Abstract:
In this thesis different numerical techniques are investigated for solving compressible spe-
cial relativistic hydrodynamic models. Special relativistic flows are encountered in high
energy astrophysical jets, gamma-ray bursts, microquasars, active galactic nuclei, and so
on. The mathematical models describing these phenomena involve nonlinear complex sys-
tems of hyperbolic partial differential equations. These equations are more complicated
than the non-relativistic ones due to the nonlinear and implicit relations between conser-
vative and primitive variables. The nonlinearity of the systems and flows near the speed
of light pose major challenges to the theoretical and numerical investigations. It is desired
that the numerical methods for these systems should produce approximate solutions that
remain accurate near the shock waves and should be efficient and robust. Failure to ac-
complish this often leads to unphysical solutions. Therefore, our goal is to develop and
implement simpler, robust, and accurate numerical frame works for solving the system of
special relativistic hydrodynamic (SRHD) equations. The space-time CESE method, the
discontinuous Galerkin finite element method, the central scheme and the KFVS method
are proposed for the numerical simulation of such flows. For validation, several test prob-
lems are presented and the numerical results of the schemes are compared with each other
and already published results. The numerical results of our proposed methods were found
in good agreement with available results from well-established finite volume schemes. In
some case studies, the suggested schemes produced better results.
