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

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.