Numerical Investigation on the Dynamic Behavior of Compressible Special Relativistic Flows

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.