We developed a framework for numerical simulation of the aerodynamics of moving bodies prescribed by the immersed boundaries on unstructured meshes. To improve the accuracy of simulations, we use the dynamic mesh adaptation based on node-redistribution techniques. Its implementation implies the solution of additional differential equation governing the mesh movement. This method allows us to keep a topology of the initial mesh and does not significantly increase the computational costs. The technology is developed for 2D formulations and verified on model problems.