Unstructured Mesh Adaptation for Moving Bodies in Immersed Boundary Methods

The paper presents a method for simulating the flow of a viscous compressible gas around a moving obstacle, specified by the immersed boundary method on a simply connected unstructured mesh, and the features of its application for bodies of different configuration. An advantage of the developed moving-mesh method is that it keeps the topology of an initial mesh and 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 the distance and normal to the body surface. The paper also describes a special technique to improve the efficiency of adaptation. The technique is based on the prediction of the body location in some automatically chosen time. This trick allows to find the coordinates of mesh vertices during the predicted time interval by interpolation. The integral strategy combining the immersed boundary method with the developed moving-mesh adaptation is tested on several model cases in twoand three-dimensional formulations. However, the paper does not consider the numerical results of the cases, it is mostly targeted at the meshing details.