  In this article, we introduce a new type of mean curvature flow for bounded
star-shaped domains in space forms and prove its longtime existence,
exponential convergence without any curvature assumption. Along this flow, the
enclosed volume is a constant and the surface area evolves monotonically.
Moreover, for a bounded convex domain in R n+1, the quermassintegrals evolve
monotonically along the flow which allows us to prove a class of
Alexandrov-Fenchel inequalities of quermassintegrals.
