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Many geophysical and astrophysical phenomena such as the generation ofthe magnetic fields, or the differential rotation observed in theatmospheres of the major planets are studied by means of numericalsimulations of the Navier-Stokes equations in rotating sphericalshells.Two different computational codes, spatially discretized usingspherical harmonics in the angular variables, are presented. The firstcode, PaRoDy, solves the magnetohydrodynamic anelastic convectiveequations with finite difference discretization in the radialdirection. This allows the parallelization on distributed memorycomputers to perform massive numerical simulations of second order intime. It is mainly designed to perform direct numerical simulations.The second code solves the fully spectral Boussinesq convectiveequations parallelized on shared memory architectures and it usesoptimized linear algebra libraries. High-order time integrationmethods are implemented to allow the use of dynamical systems toolsfor the study of complex dynamics.

simulation, numerical methods, parallelization