论文标题
超相关欧拉方程的径向对称解
Radially symmetric solutions of the ultra-relativistic Euler equations
论文作者
论文摘要
根据压力$ p $，\ r^3 $的空间部分$ \ r^3 $，描述了理想气体的超相关EULER方程。研究了这些方程的径向对称解。为线性化系统提供了分析解决方案。对于原始的非线性方程，我们设计和分析了一个数值方案，用于在三个空间维度中模拟径向对称解。该方案的良好表现通过数值示例证明。特别是，观察到该方法具有准确捕获由原点的冲击波反射引起的压力奇异性形成。
The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure $p$, the spatial part $\underline{u} \in \R^3$ of the dimensionless four-velocity and the particle density $n$. Radially symmetric solutions of these equations are studied. Analytical solutions are presented for the linearized system. For the original nonlinear equations we design and analyze a numerical scheme for simulating radially symmetric solutions in three space dimensions. The good performance of the scheme is demonstrated by numerical examples. In particular, it was observed that the method has the capability to capture accurately the pressure singularity formation caused by shock wave reflections at the origin.
