### All Figures

 Figure 1: Solution to the Riemann problem with initial conditions , , , and . The solid line represents the dust density and the dots represent the gas density, both at t=0.5. For the gas, the speed of sound was set to 1.0. Open with DEXTER

In the text

 Figure 2: Numerical results for the Riemann problem of Fig. 1 for gas (dots) and dust (solid line). The top row shows the density, the bottom row the velocity. Left panels: no gas-dust interaction. Middle panels: . Right panels: . Open with DEXTER

In the text

 Figure 3: Relative radial velocity of gas and dust (1 mm) in a disk without a planet. The dots represent the numerical solution, and the solid line represents Eq. (15). Open with DEXTER

In the text

 Figure 4: Close-up on a spiral density wave, with relative velocity arrows superimposed. Outside of the spiral wave, the dust drift is directed inward, according to Eq. (15). Close to the spiral, the particles move towards the centre of the wave. For 5 mm dust particles, as shown here, the maximum relative velocity is 2.6  10-6, in units of the orbital velocity of the planet. Open with DEXTER

In the text

 Figure 5: Surface density of gas and dust (s=0.1 cm) after 500 orbits of a 0.1   planet at (opposite to the planet). The dust density is multiplied by 100. The dots indicate the positions of the 2:3, the 3:2, and the 2:1 resonances. Open with DEXTER

In the text

 Figure 6: Azimuthally averaged radial acceleration a of dust particles after 100 orbits of a 0.1   planet. The close-up shows a in the outer region of the disk. The 2:1 mean motion resonance is visible as a small bump in a. Open with DEXTER

In the text

 Figure 7: Radial density cut opposite to the planet for four different particle sizes after 100 orbits of a 0.1   planet. The dust densities are multiplied by 100. Open with DEXTER

In the text

 Figure 8: Radial density cut opposite to the planet for four different planetary masses after 100 orbits and for a particle size of 1 mm. The dust densities are multiplied by 100, and the planetary masses are in units of  . Open with DEXTER

In the text

 Figure 9: Surface density of 1 mm dust particles after 100 orbits of a 0.5   planet. Open with DEXTER

In the text

 Figure 10: Azimuthal averages of the radial acceleration a (solid line) and gas surface density  (dashed line, shown for ) for a 1   planet after 400 orbits. Open with DEXTER

In the text

 Figure 11: Scatter plot of the relative velocity in the direction of a 0.1   planet. The distance to the planet is in units of the Roche lobe  , and the unit of relative velocity is the Kepler velocity at the position of the planet. The size of the dust particles in this simulation is 2 mm. Open with DEXTER

In the text

 Figure 12: Accretion of gas and dust onto a 0.1   planet. Left panel: gas and dust mass accreted on the planet. Right panel: relative accretion rate of dust with respect to the gas. For both panels, the dust mass is multiplied by 100 to compare it with the gas. Open with DEXTER

In the text