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A new one-dimensional, inviscid, and vertically integrated disk model withprescribed infall is presented. The flow is computed using a second-ordershock-capturing scheme. Included are vertical infall, radial infall at theouter radial boundary, radiative cooling, stellar irradiation, and heataddition at the disk-surface shock. Simulation parameters are chosen to targetthe L1527 IRS disk which has been observed using ALMA (Atacama Large MillimeterArray). The results give an outer envelope of radial infall and $u_\phi \propto1/r$ which encounters a radial shock at $r_\mathrm{shock} \sim 1.5\ \times$ thecentrifugal radius ($r_\mathrm{c}$) across which the radial velocity is greatlyreduced and the gas temperature rises from a pre-shock value of $\approx 25$ Kto $\approx 180$ K over a spatially thin region calculated using a separateshock structure code. At $r_\mathrm{c}$, the azimuthal velocity $u_\phi$transitions from being $\propto 1/r$ to being nearly Keplerian. These resultsqualitatively agree with recent ALMA observations which indicate a radial shockwhere SO is sublimated as well as a transition from a $u_\phi \sim 1/r$ regionto a Keplerian inner disk. However, in one set of observations, theposition-velocity map of cyclic-C$_3$H$_2$, together with a certain ballisticmaximum velocity relation, has suggested that the radial shock coincides with aballistic centrifugal barrier, which places the shock at $r_\mathrm{shock} =0.5 r_\mathrm{c}$, i.e, inward of $r_\mathrm{c}$, rather than outward as givenby our simulations. It is argued that radial velocity plots from previousmagnetic rotating-collapse simulations also indicate that the radial shock islocated outward of $r_\mathrm{c}$. The discrepancy with observations isanalyzed and discussed, but remains unresolved.

Protostellar disks subject to infall: a one-dimensional inviscid model and comparison with ALMA observations