Well-Balanced Positivity Preserving Central-Upwind Scheme on Triangular Grids for the Saint-Venant System

Yekaterina Epshteyn
Department of Mathematics
University of Utah
Salt Lake City, Utah, USA


In this talk we will introduce and discuss simple second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. This system is widely used in many scientific applications related to modeling of water flows in rivers, lakes and coastal areas.

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 designed 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 proposed scheme, as well as its high resolution and robustness in a number of numerical examples.

Joint work with Jason Albright, Steve Bryson, Alexander Kurganov and Guergana Petrova