source: production/onslow_2006/report/computational_setup.tex @ 3261

To initiate the modelling, a triangular mesh is constructed to
cover the study region which has an area of around 6300 km$^2$. 
The cell size is chosen to balance
computational time and desired resolution in areas of interest,
particularly in the interface between the on and offshore.
Figure \ref{fig:onslow_area} illustrates the data extent for the 
scenario, the study area and where further mesh refinement has been made. 
The choice
of the refinement is based around the inter-tidal zones and
other important features such as islands and rivers. 
The study area covers approximately 100km of
coastline and extends offshore to the 100m contour line and inshore to 
approximately 10m elevation.

{\bf Need some words here about why pick 100m.}
Preliminary investigations indicate that MOST and ANUGA compare
well at the 100m contour line.

\begin{figure}[hbt]

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

  \caption{Study area for Onslow scenario highlighting areas of increased 
refinement. 
}
  \label{fig:onslow_area}
\end{figure}

In addition to refining the mesh in regions where complex behaviour 
will occur, it is important that the mesh also be
commensurate with the underlying data. Referring to the onshore data 
discussed
in Section \ref{sec:data}, we choose a cell area of 500 m$^2$ per triangle 
for the region surrounding the Onslow town centre. 
It is worth noting here 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.
In contrast to the onshore data, the offshore
data is a series of survey points which is typically not supplied on a fixed 
grid which complicates the issue of determining an appropriate cell area. 
In addition, the data is not necessarily complete, as can be
seen in Figure \ref{fig:onslow_area}.

In the deep water modelling such as MOST,
the minimum model resolution is chosen so that there at
least ten cells per wavelength. In developing the 
preliminary hazard map for the Western Australia coastline,
\cite{BC:FESA}, a grid resolution of blah was used
which can adequately model tsunamis with a wavelength of 
50km. For this scenario, the wavelength of the tsunami wave is
approximately 1km near the boundary indicating that a minimum
grid resolution of 100m would be required.
With this information, the remaining cell areas are
2500 m$^2$ for the region surrounding the coast,
20000 m$^2$ for the region reaching approximately the 50m contour line, with
the remainder of the study area having a cell area of 100000 m$^2$.
These choice of cell areas is more than adequate to propagate the tsunami wave
in the deepest sections of the study area.\footnote{
With a wavelength of 1km, the minimum (square) grid resolution would
be 100m which results in a square cell area of 10000 m$^2$. A minimum
triangular cell area would therefore be 5000 m$^2$.}
The resultant computational mesh is shown in Figure \ref{fig:mesh_onslow}.

With these cell areas, the study area consists of 440150 triangles
in which water levels and momentums are tracked through time.
The associated lateral accuracy 
for these cell areas is approximatly 30m, 70m, 200m and 445m for the respective
areas. This means
that we can only be confident in the calculated inundation extent to 
approximately 30m lateral accuracy within the Onslow town centre. 

\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}

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}\\ 
\end{tabular} 
 \caption{Point locations used to illustrate the form of the tsunami wave and the
corresponding surface function.} 
 \label{fig:MOSTsolution} 
 \end{figure}