有限体积框架下中尺度大气流动可压缩 Euler 方程不同表述形式的比较计算研究
A comparative computational study of different formulations of the compressible Euler equations for mesoscale atmospheric flows in a finite volume framework
AI总结：
本文在有限体积压力求解框架下比较三种弱可压缩 Euler 方程守恒形式，经六个平坦地形与山地基准测试表明 CE3 最准确、可靠且稳健。
摘要：
我们考虑三种弱可压缩 Euler 方程的守恒形式，分别称为 CE1、CE2 和 CE3，目标是理解在有限体积环境中哪一种形式能够产生最准确、最稳健的基于压力的求解器。CE1 和 CE2 形式均以密度、动量和比焓书写，但对浮力项和压力梯度项采用两种不同处理：CE1 采用开源有限体积求解器（例如 OpenFOAM）中实现的标准压力分裂，而 CE2 采用计算大气研究中常见的典型压力分裂。CE3 形式以密度、动量和位温书写，其浮力项和压力项的处理与 CE2 相同。对于每种表述，我们都采用一种计算高效的分裂方法。通过六个涉及干燥空气越过平坦地形或山地流动的基准测试，对三种表述进行了全面评估和比较。我们发现，尽管基于 CE2 和 CE3 形式的求解器更为稳健，但三种模型都能够在平坦地形测试中给出准确结果。至于山地测试，CE1 解变得不稳定，而 CE2 和 CE3 模型给出的结果与文献中的数据非常吻合，其中 CE3 模型最为准确。因此，在使用基于压力的方法和有限体积法进行空间离散来模拟中尺度大气流动时，CE3 模型是最准确、最可靠且最稳健的。
英文摘要：
We consider three conservative forms of the mildly compressible Euler equations, called CE1, CE2 and CE3, with the goal of understanding which leads to the most accurate and robust pressure-based solver in a finite volume environment. Forms CE1 and CE2 are both written in density, momentum, and specific enthalpy, but employ two different treatments of the buoyancy and pressure gradient terms: for CE1 it is the standard pressure splitting implemented in open-source finite volume solvers (e.g., OpenFOAM), while for CE2 it is the typical pressure splitting found in computational atmospheric studies. Form CE3 is written in density, momentum, and potential temperature, with the buoyancy and pressure terms addressed as in CE2. For each formulation, we adopt a computationally efficient splitting approach. The three formulations are thoroughly assessed and compared through six benchmark tests involving dry air flow over a flat terrain or orography. We found that all three models are able to provide accurate results for the tests with a flat terrain, although the solvers based on the CE2 and CE3 forms are more robust. As for the mountain tests, CE1 solutions become unstable, while the CE2 and CE3 models provide results in very good agreement with data in the literature, the CE3 model being the most accurate. Hence, the CE3 model is the most accurate, reliable, and robust for the simulation of mesoscale atmospheric flows when using a pressure-based approach and space discretization by a finite volume method.
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