论文标题
海冰模拟的面向目标误差估计器和网状适应性
A goal oriented error estimator and mesh adaptivity for sea ice simulations
论文作者
论文摘要
我们第一次引入一个误差估计器，以实现描述海冰动力学的方程式的数值近似。估计器的想法是确定来自空间和时间离散化的不同误差贡献，以及来自耦合系统其他部分的冰分动量方程的分裂。误差估计器的新颖性在于考虑分裂误差，事实证明，由于网格分辨率的增加，其占主导地位。错误是在用户指定的功能输出中测量的，例如总海冰范围。误差估计器基于双重加权剩余方法，该方法要求解决其他双重问题以获取灵敏度信息。估计的误差可用于验证解决方案的准确性，更相关地通过引导自适应算法来降低离散误差，从而最佳地平衡网格大小和时间步长以提高模拟的效率。
For the first time we introduce an error estimator for the numerical approximation of the equations describing the dynamics of sea ice. The idea of the estimator is to identify different error contributions coming from spatial and temporal discretization as well as from the splitting in time of the ice momentum equations from further parts of the coupled system. The novelty of the error estimator lies in the consideration of the splitting error, which turns out to be dominant with increasing mesh resolution. Errors are measured in user specified functional outputs like the total sea ice extent. The error estimator is based on the dual weighted residual method that asks for the solution of an additional dual problem for obtaining sensitivity information. Estimated errors can be used to validate the accuracy of the solution and, more relevant, to reduce the discretization error by guiding an adaptive algorithm that optimally balances the mesh size and the time step size to increase the efficiency of the simulation.
