We introduce new coupling conditions for isentropic flow on networks based on an artificial density at the junction. The new coupling conditions can be derived from a kinetic model by imposing a condition on energy dissipation. Existence and uniqueness of solutions to the generalized Riemann and Cauchy problem are proven. The result for the generalized Riemann problem is globally in state space. Furthermore, non-increasing energy at the junction and a maximum principle are proven. A numerical example is given in which the new conditions are the only known conditions leading to the physically correct wave types. The approach generalizes to full gas dynamics.

中文翻译：

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网络上等熵流的新耦合条件

我们基于交界处的人工密度，为网络上的等熵流引入了新的耦合条件。通过对能量耗散施加条件，可以从动力学模型中得出新的耦合条件。证明了广义黎曼和柯西问题解的存在唯一性。广义黎曼问题的结果在状态空间中是全局的。此外，还证明了结点处的能量不增加和最大原理。给出了一个数值示例，其中新条件是导致物理上正确的波类型的唯一已知条件。该方法推广到完整的气体动力学。