The Generation of Valid Curvilinear Meshes

It is now well-known that a curvilinear discretization of the geometry is most often required to benefit from the computational efficiency of high-order numerical schemes in simulations. In this article, we explain how appropriate curvilinear meshes can be generated. We pay particular attention to the problem of invalid (tangled) mesh parts created by curving the domain boundaries. An efficient technique that computes provable bounds on the element Jacobian determinant is used to characterize the mesh validity, and we describe fast and robust techniques to regularize the mesh. The methods presented in this article are thoroughly discussed in Ref. [1,2], and implemented in the free mesh generation software Gmsh [3,4].