Numerical Analysis Seminar

Date: October 27, 2021

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Giselle Sosa Jones, University of Houston

Title: A space-time hybridizable discontinuous Galerkin method for free-surface waves

Abstract: The numerical modeling of free-surface waves requires the solution of a system of partial differential equations that govern the movement of the fluid, coupled with free-surface boundary conditions that describe the free-surface. In these problems, the domain where the partial differential equations are posed depends on the free-surface which leads to a strong coupling between the flow equations and the free-surface. In order to effectively track the free-surface, we require an accurate discretization technique that can handle moving domains. Moreover, it is desirable for the discretization to handle the mesh movement without postprocessing techniques. In this talk, we present a space-time hybridizable discontinuous Galerkin discretization of linear and nonlinear free-surface wave problems. We obtain a priori error estimates for the linearized problem, and present various numerical examples that demonstrate the capabilities of the method.