A Feature-Based Grid Adaptation Method with Gradient-Based Smoothing

A Feature-Based Grid Adaptation Method with Gradient-Based Smoothing

Weiyang Lin, Steve L. Karman

The primary interest of this report is the feature-based adaptation methods, as opposed to the so-called error-based or adjoint-based adaptations. The overall algorithm may be described as an iterative procedure of adding and deleting points so that the places of high-gradients may be sufficiently resolved. 

An adapted grid may be illustrated using the figure below:

A statistic technique is used to decide if an edge is to be refined or coarsened, and a triangular sub-division is processed after the edges being marked as either case. The deletion has to be accompanied with a re-connection of mesh points. For simplicity the Trimesh algorithm is used along after each deletion. The Trimesh algorithm can also be employed to optimize the connectivity of the mesh after each refinement pass.

A smoothing procedure is usually called after each adaptation pass to improve the mesh quality. In this report, the optimization-based smoothing is used [1]. The traditional smoothing, optimization-based adaptation (OBA) and another point-movement method are described in the following sections.

The test case is chosen to be the "fishtail" case, where Mach number of 0.95 and angle-of-attack of 0 are run on a NACA0012 airfoil. Start from a relatively uniform grid:

The adapted grid based on pressure gradient information are (iteration 1 and iteration 8, respectively)

Formulations and more details can be found in the report here [PDF]. 

Reference

Karman, S. L. "Adaptive Optimization-Based Smoothing for Tetrahedral Meshes," AIAA SciTech 2015 conference. Vol. 14, 2015.