Adaptive optimization-based smoothing for tetrahedral meshes

A tetrahedral mesh smoothing method is presented that uses an optimization-based node perturbation technique to minimize a cost function. The cost function is based on the element condition number of the surrounding tetrahedra. This condition number incorporates a weight matrix that transforms the element from physical space to a reference space. Feature-based adaptation is incorporated into the element weight matrix to influence the node perturbation scheme to favor non-unit aspect ratio elements. The smoothing scheme produces meshes that cluster grid points in high gradient regions of the selected adaptation function. Results for several inviscid, three-dimensional cases are included.