2$ (lateral accuracy 445 m).
}
  \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}