A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers
A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers
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DOI：
10.1029/96jc02775
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发表时间：
1997-03-15
影响因子：
3.6
通讯作者：
Heisey, C
中科院分区：
文献类型：
--
作者：
Marshall, J;Adcroft, A;Heisey, C
本文描述了一个基于不可压缩的Navier-Stokes方程的海洋模式的数值实现，该模式是为研究小于海洋深度的水平尺度的海洋环流而设计的，直到全球尺度。采用“压力修正”方法，用泊松方程求解具有Neumann边界条件的压力场，其几何形状与大洋盆地一样复杂。这项研究的一个主要目标是使这种反演，从而使非静力海洋模拟在并行计算机上有效。压力场分为表面成分、静水成分和非静水成分。首先，像在静水模型中一样，对地表压力进行二维问题的反演，然后利用该问题对非静水压力进行三维反演。利用预条件共轭梯度迭代法对二维和三维对称椭圆算子进行了逆运算。设计了物理激励的预处理器，该预处理器可以有效地减少计算量和最小化处理器之间的通信。我们的方法利用了这样一个事实，即当运动的水平尺度变得比垂直尺度大得多时，运动变得越来越静水，三维泊松算符变得越来越各向异性，并由垂直轴主导。因此，使用了预条件，在静力极限中，它是泊松算子的精确积分，因此导致了从非静力极限无缝移动到静力极限的单一算法。因此，在流体静力学极限下，该模型是“快速的”，与目前使用的基于流体静力学原始方程的最快海洋气候模型相竞争。但随着分辨率的提高，模型的动力学渐近于Navier-Stokes方程，因此可以用来处理小尺度过程。采用有限体积法在空间中离散模型，其中属性通量被定义为垂直于描绘体积的面。这种方法使得对边界的一种新的处理成为可能，在这种处理中，毗邻底部或海岸的单元格可以呈现不规则的形状，并被“修剪”以适应边界。该算法可以方便地利用大规模并行计算机，并提出了一种区域分解，将垂直海洋柱分配给每个处理单元。得到的模型可以处理任意复杂的几何图形，是高效和可扩展的，并已映射到使用数据并行FORTRAN的连接机(CM5)和使用隐式并行语言ID的麻省理工学院数据流机器季风等大规模并行多处理器上。
The numerical implementation of an ocean model based on the incompressible Navier Stokes equations which is designed for studies of the ocean circulation on horizontal scales less than the depth of the ocean right up to global scale is described. A ''pressure correction'' method is used which is solved as a Poisson equation for the pressure field with Neumann boundary conditions in a geometry as complicated as that of the ocean basins. A major objective of the study is to make this inversion, and hence nonhydrostatic ocean modeling, efficient on parallel computers. The pressure field is separated into surface, hydrostatic, and nonhydrostatic components. First, as in hydrostatic models, a two-dimensional problem is inverted for the surface pressure which is then made use of in the three-dimensional inversion for the nonhydrostatic pressure. Preconditioned conjugate-gradient iteration is used to invert symmetric elliptic operators in both two and three dimensions. Physically motivated preconditioners are designed which are efficient at reducing computation and minimizing communication between processors. Our method exploits the fact that as the horizontal scale of the motion becomes very much larger than the vertical scale, the motion becomes more and more hydrostatic and the three-dimensional Poisson operator becomes increasingly anisotropic and dominated by the vertical axis. Accordingly, a preconditioner is used which, in the hydrostatic limit, is an exact integral of the Poisson operator and so leads to a single algorithm that seamlessly moves from nonhydrostatic to hydrostatic limits. Thus in the hydrostatic limit the model is ''fast,'' competitive with the fastest ocean climate models in use today based on the hydrostatic primitive equations. But as the resolution is increased, the model dynamics asymptote smoothly to the Navier Stokes equations and so can be used to address small-scale processes. A ''finite-volume'' approach is employed to discretize the model in space in which property fluxes are defined normal to faces that delineate the volumes. The method makes possible a novel treatment of the boundary in which cells abutting the bottom or coast may take on irregular shapes and be ''shaved'' to fit the boundary. The algorithm can conveniently exploit massively parallel computers and suggests a domain decomposition which allocates vertical columns of ocean to each processing unit. The resulting model, which can handle arbitrarily complex geometry, is efficient and scalable and has been mapped on to massively parallel multiprocessors such as the Connection Machine (CM5) using data-parallel FORTRAN and the Massachusetts Institute of Technology data-flow machine MONSOON using the implicitly parallel language Id.