Benjamin A. Hyatt

Research Areas

Stability analysis of IMEX timestepping schemes

I use the pseudospectral code Dedalus which employs multi-step and multi-stage implicit-explicit (IMEX) timestepping schemes to discretize problems in time. The stability properties of these schemes are well understood in the context of linear theory, but there remain open questions when evolving nonlinear flows. Recently, I have used methods from multiscale asymptotics to develop an analytical framework to determine the stability of IMEX schemes when used to evolve nonlinear waves. A preprint on this work is available on the arxiv here. This analysis has so far been successfully applied to dispersive problems (e.g., soliton propagation), but future work can look to extend this analysis to problems with dissipation and to other classes of timestepping schemes.

Convective boundary mixing in massive stars

Models of stellar evolution rely on parameterizations that are primarily developed by studying dynamics in direct numerical simulations. Previous work (e.g., Anders et al. (2022)) has used 3D hydrodynamical simulations to study convective penetration, which is a source of uncertainty in current stellar evolution models. I am currently running simulations to explore the effects of rotation on convective penetration, which previous studies have not yet incorporated.

Operator splitting and multirate methods for timestepping in geophysical systems

In Summer 2024, I worked in the Center for Applied Scientific Computing at Lawrence Livermore National Laboratory. There I tested out various forms of operator splitting methods which are used to couple the different physical processes included in the E3SM atmosphere model. An abstract describing what I presented at AGU24 can be found here. I am currently interested in testing multirate process coupling methods (e.g., see Sandu (2019)) on problems with turbulent convection.