Based on the stratified approximation, we have developed a semi-implicit spherical spectral method to perform the global simulations of compressible convection in stars. In this method, a full set of three-dimensional compressible hydrodynamic equations with rotation has been solved. With the semi-implicit treatment, we are able to overcome the severe time step problem arising from the restricted CFL condition associated with acoustic waves. The numerical scheme is both accurate and efficient, based on fast spectral transforms on the spatial directions. We have applied this method to investigate the effects of solid core size on the surface wind of giant planets. The result shows that the Reynolds stress plays an important role in driving the prominent equatorial zonal jet, and the width of the zonal jet is basically controlled by the tangent cylinder associated with the solid core when the solid core size is large.

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