Abstract: The system of shallow water equations and related models are

widely used in oceanography to model hazardous phenomena such as tsunamis

and storm surges. Unfortunately, the inherent uncertainties in the system

will inevitably damage the credibility of decision-making based on the

deterministic model. The stochastic Galerkin (SG) method seeks a solution

by applying the Galerkin method to the stochastic domain of the equations

with uncertainty. However, the resulting system may fail to preserve the

hyperbolicity of the original model. In this talk, we will discuss a

strategy to preserve the hyperbolicity of the stochastic systems. We will

also discuss a well-balanced hyperbolicity-preserving central-upwind

scheme for the random shallow water equations and illustrate the

effectiveness of our schemes on some challenging numerical tests.

# Applied math. talk: Hyperbolicity-Preserving Stochastic Galerkin Method for Shallow Water Equations by Dihan Dai, Department of Mathematics, University of Utah

- This event has passed.