In this article, we present a front capturing method for compressible reactive flows, where a shock tracking technique is applied with level set method. In stiff reaction problems, the difficulty arises when the time scale of the source term is significantly shorter than the time scale of the homogeneous conservation law. The spurious numerical phenomenon may occur due to the smeared out shock profiles. In order to overcome the difficulty, the detonation front is captured sharply by level set technique, and a modified finite volume scheme is developed at the computational cells cut by detonation front. The mass, momentum, and energy transitions are occurred on shock front for chemical reactive flows. In our method, the interface exchanges are calculated by considering a Riemann problem. Unlike the standard level set/ghost fluid method, our method can maintain the conservation on the shock discontinuity. One- and two-dimensional numerical examples including stable and unstable detonation problems are illustrated to verify the good reliability and robustness of our method.

中文翻译：

---

反应性欧拉方程的水平集方法前沿捕获

在本文中，我们提出了一种用于可压缩反应流的前端捕获方法，其中使用水平集方法应用了冲击跟踪技术。在刚性反应问题中，当源项的时间尺度明显短于齐次守恒定律的时间尺度时，就会出现困难。由于模糊的冲击剖面，可能会出现虚假数值现象。为克服这一困难，采用水平集技术对爆轰前沿进行了清晰捕捉，并在爆轰前沿切割的计算单元上开发了一种改进的有限体积方案。质量、动量和能量转换发生在化学反应流的激波前沿。在我们的方法中，界面交换是通过考虑黎曼问题来计算的。与标准水平集/幽灵流体方法不同，我们的方法可以保持激波不连续性的守恒。包括稳定和不稳定爆轰问题的一维和二维数值例子被说明，以验证我们方法的良好可靠性和鲁棒性。