Coupling a mass‐conserving semi‐Lagrangian scheme (SLICE) to a semi‐implicit discretization of the shallow‐water equations: Minimizing the dependence on a reference atmosphere
Coupling a mass‐conserving semi‐Lagrangian scheme (SLICE) to a semi‐implicit discretization of the shallow‐water equations: Minimizing the dependence on a reference atmosphere
复制标题
将质量守恒半拉格朗日方案（SLICE）与浅水方程的半隐式离散耦合：最小化对参考大气的依赖
DOI：
10.1002/qj.517
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发表时间：
2010
影响因子：
8.9
通讯作者：
A. Staniforth
中科院分区：
文献类型：
--
作者：
J. Thuburn;M. Zerroukat;N. Wood;A. Staniforth
在最近的一篇文章中，将一个保守的半拉格朗日质量输运格式SLICE耦合到一个求解浅水方程的半隐式半拉格朗日格式。该算法涉及非线性Helmholtz问题在每个时间步长的解，该问题是通过迭代解一个线性“内部”Helmholtz问题来实现的；该框架以及线性Helmholtz算子本身与用于质量传输的非保守内插半拉格朗日格式是相同的。然而，为了做到这一点，在离散中引入了地球位势的参考值。这里表明，这导致了结果对该参考值的弱依赖性。因此，提出了一种替代耦合，它保持相同的解框架和线性Helmholtz算子，但在非线性求解器收敛时，不依赖于参考值。然而，为了在大时间步长下保持准确性，该方法需要修改Slice执行其重新映射的方式。消除对参考值的依赖的一个优点是，该方案随后提供一致的示踪剂传输。版权所有©2010皇家气象学会和皇冠版权所有。作者：John Wiley&Sons，Ltd.
In a recent paper, a conservative semi‐Lagrangian mass transport scheme SLICE has been coupled to a semi‐implicit semi‐Lagrangian scheme for the shallow‐water equations. The algorithm involves the solution at each timestep of a nonlinear Helmholtz problem, which is achieved by iterative solution of a linear ‘inner’ Helmholtz problem; this framework, as well as the linear Helmholtz operator itself, are the same as would be used with a non‐conservative interpolating semi‐Lagrangian scheme for mass transport. However, in order to do this, a reference value of geopotential was introduced into the discretization. It is shown here that this results in a weak dependence of the results on that reference value. An alternative coupling is therefore proposed that preserves the same solution framework and linear Helmholtz operator but, at convergence of the nonlinear solver, has no dependence on the reference value. However, in order to maintain accuracy at large timesteps, this approach requires a modification to how SLICE performs its remapping. An advantage of removing the dependence on the reference value is that the scheme then gives consistent tracer transport. Copyright © 2010 Royal Meteorological Society and Crown Copyright. Published by John Wiley & Sons, Ltd.