A semi-Lagrangian method for the solution of the transport equation on a sphere is presented. The method evolves the inverse flow-map using the Characteristic Mapping (CM) [1] and Gradient-Augmented Level Set (GALS) [2] frameworks. Transport of the advected quantity is then computed by composition with the numerically approximated inverse flow-map. This framework allows for the advection of complicated sets and multiple quantities with arbitrarily fine-features using a coarse computational grid. We discuss the CM method for linear transport on the sphere and its computational implementation. Standard test cases for solid body rotation, deformational and divergent flows, and numerical mixing are presented. The unique features of the method are demonstrated by the transport of a multi-scale function and a fractal set in a complex flow environment.

翻译：介绍了一种半Lagrangian方法来解决球体上的运输方程。该方法使用特征绘图[1]和梯度降级标准标准值框架[2]来演化逆流图。平面量的运输随后以数字近似逆流图组成来计算。这个框架允许使用粗略的计算网格来对复杂机组和多量进行倾斜,使用任意的细微特性。我们讨论了球体线性运输的CM方法及其计算执行。介绍了固体体旋转、变形和不同流和数字混合的标准测试案例。该方法的独特特征表现为多尺度功能的运输以及复杂流环境中的分形装置。