Adaptive optimization-based improvement of tetrahedral meshes

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