  An immersed-boundary (IB) method is proposed and applied in the gas-kinetic
BGK scheme to simulate incompressible/compressible viscous flow with
stationary/moving boundary. In present method the ghost-cell technique is
adopted to fulfill the boundary condition on the immersed boundary. A novel
idea "local boundary determination" is put forward to identify the ghost cells,
each of which may have several different ghost-cell constructions corresponding
to different boundary segments, thus eliminating the singularity of the ghost
cell. Furthermore, the so-called "fresh-cell" problem when implementing the IB
method in moving-boundary simulation is resolved by a simple extrapolation in
time. The method is firstly applied in the gas-kinetic BGK scheme to simulate
the Taylor-Couette flow, where the second-order spatial accuracy of the method
is validated and the "super-convergence" of the BGK scheme is observed. Then
the test cases of supersonic flow around a stationary cylinder, incompressible
flow around an oscillating cylinder and compressible flow around a moving
airfoil are conducted to verify the capability of the present method in
simulating compressible flows and handling the moving boundary.
