New spectral methods for fluid dynamical applications on the sphere

许多大尺度地球物理系统的模拟，如气候、地幔对流和地核磁场的产生，都需要在球形几何中进行计算。传统的计算机模型相对较慢，因为在固定半径下相关物理变量（例如温度）的空间依赖性由有点复杂的数学函数表示，即所谓的“球谐函数”。在一个新的坐标系中发现了一种新的、更简单的表示法，这项工作涉及利用这种表示法来开发新的计算效率高的方法，以便在球面几何中模拟这些系统

Simulations of many large-scale geophysical systems, such as climate, mantle convection and magnetic field generation in the core require computations in a spherical geometry. Traditional computer models are relatively slow because the spatial dependence of relevant physical variables (e.g. temperature) at fixed radius are represented by somewhat complicated mathematical functions, the so-called 'spherical harmonics'. A new, simpler representation has been found in a new coordinate system and this work is concerned with exploiting this representation in the development of new computationally efficient methods for simulating these systems in a spherical geometry