Abstract: Our
work focuses on oceanographic flows which can be adequately described by a
two-dimensional shallow water system which governs the evolution of the
depth-averaged flow velocities, and
and
water column height, h. The model incorporates gravity, Coriolis, frictional, and wind
forces.
The
traditional Eulerian formulation of the shallow water system involves solving a
free-boundary problem for the wet-dry interface where This
interface is not a-priori known and must be determined as part of the solution.
We take a different approach. We develop a Lagrangian reformulation of the
Eulerian system. This represents an essential simplification since we are now
confronted with a system which holds on a fixed spatial domain, namely the wet
region at time which is known. We
develop an effective computational model for the Lagrangian reformulation. This
computational model parallelizes naturally and our codes, both serial and
parallel, reproduce exact solutions when the bottom surface is a paraboloid.
