  In the computation of compressible fluid flows, numerical boundary conditions
are always necessary for all physical variables at computational boundaries
while just partial physical variables are often prescribed as physical boundary
conditions. Certain extrapolation technique or ghost cells are often employed
traditionally for this issue but spurious wave reflections often arise to cause
numerical instability. In this paper, we associate this issue with the
one-sided generalized Riemann problem (GRP) solver motivated by the accelerated
piston problem in gas dynamics so that the extrapolation technique can be
actually avoided. In fact, the compatibility arguments naturally requires to
formulate the one-sided generalized Riemann problem and incorporate it into the
numerical procedure of boundary conditions. As far as the interaction of
nonlinear waves with physical boundaries, such a one-sided GRP solver shows
significant effects, as numerical experiments demonstrate, on avoiding spurious
wave reflections at the computational boundaries.
