Numerical convergence of viscous‐plastic sea ice models
Numerical convergence of viscous‐plastic sea ice models
复制标题
粘塑性海冰模型的数值收敛
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
B. Tremblay
中科院分区：
文献类型：
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作者：
J. Lemieux;B. Tremblay
[1]本文研究了粘塑性海冰模型非线性求解器的收敛性。更具体地说，我们研究的非线性求解器是基于隐式解的线性方程组和外循环（OL）迭代（或伪时间步长）。当时间步长与强迫时间尺度相当时，少量的OL迭代导致模拟速度场中的误差与平均漂移具有相同的数量级。收敛速度慢是所有空间分辨率的问题，但随着网格的细化，收敛速度更慢。海冰建模社区用来评估收敛性的指标是误导性的。事实上，当执行10个OL迭代与6小时的时间步长，平均动能的包总是在2%的完全收敛值。然而，漂移的误差与平均漂移具有相同的数量级。此外，虽然40次OL迭代提供了VP解（屈服曲线内或屈服曲线上的应力状态），但该域的大部分区域的误差为0.5-1.0 cm s-1。最大的错误是本地化的大海冰变形的区域，其中存在强冰相互作用。为了准确地解决这些变形，我们发现需要超过100次OL迭代。为了得到一个连续可微的动量方程，我们用一个切双曲函数代替了粘性系数的公式。这将达到某个残差范数所需的OL迭代次数减少了1/2。
[1] We investigate the convergence properties of the nonlinear solver used in viscous-plastic (VP) sea ice models. More specifically, we study the nonlinear solver that is based on an implicit solution of the linearized system of equations and an outer loop (OL) iteration (or pseudo time steps). When the time step is comparable to the forcing time scale, a small number of OL iterations leads to errors in the simulated velocity field that are of the same order of magnitude as the mean drift. The slow convergence is an issue at all spatial resolution but is more severe as the grid is refined. The metrics used by the sea ice modeling community to assess convergence are misleading. Indeed, when performing 10 OL iterations with a 6 h time step, the average kinetic energy of the pack is always within 2% of the fully converged value. However, the errors on the drift are of the same order of magnitude as the mean drift. Also, while 40 OL iterations provide a VP solution (with stress states inside or on the yield curve), large parts of the domain are characterized by errors of 0.5–1.0 cm s−1. The largest errors are localized in regions of large sea ice deformations where strong ice interactions are present. To resolve those deformations accurately, we find that more than 100 OL iterations are required. To obtain a continuously differentiable momentum equation, we replace the formulation of the viscous coefficients with capping with a tangent hyperbolic function. This reduces the number of OL iterations required to reach a certain residual norm by a factor of ∼2.