Partial differential equations posed on moving domains arise in many applications, such as air turbine modeling, flow past airplane wings, etc. The time-dependent nature of the flow domain poses an additional challenge when devising numerical methods for the discretization of such problems. One alternative when dealing with time-dependent domains is to pose the problem on a space-time domain and apply, for example, a finite element method in both space and time. These space-time methods can easily handle the time-dependent nature of the domain. In this talk, we present a space-time hybridizable discontinuous Galerkin method for the discretization of the incompressible Navier-Stokes equations on moving domains. This discretization is pointwise mass conserving and pressure robust, even on time-dependent domains. Moreover, high order can be achieved both in space and time. Numerical experiments will demonstrate the capabilities of the method.

BIO: Tamás Horváth received his PhD from Eötvös Loránd University in Budapest, Hungary. He spent two years at the Von Kármán Institute in Belgium and two years at the University of Waterloo in Canada as a postdoctoral researcher before joining Oakland University in 2018. His main research interests include hybridizable discontinuous Galerkin methods and space-time finite element techniques.