On mesh adaptation for supercomputer simulation of flows around solid bodies defined by immersed boundary method

Abstract

Abstract The paper presents the numerical method to simulate viscous compressible flows near moving bodies of different shapes on unstructured meshes. The boundary method is used to define the moving bodies. It allows us to operate in simply connected computational domains, while the solid objects are modeled by adding extra source terms in the governing gasdynamic equations. To improve the quality of mesh resolution near the boundary of immersed body, a specific method of dynamic mesh adaptation is developed. This method uses the variational approach. It moves the mesh nodes without changing the mesh topology. The body shape might be described analytically, however, in the general case, the level-set interpolation grid is used for this purpose. It serves as a carrier of the distance function values and its gradients. In the present work the combination of the described techniques is verified on the two-dimensional case which simulates the flow induced by the forced oscillation of a cylinder.