分层海洋模式中气压梯度力的高精度有限体积公式
High-order accurate finite-volume formulations for the pressure gradient force in layered ocean models
摘要：
本文提出了一套计算分层海洋模式中气压梯度力的高精度有限体积公式。提出了一对新的方案，都是基于积分的周边的相关的动量控制体积的接触压力。这两种方法在控制体积几何形状的选择上有所不同。高阶精确的数值积分技术，在这两个计划中占的基本状态方程的定义和热力学配置文件的非线性，并详细讨论了相关的垂直插值和正交计划的细节。数值实验证实了两种方法的一致性，并证明了新方法在强倾斜分层几何、非线性状态方程定义和非均匀垂直层结剖面的情况下仍能保持流体静力和温压平衡.此外，一个方案是保持高水平的一致性，在存在非线性热力学分层。讨论了新的气压梯度力公式在混合垂直坐标和/或地形跟踪大气环流模式中的应用。
英文摘要：
The development of a set of high-order accurate finite-volume formulations for evaluation of the pressure gradient force in layered ocean models is described. A pair of new schemes are presented, both based on an integration of the contact pressure force about the perimeter of an associated momentum control-volume. The two proposed methods differ in their choice of control-volume geometries. High-order accurate numerical integration techniques are employed in both schemes to account for non-linearities in the underlying equation-of-state definitions and thermodynamic profiles, and details of an associated vertical interpolation and quadrature scheme are discussed in detail. Numerical experiments are used to confirm the consistency of the two formulations, and it is demonstrated that the new methods maintain hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer-wise geometry, non-linear equation-of-state definitions and non-uniform vertical stratification profiles. Additionally, one scheme is shown to maintain high levels of consistency in the presence of non-linear thermodynamic stratification. Use of the new pressure gradient force formulations for hybrid vertical coordinate and/or terrain-following general circulation models is discussed.
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