Scaled three-dimensional simulations of giant-planet accretion and disk clearing

We develop accelerated three-dimensional simulations of growing planet pairs that draw on a finite gas reservoir. An annulus compression (Scaling A) shortens the predicted clearing time and shrinks the computational domain at equal grid resolution while preserving key physical parameters. Planetary seeds start with Hill radii equal to the disk scale height, retaining three-dimensional accretion. We demonstrate the method in scaled PDS 70 and Solar-System configurations, assuming perfect Hill capture by growing planets on circular orbits. We compare Scaling A at radius-compression factor Γ=1.75 with the unscaled PDS system at matched resolution, through a 1% reduction of the interplanetary gas inventory. The scaled run is nearly an order of magnitude faster, with similar accreted mass and a comparable partition of gas between the planets. For the Solar-System configuration at Γ=3, the scaling forecasts a speedup of nearly two orders of magnitude at equal local resolution. The scaling is complementary to orbital advection. On eight CPU cores of a desktop computer, the scaled PDS 70 and Solar-System runs reduce the gas inventory between the orbiting planets by roughly half in less than a day. Accretion-driven orbital convergence narrows the shared feeding zone and, together with gas clearing, limits the planetary growth budget. In our scaled PDS 70 and Solar-System runs, the angular momentum carried by meridional inflow directly constrains delivery theory. These results establish a practical route to testing accretion theory against simulations at matched scaled parameters, before applying it to unscaled planetary systems.