自适应网格技术在数值模式中的应用研究 II.二维问题

用一个具有解析解的二维动力锋生成过程算例，对比自适应网格方案和固定网格方案的优劣，结果表明:同等误差要求下，固定网格方案的网格点数为自适应网格方案的3倍。从时间演化上看，自适应网格对温带气旋的预报，在同等误差要求下，可比固定网格的预报延长10小时以上。文章对加权系数选取及对解的影响进行了分析，从几个切面的计算结果展示了自适应网格对网格的优良安排并能抓住锋面特征结构。文章分析了光滑性、正交性对结果的影响。结果表明:网格的光滑性影响有一个优化值；在网格适当安排情况下，要适度考虑正交性。

A Study of Application of Adaptive Grids Technique in Numerical Model Part II: Two-Dimensional Case Test

A two-dimensional kinematic frontogenesis process is considered in examing the use of adaptive grids of numerical models. From the comparison of the numerical results using fixed and adaptive grids with exact solution, it is found that the adaptive runs with 1 / 3 fewer grid points has the same accuracy, and it can catch the structure of the front because of its excellent redistribution of grid points. The results also shows that the adaptive runs can increase by more than 10 hours for the forecasting of extratropical cyclone with the same accuracy in comparison with fixed grids. The sensitivity of results to the choice of weight function is great. There is an optimum value for grid smoothness and the errors increase as the grid orthogonality is considered.