ITR: Collaborative Research on Multiresolution Adaptive Spectral Element Solvers for Atmospheric Fluid Dynamics

本项目将发展一种多分辨率数值方法来求解球上流体动力学的偏微分方程，并将其应用于实际的大气流动模拟。它的出发点是谱元法（SEM），它保留了球调和变换方法的谱精度，而没有后者在极点附近的问题。观察到通过SEM和多小波（在最精细尺度上）进行的空间离散是相同的，研究人员将开发一种自适应多分辨率多小波求解器，并使用标准大气模拟基准进行测试。虽然人们很清楚大气现象涉及强多尺度相互作用，但目前还没有自适应的多分辨率解算器。考虑到问题的多尺度性质的必要数学工具直到最近才出现，并形成了本研究的基础。该项目的成功将对大气模拟和天气预报的速度和准确性产生重大影响。

This project will develop a multiresolution numerical methodology for solving the partial differential equations of fluid dynamics on the sphere, and apply it to practical atmospheric-flow simulations. Its starting point is the spectral-element method (SEM), which retains the spectral accuracy of spherical-harmonic transform methods, without the latter's problems near the poles. Observing that the spatial discretization via SEM and via multiwavelets (on the finest scale) are the same, the researchers will develop an adaptive multiresolution multiwavelet solver, and test it using standard atmospheric simulation benchmarks.Although it is well understood that atmospheric phenomena involve strong multiscale interactions, today there are no adaptive multiresolution solvers. The necessary mathematical tools that take the multiscale nature of the problem into account have appeared only recently, and form the foundation for this research. The success of this project will have a significant impact on both the speed and the accuracy of atmospheric simulations and weather prediction.