  Reliable tracking of moving boundaries is important for the simulation of
compressible fluid flows and there are a lot of contributions in literature. We
recognize from the classical piston problem, a typical moving boundary problem
in gas dynamics, that the acceleration is a key element in the description of
the motion and it should be incorporated into the design of a moving boundary
tracking (MBT) method. Technically, the resolution of the accelerated piston
problem boils down to a one-sided generalized Riemann problem (GRP) solver,
which is taken as the building block to construct schemes with the high order
accuracy both in space and time. In this paper we take this into account,
together with the cell-merging approach, to propose a new family of high order
accurate moving boundary tracking methods and verify its performance through
one- and two-dimensional test problems, along with accuracy analysis.
