  We study supersymmetric domain wall solutions in four dimensions arising from
the compactification of type II supergravity on a SU(3)xSU(3) structure
manifold. Using a pure spinor approach, we show that the supersymmetry
variations can be reinterpreted as a generalisation of the Hitchin flow
equations and describe the embedding of a SU(3)xSU(3) structure manifold into a
G_2xG_2 structure manifold. We find a precise agreement between the four- and
ten-dimensional supergravity results. The flow equations derived here should
have applications in constructing the gravity duals of Chern-Simons-matter
conformal field theories.
