Numerical Simulations of Short Gamma-Ray Bursts

该项目的目的是通过数值方法模拟涉及中子星和黑洞的致密物体的合并，以模拟短伽马射线爆发的动力学。模拟中需要考虑的物理相互作用是多方面的：自重力、流体动力运动、中微子发射和反反应、引力波发射和反反应、微物理状态方程效应、高温高密度核反应、磁场等。这些物理效应通过不同的算法在数值和数学上反映出来：椭圆方程通过快速傅立叶变换求解，双曲方程在保守形式的嵌套网格上求解，状态方程的大表采用三线性插值，广义相对论效应被视为后牛顿展开，数值代码在线程中并行化。一个Fortran代码将提供给学生。这涵盖了上面提到的大部分效应，但还有许多改进和更详细的分析途径供学生追求，包括但不限于：磁场效应，中微子反反应，状态方程的变体，狭义和广义相对论。如果学生喜欢追求不同的方向，有免费可用的社区代码，可以适应这个调查主题，或者学生可以建立在以前的博士生在他们的论文中所做的改变。

The aim of this project is to simulate by numerical means the merging of compact objects involving a neutron star and a black hole in order to mimic the dynamics of short gamma-ray bursts. The physical interactions which need to be included in the simulations are manifold: self-gravity, hydrodynamic motion, neutrino emission and back-reaction, gravitational wave emission and back-reaction, micro-physical equation-of-state effects, nuclear reactions at high temperature and densities, and magnetic fields. These physical effects are reflected numerically and mathematically by diverse algorithms: elliptic equations are solved by fast-Fourier transforms, hyperbolic equations are solved on a nested grid in conservative form, large tables for the equation-of-state are interpolated tri-linearly, general relativistic effects are treated as post-Newtonian expansion, and the numerical code is parallelised in threads. A Fortran code will be provided to the student. This covers most of the effects mentioned above, but there are many avenues for improvement and more detailed analysis for the student to pursue, including but not restricted to: magnetic field effects, neutrino back-reaction, variants of equations-of-state, relativity both special and general. Should the student prefer to pursue a different direction there are freely available community codes available which could be adapted to this topic of investigation or the student could build on the alterations which previous PhD students have done in their theses.