关于超临界流体保持压力平衡的数值通量存在性
On the Existence of Pressure-Equilibrium-Preserving Numerical Fluxes for Supercritical Fluids
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中文总结 AI 辅助
本文提出超临界流体压力平衡保持数值通量存在性定理，将存在性关联到状态方程几何性质，并通过数值实验验证条件的严格性及数值问题机制。
中文摘要 AI 辅助
在这项工作中，我们为超临界流体的数值通量函数提出了一个新的存在性定理，该通量函数具有压力平衡保持（PEP）性质。特别地，我们刻画了满足代数PEP性质的一致数值通量函数的存在性。我们的理论将PEP格式的存在性与描述流体热力学性质的状态方程的几何性质联系起来。当同一等压线上的两个状态不满足这些几何性质时，在包含这些状态的域上，所考虑形式的PEP格式不存在。在我们的分析中，状态方程本身可以是完全一般的，只需满足一些基本的热力学原理。最近，针对一般状态方程的PEP相容性条件已被推导出来（见参考文献[channodal]），这些条件依赖于某些热力学导数的存在，而这些导数在基本热力学原理下并不保证有定义。我们理论中的几何条件不依赖于这些导数的存在，并且在这些导数有定义的情况下，可以恢复最近的相容性条件。最后，通过数值实验，我们针对两种超临界流体证明了我们的存在性条件是严格的，因此在我们指定的这些流体的域上，所考虑形式的PEP格式不存在。利用我们的几何视角，我们还阐明了PEP格式可能产生数值问题的机制，并通过数值实验进行了演示。
英文摘要
In this work we propose a new existence theorem for numerical-flux functions for supercritical fluids that are pressure-equilibrium-preserving (PEP). In particular, we characterize the existence of consistent numerical-flux functions that satisfy an algebraic PEP property. Our theory links the existence of PEP schemes to geometric properties of the equation of state describing the thermodynamics of the fluid. When these geometric properties fail for a pair of states on the same isobar, no PEP schemes of the considered form can exist on a domain containing those states. In our analysis the equation of state itself can be fully general only needing to satisfy some fundamental thermodynamic principles. Recently, PEP compatibility conditions for general equations of state have been derived [1] that rely on the existence of certain thermodynamic derivatives which are not guaranteed to be defined under fundamental thermodynamic principles. The geometric conditions in our theory do not depend on the existence of these derivatives and recover the recent compatibility conditions in the case that these derivatives are defined. Finally, using numerical experiments we demonstrate for two supercritical fluids that our existence conditions are restrictive and thus that no PEP schemes of the form we consider exist on the domain we specify for these fluids. Using our geometric perspective, we also shed light on mechanisms by which PEP schemes can develop numerical issues, which we also demonstrate using numerical experiments.
发表机构
- Delft University of Technology（代尔夫特理工大学）
- Centrum Wiskunde & Informatica（荷兰数学与计算机科学研究中心）
机构由 AI 辅助整理，请以论文原文为准。
