  In circumstellar disks, the size of dust particles varies from submicron to
several centimeters, while planetesimals have sizes of hundreds of kilometers.
Therefore, various regimes for the aerodynamic drag between solid bodies and
gas can be realized in these disks, depending on the grain sizes and
velocities: Epstein, Stokes, and Newton, as well as transitional regimes
between them. For small bodies moving in the Epstein regime, the time required
to establish the constant relative velocity between the gas and bodies can be
much less than the dynamical time scale for the problem - the time for the
rotation of the disk about the central body. In addition, the dust may be
concentrated in individual regions of the disk, making it necessary to take
into account the transfer of momentum between the dust and gas. It is shown
that, for a system of equations for gas and monodisperse dust, a semi-implicit
first-order approximation scheme in time in which the interphase interaction is
calculated implicitly, while other forces, such as the pressure gradient and
gravity are calculated explicitly, is suitable for stiff problems with intense
interphase interactions and for computations of the drag in non-linear regimes.
The piece-wise drag coefficient widely used in astrophysical simulations has a
discontinuity at some values of the Mach and Knudsen numbers that are realized
in a circumstellar disk. A continuous drag coefficient is presented, which
corresponds to experimental dependences obtained for various drag regimes.
