Tensor calculus in spherical coordinates using Jacobi polynomials, Part-II: Implementation and Examples

Understand

We present a simulation code which can solve broad ranges of partial differential equations in a full sphere.

• The code expands tensorial variables in a spectral series of spin-weighted spherical harmonics in the angular directions and a scaled Jacobi polynomial basis in the radial direction, as described in Part-I.
• Nonlinear terms are calculated by transforming from the coefficients in the spectral series to the value of each quantity on the physical grid, where it is easy to calculate products and perform other local operations.
• The expansion makes it straightforward to solve equations in tensor form (i.e., without decomposition into scalars).