黎曼问题II的宏观和微观解的比较。两相激波管
Comparison of Macro- and Microscopic Solutions of the Riemann Problem II. Two-Phase Shock Tube
摘要：
黎曼问题是计算流体力学数值方法的基本组成部分之一。尽管如此，在复杂热力学行为的理论和建模方面仍然存在开放性问题和差距。在这个系列中，我们比较了宏观流动方程的数值解与分子动力学模拟数据。为了使分子动力学在足够大的时间和空间尺度上，我们选择了截断和移位的Lennard-Jones势，对于该势，也可以获得高度精确的状态方程。两相黎曼问题的比较显示，其中涉及液体和蒸汽相，与正在进行的相变。双曲性的丧失允许异常波结构的发生。我们成功地比较了分子动力学的数据与两个宏观数值解通过假设本地相平衡或施加动力学关系，并允许亚稳态。
英文摘要：
The Riemann problem is one of the basic building blocks for numerical methods in computational fluid mechanics. Nonetheless, there are still open questions and gaps in theory and modelling for situations with complex thermodynamic behavior. In this series, we compare numerical solutions of the macroscopic flow equations with molecular dynamics simulation data. To enable molecular dynamics for sufficiently large scales in time and space, we selected the truncated and shifted Lennard-Jones potential for which also highly accurate equations of state are available. A comparison of a two-phase Riemann problem is shown, which involves a liquid and a vapor phase, with an undergoing phase transition. The loss of hyperbolicity allows for the occurrence of anomalous wave structures. We successfully compare the molecular dynamics data with two macroscopic numerical solutions obtained by either assuming local phase equilibrium or by imposing a kinetic relation and allowing for metastable states.
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