Mesh improvement methodology for 3D volumes with non-planar surfaces

A mesh improvement methodology is presented which aims to improve the quality of the worst elements in 3D meshes with non-planar surfaces which cannot be improved using traditional methods. A numerical optimisation algorithm, which specifically targets the worst elements in the mesh, but is a smooth function of nodal positions is introduced. A method of moving nodes on curved surfaces whilst maintaining the domain geometry and preserving mesh volume is proposed. This is shown to be very effective at improving meshes for which traditional mesh improvers do not perform well.