Implementation and Technical Developments of ExaHyPE2 for Astrophysics Applications

Abstract

This thesis presents the two astrophysics applications we develop on the code platform exahype, along with the technical advancement we achieved during their implementation.

Our first application focuses on simulating the spherical accretion of collisional gas, considering both the standard and a specific extension of Dvali-Gabadadze-Porrati (DGP) gravity. The spherical accretion scenario has significant importance in cosmology since it captures several crucial aspects of structure formation. While it has been widely studied in standard gravity, we discover a self-similar solution under modified gravity for the first time in this scenario. The application successfully reproduces the theoretical prediction and the self-similarity is observed under both standard and modified gravity in our simulations. This good agreement confirms the reliability of our application in modelling astrophysical processes in the spherical collapse scenario.

Our second application is a complete numerical relativity code designed for astrophysics scenarios in black hole spacetimes. Numerical relativity is a widely utilized approach in simulating astrophysics systems in the strong field regions of gravity and is also used in extracting gravitational wave signals from them. In this thesis, we report the theoretical background, detailed code implementations and simulation tests of our code. The results demonstrate that our code can effectively perform simulations in the black hole spacetime, and exhibit stable evolutions in the dynamics systems, including the rotating binary black hole mergers. Furthermore, we can properly extract the gravitational wave signal from the domain in our tests. However, we have also observed some instability affecting the long-term evolution in our simulations, which has become the focus of our ongoing investigation.

In addition to reporting our astrophysics applications, we introduce the powerful partial derivative equations (PDEs) solving engine exahype in this thesis. This engine offers a relatively flexible code structure, allowing users to implement simulations according to their specific needs. In this regard, this thesis describes the kernel computational solvers, the refinement transition strategy, the radiative boundary condition and the particle module, which are all new features developed during the implementation of our astrophysics code. These advancements enhance the overall capability of exahype to address various problems across different branches of science and engineering in the future.

Supervisors
Prof. Baojiu Li (The Institute for Computational Cosmology, Durham University
Prof. Tobias Weinzierl (Department of Computer Science, Durham University