Adaptive deformation of 3D unstructured meshes with curved body fitted boundaries with application to unsteady compressible flows

We present an adaptive moving mesh method for unstructured meshes which is a three-dimensional extension of the previous works of Ceniceros et al. [10], Tang et al. [40] and Chen et al. [11]. The iterative solution of a variable diffusion Laplacian model on the reference domain is used to adapt the mesh to moving sharp solution fronts while imposing slip conditions for the displacements on curved boundary surfaces. To this aim, we present an approach to project the nodes on a given curved geometry, as well as an a-posteriori limiter for the nodal displacements developed to guarantee the validity of the adapted mesh also over non-convex curved boundaries with singularities. We validate the method on analytical test cases, and we show its application to two and three-dimensional unsteady compressible flows by coupling it to a second order conservative Arbitrary Lagrangian-Eulerian flow solver.