  In simulations of viscously evolving accretion disks, the inner boundary
condition is particularly important. If treated incorrectly, it induces
incorrect behavior very quickly, because the viscous time is shortest near the
inner boundary. Recent work has determined the correct inner boundary in
Eulerian simulations. But in quasi-Lagrangian simulations (e.g., SPH, moving
mesh, and mesh-less), where the inner boundary is modeled by removing mass
within a finite zone, the inner density profile typically becomes anomalously
depleted. Here we show how the boundary condition should be applied in such
codes, via a simple modification of the usual approach: when one removes mass,
one must speed up the remaining material so that the disk's angular momentum is
unchanged. We show with both 1D and 2D moving-mesh (AREPO) simulations that
this scheme works as desired in viscously evolving disks. It produces no
spurious density depletions and is independent of the mass removal rate,
provided that the disk is adequately resolved and that the mass removal rate is
not so extreme as to trigger instabilities. This "torque-free" mass removal
technique permits the use of quasi-Lagrangian codes to simulate viscously
evolving disks, while including a variety of additional effects. As an example,
we apply our scheme to a 2D simulation of an accretion disk perturbed by a very
massive planet, in which the disk is evolved to viscous steady state.
