Time

Feb 16 2012 - 2:30pm - 3:30 pm

Location

MW 154

Speaker

Yulong Xing (University of Tennessee, Knoxville & Oak Ridge National Laboratory)

Abstract

Shallow-water equations with a non-flat bottom topography have been widely
used to model flows in rivers and coastal areas. An important difficulty
arising in these simulations is the appearance of dry areas, and standard
numerical methods may fail in the presence of these areas. These equations
also have steady-state solutions in which the flux gradients are non-zero
but exactly balanced by the source term.

In this presentation, we propose some recently developed high-order
discontinuous Galerkin and weighted essentially non-oscillatory methods,
which can preserve the steady-state exactly, and at the same time are
positivity preserving without loss of mass conservation. Some numerical
tests are performed to verify the positivity, well-balanced property,
high-order accuracy, and good resolution for smooth and discontinuous
solutions.