Thursday,
September 23, 1999, 12:15 p.m. in GWC Room 604
James Gleeson
Department of Mathematics
The spectral viscosity method applied to the shallow water equations
Abstract
The goal of the spectral viscosity method is the spectrally accurate
solution of hyperbolic equations. In traditional spectral methods, the Gibbs
phenomenon which arises in the presence of discontinuities (shocks) leads to
instability and causes global deterioration of the convergence rate. The
spectral viscosity method has been proven to be stable and to recover spectral
accuracy away from shocks. We apply the spectral viscosity method to the
shallow water equations in one and two dimensions. Results are compared to
analytical solutions, including the so-called dam break problem which is used
to model surge waves following catastrophic dam collapse.
