  In this paper we describe a new method for studying the hydrodynamical
problem of a planet embedded in a gaseous disk. We use a finite volume method
with an approximate Riemann solver (the Roe solver), together with a special
way to integrate the source terms. This new source term integration scheme
sheds new light on the Coriolis instability, and we show that our method does
not suffer from this instability. The first results on flow structure and gap
formation are presented, as well as accretion and migration rates. For Mpl <
0.1 M_J and Mpl > 1.0 M_J (M_J = Jupiter's mass) the accretion rates do not
depend sensitively on numerical parameters, and we find that within the disk's
lifetime a planet can grow to 3-4 M_J. In between these two limits numerics
play a major role, leading to differences of more than 50 % for different
numerical parameters. Migration rates are not affected by numerics at all as
long as the mass inside the Roche lobe is not considered. We can reproduce the
Type I and Type II migration for low-mass and high-mass planets, respectively,
and the fastest moving planet of 0.1 M_J has a migration time of only 2.0 10^4
yr.
