Multigrid Methods for Atmospheric Flow Problems

大气运动的大范围空间和时间尺度对数值天气预报和模拟提出了根本性的挑战。不仅在锋面和气旋等现象上存在空间差异，而且在发生的波浪运动类型上也存在空间差异。有效地求解运动方程并避免产生假解是相当复杂的。本研究的总体目标是研究多网格方法在大气模型中的潜在应用，作为克服这些困难的一种手段。这项研究将集中在两个主要领域。首先，首席研究员将通过开发三维半转可逆性关系的多网格求解器来扩展他目前关于非线性椭圆问题的快速多网格求解器的研究成果。该模型还研究了多网格处理与基于估计局部截断误差的自适应网格细化的耦合。其次，研究了原始方程模型中半隐式时差的多网格加速问题。

The wide range of space and time scales of atmospheric motions poses a fundamental challenge in numerical weather prediction and modeling. Not only is there spatial differences in phenomena such as fronts and cyclones, but also in the types of wave motions which occur. Solving the equations of motion efficiently and in a way that avoids the development of spurious solutions is quite complex. The overall goal of this research is to investigate the potential application of multigrid methods to atmospheric models as a means of overcoming some of these difficulties. The study will concentrate on two main areas. First, the principal investigator will extend his current results on fast multigrid solvers for nonlinear elliptic problems by developing a multigrid solver for the semigeostrophic invertibility relation in three dimensions. The coupling of the multigrid processing with adaptive mesh refinement based on the estimated local truncation error will also be studied in this model. Second, multigrid acceleration of semi-implicit time differencing in primitive equation models will be investigated.