AI 中文总结
研究瞬态相对论流体动力学中以色列 - 斯图尔特框架下激波解正则性问题，通过数值模拟证实解连续性崩溃，提出三阶扩展和引入小数值体粘性两种正则化程序，有效扩展连续激波解范围，揭示该框架局限性。
AI 中文摘要
在这项工作中，我们证明了在以色列 - 斯图尔特框架下，一旦激波速度达到临界值，激波解就会失去正则性，并且在解中会出现间断，这可被解释为第二个激波。这个子激波是以色列 - 斯图尔特理论中信息传播有限速度的结果。我们进行了数值模拟以证实解的连续性崩溃。随后，我们提出了两种正则化程序来扩展连续激波解的范围。第一种采用三阶扩展，引入了新的动力学场，而第二种纳入了小的数值体粘性。两种方法都有效地提高了以色列 - 斯图尔特理论的最大传播速度，并扩展了正则激波解存在的范围。因此，我们证实这种正则性的丧失是以色列 - 斯图尔特框架的直接结果。这些结果表明，以色列 - 斯图尔特理论可能无法充分描述超相对论激波。
英文摘要
In this work, we demonstrate that shock solutions in the Israel-Stewart framework lose regularity once the shock velocity reaches a critical value, and a discontinuity emerges in the solution, which can be interpreted as a second shock wave. This subshock arises as a consequence of the finite speed of information propagation inherent to the Israel-Stewart theory. We then perform numerical simulations to confirm the breakdown of solution continuity. Subsequently, we propose two regularization procedures to extend the domain of continuous shock solutions. The first employs a third-order extension, which introduces new kinetic fields, while the second incorporates a small numerical bulk viscosity. Both methods effectively increase the maximum propagation speed of the Israel-Stewart theory and extend the range over which regular shock solutions exist. Thus, we confirm that this loss of regularity is a direct consequence of the Israel-Stewart framework. These results suggest that Israel-Stewart theory may not provide an adequate description of ultra-relativistic shock waves.
