SUMMARYWe propose and analyze an algorithm for the robust construction of curved meshes in two and three dimensions. The meshes are made of curved simplexes. The algorithm starts from a mesh made of straight simplexes, and using a linear elasticity analogy applied on well‐chosen data, one can generate a curved mesh. Note that if the initial mesh has a boundary layer, this method allows to conserve it on the final mesh. This algorithm is used on several airfoils in two and three dimensions, including a turbulent M6 wing. Copyright © 2014 John Wiley & Sons, Ltd.

We present an adaptive moving mesh method for unstructured meshes which is a threedimensional extension of the previous works of Ceniceros et al. Ceniceros2001[10], Tang et al.Tang2003 [40] and Chen et al. Chen2008[11]. The iterative solution of a variable di↵usion 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.

We present a parallel unstructured mesh adaptation algorithm based on iterative remeshing and mesh repartitioning. The algorithm rests on a two-level parallelization scheme allowing to tweak the mesh group size for remeshing, and on a mesh repartitioning scheme based on interface displacement by front advancement. The numerical procedure is implemented in the open source ParMmg software package. It enables the reuse of existing sequential remeshing libraries, a non-intrusive linkage with thirdparty solvers, and a tunable exploitation of distributed parallel environments. We show the efficiency of the approach by comparing interface displacement repartitioning with graph-based repartitioning, and by showing isotropic weak-scaling tests and preliminary anisotropic tests.