Tuesday,
April 6, 12:15 p.m. GWC 604
Balanced Schemes for the Shallow Water Equations
Abstract
The Saint-Venant (SV) system is commonly used to model flows in
rivers or coastal areas. This system describes the flow as a
conservation law with an additional source term due to bottom
topography. Similarly to other balance laws, the SV system admits
steady-state solutions in which nonzero flux gradients are exactly
balanced by the source terms. Such steady-states as well as their
perturbations, are difficult to capture numerically. Standard
numerical schemes for conservation laws will, in general, fail
to preserve the delicate balance between the fluxes and the
source terms.
In this talk we will show how to derive semi-discrete
Godunov-type central schemes that preserve stationary
steady-state solutions of the SV system. The main idea is
to combine modern methods for approximating solutions of
multidimensional systems of hyperbolic conservation
laws with a careful discretization of the source terms.
The schemes will be constructed both on Cartesian meshes
and on unstructured grids. Along the way, we will comment
on some recent developments in the areas of non-oscillatory
approximations and high-order schemes for conservation laws.
For further information please contact:
mittelmann@asu.edu