Аннотация:The paper presents a method for simulating the flow of a viscous compressible gasaround a moving obstacle, specified by the immersed boundary method on a simply connectedunstructured mesh, and the features of its application for bodies of different configuration. Anadvantage of the developed moving-mesh method is that it keeps the topology of an initial meshand provides an anisotropic mesh refinement to the “immersed” surface of a streamlined body.The position and shape of the body are determined by the interpolation grid, which stores thedistance and normal to the body surface. The paper also describes a special technique toimprove the efficiency of adaptation. The technique is based on the prediction of the bodylocation in some automatically chosen time. This trick allows to find the coordinates of meshvertices during the predicted time interval by interpolation. The integral strategy combining theimmersed boundary method with the developed moving-mesh adaptation is tested on severalmodel cases in two- and three-dimensional formulations. However, the paper does not considerthe numerical results of the cases, it is mostly targeted at the meshing details.