Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations

Area of Science:

• Astrophysics
• Computational Physics
• Numerical Relativity

Background:

• Accurate modeling of high-energy astrophysical phenomena necessitates solving Einstein and special relativistic hydrodynamics (SRHD) equations.
• Non-relativistic models are insufficient due to complex nonlinear relationships in SRHD.

Purpose of the Study:

• To implement and validate a high-resolution shock-capturing central upwind scheme for SRHD.
• To assess the scheme's accuracy and robustness in relativistic astrophysical scenarios.

Main Methods:

• Developed a central upwind scheme utilizing local propagation speeds to reduce numerical diffusion.
• Achieved second-order accuracy via MUSCL-type reconstruction and Runge-Kutta time stepping.
• Validated the scheme with 1D and 2D test problems, comparing results against staggered central and kinetic flux-vector splitting methods.

Main Results:

• The implemented scheme demonstrates robustness and efficiency in solving SRHD equations.
• Results show high accuracy, comparable to sophisticated algorithms, even for complex 2D relativistic problems.
• The technique effectively minimizes numerical diffusion, preserving solution fidelity.

Conclusions:

• The high-resolution shock-capturing central upwind scheme is a reliable tool for astrophysical modeling.
• The method offers a balance of accuracy, efficiency, and robustness for relativistic simulations.
• This approach advances the capability to simulate high-energy astrophysical events.