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\title{An Integrated Finite Difference Method for the Semi-Lagrangian Shallow Water Equations}
\author{Mark Trew \and Michael O'Sullivan}
\begin{document}
\maketitle
\begin{abstract}
Semi-Lagrangian shallow water numerical models have emerged in the past decade
based on a Lagrangian advective transport representation. Some are Galerkin
Finite Element based and others are Finite Difference based. Although the
mixed order Galerkin Finite Element method has proven itself to have overcome
early numerical problems, analysis shows that the staggered variable Finite
Difference methods have more attractive numerical properties. The Finite
Difference methods are constrained however, to orthogonal or curvilinear
computational grids. This paper proposes a method that combines the attractive
numerical properties of a Finite Difference method with the grid flexibility
of a Galerkin Finite Element method. The Integrated Finite Difference Method
is built on a set of integration equations that are discretely expressed on a
vertex staggered, unstructured grid of quadrilaterals or triangular cells. The
advective transport is represented in a Lagrangian sense. The discrete
equations are non-linear and are solved using a Newton-Raphson technique.
\end{abstract}
\section{Introduction}
\section{The Semi-Lagrangian Shallow Water Equations in Integral Form}
\section{Staggered Variables and Mixed Interpolations}
\section{The Integrated Finite Difference Method}
\section{Lagrangian Advective Representations}
\section{Applications}
\section{Conclusions}
\end{document}