A method to generate unstructured adaptive 2-D meshes is presented for simulating flows with moving bodies. Delaunay triangulation criterion in conjunction with the automatic point creation is used to generate 2-D unstructured grids. A local grid regeneration method is proposed to cope with moving boundaries. Numerical examples include a flow field induced by a moving circle plate, the interactions of shock waves with movable bodies and the movement of a projectile within a ram accelerator, illustrating an efficient and robust mesh generation method developed in the paper.