Techniques for unstructured mesh adaptation with elliptic smoothing

A new mesh adaptation method for unstructured grids is presented. The technique uses virtual control volumes that are iteratively manipulated to conform the mesh to match either a Riemannian metric tensor field or an equal distribution of scalar weights. Forcing functions similar to those used for structured grids are employed such that the resulting meshes can be compared with those generated using the new adaptation method. Several test cases using analytic functions to drive the mesh adaptation are presented and compared with the new method. Mesh adaptation results driven by solution data are also compared to those adapted using analytical functions, as well as those adapted using the virtual control volume approach. Strengths and weaknesses of the various adaptation methods are investigated, and suggestions for further research are discussed.