  Taking optically thin accretion flows as an example, we investigate the
dynamics and the emergent spectra of accretion flows with different outer
boundary conditions (OBCs) and find that OBC plays an important role in
accretion disk model. This is because the accretion equations describing the
behavior of accretion flows are a set of {\em differential} equations,
therefore, accretion is intrinsically an initial-value problem. We argue that
optically thick accretion flow should also show OBC-dependent behavior. The
result means that we should seriously consider the initial physical state of
the accretion flow such as its angular momentum and its temperature. An
application example to Sgr A$^*$ is presented.
