4 research outputs found
A Characteristic Mapping Method for Transport on the Sphere
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