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We present a simulation code which can solve broad ranges of partialdifferential equations in a full sphere. The code expands tensorial variablesin a spectral series of spin-weighted spherical harmonics in the angulardirections and a scaled Jacobi polynomial basis in the radial direction, asdescribed in Part-I. Nonlinear terms are calculated by transforming from thecoefficients in the spectral series to the value of each quantity on thephysical grid, where it is easy to calculate products and perform other localoperations. The expansion makes it straightforward to solve equations in tensorform (i.e., without decomposition into scalars). We propose and study severalunit tests which demonstrate the code can accurately solve linear problems,implement boundary conditions, and transform between spectral and physicalspace. We then run a series of benchmark problems proposed in Marti et al(2014), implementing the hydrodynamic and magnetohydrodynamic equations. We areable to calculate more accurate solutions than reported in Marti et al 2014 byrunning at higher spatial resolution and using a higher-order timesteppingscheme. We find the rotating convection and convective dynamo benchmarkproblems depend sensitively on details of timestepping and data analysis. Wealso demonstrate that in low resolution simulations of the dynamo problem,small changes in a numerical scheme can lead to large changes in the solution.To aid future comparison to these benchmarks, we include the source code usedto generate the data, as well as the data and analysis scripts used to generatethe figures.

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