Section of the grid around a planet (red dot) and its Hill Radius R_H shown as a red circle. The smaller dashed circles have radii of R_H/ 2 and R_H/ 4. The accretion mechanism we use removes gas from the lighter and darker shaded cells. In the darker shaded cells the accretion fraction is increased by a factor of two. Because the planet is allowed to move in the grid it is not centered in a cell or located on cell boundaries.