相對論流體的理論與數值法之探討

THE STUDY ON RELATIVITY FLUID THEORY AND NUMERICAL METHODS

朱君偉(Chun-Wei Chu)

指導教授 ： 蔡一男

大同大學/電機資訊學院/應用數學學系所/碩士(2011年)

摘要

相對論流體力學近年來一直被廣泛探討, 相對論流體力學在科學及應用科學
扮演著非常重要的角色, 舉凡超新星的爆炸所產生的強震波, 以及星際雲碰撞後的
交互作用和星球的產生。在量子力學方面, 如物質衍射、激光、核磁共振及高能核
子碰撞之應用等等。
因此, 在本篇論文中, 首先蒐集各方對相對論流體的理論基礎並加以整理, 同
時對極端相對論尤拉方程組的數值算則和對典型尤拉方程組的數值算則做比較。數
值方法方面, 以二階的TVD 及ENO 射束算則來處理相對論震波碰撞, 並在其
邊界條件上加以調整改進, 以達到較平滑之效果。試以FTVD 算則處理相對論震
波碰撞, 並加以比較討論。

關鍵字

相對論流體力學 ； TVD ； FTVD ； ENO

並列摘要

The theory of relativity hydromechanics widely has been discussed in
recent years, it is playing the very important role in the science and the
applied science. For example, the strong shock wave produced by the supernova,
the interaction of interstellar cloud collision and the generation of
stars. In quantum mechanics, such as substance diffraction, lasers, nuclear
magnetic resonance and the application of high energy nuclear collisions
and so on.
Therefore, in this paper, the first collection of all the theoretical foundation of relativistic hydrodynamics and collated. In the same time we
compare the kinetic scheme for the ultra-relativistic Euler equations with
the corresponding kinetic scheme for the classical Euler equations. In the
way of numerical methods, we use the second order TVD and ENO beam schemes for dealing with the collision of relativistic shock wave, and improved
the boundary conditions to be adjusted to achieve a smoother effect.
Finally we discussed how to take FTVD scheme for collisions with relativistic
shock waves, and compared it.

並列關鍵字

TVD ； The theory of relativity hydromechanics ； FTVD ； ENO

參考文獻

Dimension Triangular System Of Conservation Laws. ” Mathematics

[2] Gui-Qiang Chen , Nadine Even , & Christian Klingenberg (2008),“ Hyperbolic Conservation Laws with Discontinuous Fluxes and Hydrodynamic Limit for Particle Systems ” Journal of Differential Equations, Vol.245, pp.3095-3126.

[3] Gianmarco Manzini (2009), “ A Second-Order TVD

in Simulation, Vol.79, pp.2403-2428.

[6] John B. Bell, Phillip Colella, & John A. Trangenstein