# Rayleigh: MHD in Spherical Geometry

*Rayleigh*: MHD in Spherical Geometry#

Rayleigh solves the magnetohydrodynamic (MHD) equations, in a rotating frame, within spherical shells, using the anelastic or Boussinesq approximations. Derivatives in Rayleigh are calculated using a spectral transform scheme. Spherical harmonics are used as basis functions in the horizontal direction. Chebyshev polynomials are employed in radius. Time-stepping is accomplished using the semi-implicit Crank-Nicolson method for the linear terms, and the Adams-Bashforth method for the nonlinear terms. Both methods are second-order in time.

This documentation is structured into the following sections: