  A new one-dimensional, inviscid, and vertically integrated disk model with
prescribed infall is presented. The flow is computed using a second-order
shock-capturing scheme. Included are vertical infall, radial infall at the
outer radial boundary, radiative cooling, stellar irradiation, and heat
addition at the disk-surface shock. Simulation parameters are chosen to target
the L1527 IRS disk which has been observed using ALMA (Atacama Large Millimeter
Array). The results give an outer envelope of radial infall and $u_\phi \propto
1/r$ which encounters a radial shock at $r_\mathrm{shock} \sim 1.5\ \times$ the
centrifugal radius ($r_\mathrm{c}$) across which the radial velocity is greatly
reduced and the gas temperature rises from a pre-shock value of $\approx 25$ K
to $\approx 180$ K over a spatially thin region calculated using a separate
shock structure code. At $r_\mathrm{c}$, the azimuthal velocity $u_\phi$
transitions from being $\propto 1/r$ to being nearly Keplerian. These results
qualitatively agree with recent ALMA observations which indicate a radial shock
where SO is sublimated as well as a transition from a $u_\phi \sim 1/r$ region
to a Keplerian inner disk. However, in one set of observations, the
position-velocity map of cyclic-C$_3$H$_2$, together with a certain ballistic
maximum velocity relation, has suggested that the radial shock coincides with a
ballistic 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 given
by our simulations. It is argued that radial velocity plots from previous
magnetic rotating-collapse simulations also indicate that the radial shock is
located outward of $r_\mathrm{c}$. The discrepancy with observations is
analyzed and discussed, but remains unresolved.
