Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
Smoothing unstructured grids is a critical component of many large-scale three-dimensional simulations. Few of the existing mesh smoothing techniques are capable of handling large unstructured meshes in complex geometries. For example, most smoothers generate unacceptable or even invalid grids in the neighborhood of extremely convex or concave boundaries. In contrast, a smoothing technique based on harmonic coordinates was developed by Hansen, Zardecki, Greening, and Bos, that is robust with respect to these geometric complexities. This technique defines a system of three quasi-linear diffusion equations, one for each coordinate direction. The coupling between components of this system is through the elements of the metric tensor, which defines the solution-dependent diffusion tensor. This grid smoothing is driven by a target metric tensor that is based on a coarse-graining (local averaging) of the current mesh. We use a standard vertex based Finite Element Method to discretize the variational formulation of this quasi-linear system of equations.
