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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Yekaterina Epshteyn
University of Utah
Title: Well-Balanced Positivity Preserving Central-Upwind Scheme on Triangular Grids for the Saint-Venant System

Abstract: In this talk we will first briefly discuss Saint-Venant system of shallow water equations. This system describes the flow as a conservation law with an additional source term and it is widely used in many scientific applications related to modeling of water flows in rivers, lakes and coastal areas. Then we will introduce and discuss simple second-order central-upwind scheme for the solution of the Saint-Venant system of shallow water equations on triangular grids. The development of robust and accurate numerical methods for the simulation of shallow water equations is important and challenging problem. In our talk we will show that the proposed scheme both preserves "lake at rest" steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We will demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples.

Joint work with Steve Bryson, Alexander Kurganov and Guergana Petrova

Date: Thursday, October 14, 2010
Time: 1:30 pm
Location: Wean Hall 8220
Submitted by:  David Kinderlehrer