Immersed boundary method (IBM) vs Dynamic meshing
 

IBM can be used to simulate the moving rigid body without remeshing, my question is compare with dynamic meshing which one is better, more accurate? Anyone have any idea about this?

IBM also required remeshing when applied to moving rigid body cases. The one big advantage with the IBM method is the ability to employ a simple finite difference/ volume scheme on a cartesian mesh.

I think it depends on your application. I have tried both for my moving airfoil and found that if you can use structured grid with dynamics meshing, it's much faster than IBM. IBM is more versatile but it is much slower and requires much more higher resolution for the same Re.

What do you think about IBM to deal with inviscid or viscous compressible flow. Is IBM promissing for the treatment aeroelastics?

Deforming-mesh approaches can be conservative over a timestep, making them attractive for small deformations. However, for gross boundary motions associated with large time steps the quality of the difference stencil can degrade severely due to this distortion.
The immersed boundary (IB) method simplifies the grid generation process for the simulation of flows with complex and/or moving solid boundaries, by avoiding the need for a body-fitted mesh.

no people give some conclusions about Immersed boundary method