Collaborative Research: Arbitrary Order Structure-Preserving Discontinuous Galerkin Methods for Compressible Euler Equations With Self-Gravity in Astrophysical Flows

The project aims to develop effective and efficient computational methods to model self-gravitating astrophysical flows, including the core-collapse supernovae. The research will have a direct impact on a wide range of applications, including astrophysics, climate modeling, fluid and gas dynamics, and hydraulic engineering. The project will bring together expertise in mathematics, astrophysics, and computational science to develop novel mathematical and computational tools that will improve our ability to model some of the most energetic events in the Universe. The investigators will leverage ongoing research activities at their respective institutions to train students in an interdisciplinary environment. In this collaborative project, the investigators will design novel arbitrary order discontinuous Galerkin finite element methods for astrophysical flows governed by the compressible Euler and ideal magnetohydrodynamics equations with self-gravity. These model systems will be applicable to many astrophysical settings, including the late-stage evolution and explosion of massive stars, and the study of their compact remnants known as neutron stars. The project will exploit structure-preserving numerical methods, i.e., preserving fundamental continuum properties of the underlying physical model, such as energy conservation, asymptotic limits, and maximum principles, at the discrete level. The research aims to design such structure-preserving methods in order to provide stable and efficient numerical methods for the model problem and its astrophysical applications on relatively coarse meshes, and to mitigate potential issues with standard numerical methods, including the appearance of non-physical and ill-conditioned solutions, numerical instability, and code breakdown. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.