Statistics – Computation
Scientific paper
Aug 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007phdt........18k&link_type=abstract
Proquest Dissertations And Theses 2007. Section 0771, Part 0606 129 pages; [Ph.D. dissertation].United States -- New York: Stat
Statistics
Computation
Hydrodynamics, Relativity, Radiation Transfer, Gamma-Ray Bursts, Numerical, Radiation Hydrodynamics
Scientific paper
Special relativistic physics plays an important role in many celestial phenomena such as Gamma-Ray Bursts (GRBs) and Active Galactic Nuclei (AGNs). During the past decade, many efforts have been made to simulate these phenomena by developing relativistic hydrodynamics codes with various algorithms. A realistic simulation needs to include magnetic field and radiation which makes the computational code more complicated. For my thesis research, I have developed a relativistic radiation hydrodynamics code in 3-D Cartesian coordinates. My code was developed by using PARAMESH, the Parallel Adaptive Mesh Refinement (AMR) library which makes my code run on parallel computers with AMR. My code is composed of two parts: relativistic hydrodynamics and radiation transport. For the hydrodynamics part, a Flux Corrected Transport (FCT) algorithm was used. I adopted the recent version of FCT algorithm called LCPFCT which was developed at Naval Research Lab to solve the 1-D Newtonian hydrodynamics equations in conservation form. Extension to 3-D was done using Zalesak's multi-dimensional limiter. According to previous results comparing various relativistic hydrodynamics codes based upon different algorithms, it is generally known that a relativistic hydrodynamics code developed with the FCT algorithm does not produce as accurate results as some other codes developed with high resolution shock capturing algorithms. However, the test problems simulated with my code show that the relativistic FCT code with a modification to the diffusion and antidiffusion coefficients is capable of producing results comparable to other algorithms when it is combined with AMR. The main advantage of using the FCT algorithm is its straightforward implementation when the code is extended to the relativistic radiation hydrodynamics regime because no Riemann solver is involved. For the radiation transport part of my code, I derived the governing equation of radiation transport in the comoving frame. The advantage of using the comoving frame equation is that the fundamental properties of radiation such as emissivity, absorption and scattering can be treated in the same way as when the fluid is at rest. The structure of the comoving frame equation is similar to that of the lab frame equation except that the comoving frame equation has additional terms for radiation intensity variation over angle and energy. The comoving frame equation is discretized by the implicit finite difference method and my radiation transport code solves the difference equation by using the Bi-CGSTAB method which iteratively solves linear systems of equations. The relativistic radiation hydrodynamics code is a combination of hydrodynamics and radiation transport with suitable micro- physics. At the current version of my code, an ideal gas equation of state with local thermal equilibrium (LTE) is assumed but various microphysics can be easily implemented into the code. In this dissertation, the equations to solve and the details of the code implementation are presented with a series of verification test problems. As for the astrophysical applications, I simulated the propagation of relativistic jets in the context of GRBs and AGNs with radiation included. The results show that radiation changes the morphology and dynamics of the jet in a significant way.
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