Computational Methods for Astrophysical Flows

点击翻译按钮获取中文摘要

Astrophysical fluid dynamics is a branch of physics concerned with understanding the evolution of far-away objects such as black holes and neutron stars. In order to fully understand such objects, mathematical models must incorporate general relativistic, electromagnetic, and fluid dynamic effects. The resulting equations are a large, coupled, nonlinear system of partial differential equations, some of which are evolution equations, while others are constraint equations that result from various gauge freedoms. The PI's research will focus on developing high-order schemes on unstructured grids to solve various simplified versions of the full astrophysical fluid dynamic model. For example, one problem of great interest to astrophysicists is that of mass accretion onto black holes and the resulting formation of relativistic jets; this phenomenon can be treated in the test-fluid limit (i.e., background spacetime metric is fixed). Another important problem is the generation of gravitational waves (i.e., ripples in spacetime) from the collision of two massive black holes; this problem can be first looked at in the minimally coupled scalar field limit. The PI will make use of both discontinuous Galerkin and residual distribution scheme methodologies to construct accurate and efficient schemes. In particular, these methods will be combined with adaptive mesh refinement strategies. In order to do this efficiently, the PI will construct a posteriori error estimators that can be used to dynamically diagnose where large numerical errors are being made. The resulting set of numerical methods will be incorporated into a computer code that will be made freely available on the web.Although astrophysical objects such as black hole accretion disks, extragalactic jets, and supernovae are observable using various telescopes, direct experimentation is clearly not possible. On the other hand, mathematical models that attempt to explain the physics of these objects are necessarily complex and must include gravitational, electromagnetic, and fluid dynamic effects. Exact solutions to the resulting mathematical equations can only be constructed in very special cases. Therefore, the ability to understand astrophysical phenomena from a scientific viewpoint rests largely on the ability to run accurate and efficient computer simulations, which, in turn, rests on the quality of the computational methods that are used to carry out those simulations. The PI's research is focused on developing classes of high-order computational methods for solving the equations of astrophysical fluid dynamics. One aspect of this work will involve the construction of various error indicators that can be used to dynamically diagnose and correct the accuracy of a computation. Another aspect will be to develop a software package that will be made freely available on the web. The computational methods that result from this development will be applied to two distinct problems in astrophysics: (1) the formation of astrophysical jets from black hole accretion processes and (2) the dynamics of the interaction of two black holes and the resulting generation of gravitational waves.