We 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.

Full Paper:
Abgrall R., Dobrzynski C. and Froehly A. (2014), A method for computing curved meshes via the linear elasticity analogy, application to fluid dynamics problems, International Journal for Numerical Methods in Fluids, 76, pages 246–266, doi: 10.1002/fld.3932.