Conservation of properties in a free-surface model
Conservation of properties in a free-surface model
复制标题
自由表面模型中的性质守恒
DOI：
10.1016/s1463-5003(03)00009-x
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发表时间：
2004
期刊：
影响因子：
3.2
通讯作者：
J. Marshall
中科院分区：
文献类型：
--
作者：
J. Campin;A. Adcroft;C. Hill;J. Marshall
在高度坐标海洋模式中，示踪剂（温度、盐度或任何被动示踪剂）的自然守恒要求表面单元的厚度随自由表面位移而变化，从而导致非线性自由表面公式（NLFS）。然而，NLFS并不能保证精确的守恒，除非在实施过程中特别注意，特别是Griffies等人指出的时间步进方案（Monthly Weather Rev. 129（2001）1081）。本文提出了一个一般的方法来实现一个NLFS在保守的方式，使用隐式自由表面制定。详细介绍了两个示踪剂时间步进计划，无论是在时间和空间上的二阶：两个时间级的计划，如Lax-Wendroff计划，保证精确的示踪剂守恒;三个时间级的计划，如亚当斯-Bashforth II需要进一步调整，以实现精确的局部守恒和精确的全局守恒，防止长期漂移的模型示踪剂含量。由于该方法精确地保存了任何示踪剂，因此在局部和全局守恒之间不需要妥协。除了通常使用的向后时间步长外，隐式自由面公式还提供了节省能量的Crank-Nickelson时间步长选项。这些方法在理想化的实验中进行测试，旨在强调示踪剂和能量守恒的问题。测试表明，NLFS方法的能力，以保存示踪剂，在线性自由表面制剂。能量守恒检验表明，自由表面向后时间推进强烈阻尼的解决方案。与此相反，Crank-Nickelson时间步进精确地保存能量在纯线性的情况下，并确认NLFS改善相对于线性自由表面时，动量平流。
In height coordinate ocean models, natural conservation of tracers (temperature, salinity or any passive tracer) requires that the thickness of the surface cell varies with the free-surface displacement, leading to a non-linear free-surface formulation (NLFS). However, NLFS does not guarantee exact conservation unless special care is taken in the implementation, and in particular the time stepping scheme, as pointed out by Griffies et al. (Monthly Weather Rev. 129 (2001) 1081). This paper presents a general method to implement a NLFS in a conservative way, using an implicit free surface formulation. Details are provided for two tracer time stepping schemes, both second order in time and space: a two time-level scheme, such as Lax–Wendroff scheme, guarantees exact tracer conservation; a three time-level scheme such as the Adams–Bashforth II requires further adaptations to achieve exact local conservation and accurate global conservation preventing long term drift of the model tracer content. No compromise is required between local and global conservation since the method accurately conserves any tracer. In addition to the commonly used backward time stepping, the implicit free surface formulation also offers the option of a Crank–Nickelson time stepping which conserves the energy. The methods are tested in idealized experiments designed to emphasize problems of tracer and energy conservation. The tests show the ability of the NLFS method to conserve tracers, in contrast to the linear free-surface formulation. At test of energy conservation reveals that free-surface backward time-stepping strongly damps the solution. In contrast, Crank–Nickelson time stepping exactly conserves energy in the pure linear case and confirms the NLFS improvement relative to the linear free-surface when momentum advection is included.