  A new numerical finite difference code has been developed to solve a thermal
convection of a Boussinesq fluid with infinite Prandtl number in a
three-dimensional spherical shell. A kind of the overset (Chimera) grid named
``Yin-Yang grid'' is used for the spatial discretization. The grid naturally
avoids the pole problems which are inevitable in the latitude-longitude grids.
The code is applied to numerical simulations of mantle convection with uniform
and variable viscosity. The validity of the Yin-Yang grid for the mantle
convection simulation is confirmed.
