Laplace transform integration of the shallow-water equations. Part 1: Eulerian formulation and Kelvin waves

A filtering integration scheme is developed, using a modification of the contour
used to invert the Laplace transform (LT). It is shown to eliminate components
with frequencies higher than a specified cut-off value. Thus it is valuable
for integrations of the equations governing atmospheric flow. The scheme is
implemented in a shallow water model with an Eulerian treatment of advection.
It is compared to a reference model using the semi-implicit (SI) scheme. The LT
scheme is shown to treat dynamically important Kelvin waves more accurately
than the SI scheme.