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Unsteady relativistic shock-wave diffraction by cylinders and spheres
I-Nan Tsai1, Juan-Chen Huang, Shang-Shi Tsai
1Department of Applied Mathematics, Tatung University, Taipei 104, Taiwan.
This study numerically simulates relativistic shock wave diffraction around cylinders and spheres. It details complex patterns, including shock interactions and 3D effects for spheres, enhancing understanding of high-speed gas dynamics.
Area of Science:
- Fluid Dynamics
- Relativistic Astrophysics
- Computational Physics
Background:
- Relativistic blast waves are crucial in astrophysical phenomena.
- Understanding shock wave diffraction is key to modeling high-energy events.
- Previous simulations lacked detailed analysis of complex shock interactions.
Purpose of the Study:
- To numerically simulate unsteady relativistic shock-wave diffraction patterns.
- To analyze diffraction around a circular cylinder and a sphere.
- To investigate phenomena like regular and Mach reflections and shock-on-shock interactions.
Main Methods:
- High-resolution relativistic kinetic beam schemes were employed.
- Relativistic Euler equations of gas dynamics were solved.
- Simulations were performed in a general coordinate system.
Main Results:
- Detailed diffraction patterns, including regular and Mach reflections, were observed.
- Complex shock-on-shock interactions in the wake region were analyzed.
- Three-dimensional effects for sphere cases were quantified and compared to cylinder cases.
- Flow properties like Lorentz factor and velocity streamlines were visualized.
Conclusions:
- The study provides a comprehensive analysis of relativistic shock diffraction phenomena.
- Numerical simulations reveal intricate details of shock interactions and geometric effects.
- Results offer insights into high-speed gas dynamics relevant to astrophysics and high-energy physics.
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