XSHELLS simulates incompressible fluids in a spherical cavity. In addition to the Navier-Stokes equation with an optional Coriolis force, it can also time-step the coupled induction equation for MHD (with imposed magnetic field or in a dynamo regime), as well as the temperature (and concentration) equation in the Boussinesq framework. Based also on a semi-spectral approach combining finite differences in radius and spherical harmonics, semi-implicit second-order time scheme.