A method for computing curved meshes via the linear elasticity analogy, application to fluid dynamics problems
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.
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.