On representing complex configurations as asymptotic geometry

Treating geometry as an asymptotic representation is a novel approach that allows the geometry to become a function of mesh resolution. Small-scale features are filtered and smoothed out based on the grid resolution. Increasing the mesh refinement allows the geometry to asymptote towards its exact shape. Treating geometry with an asymptotic representation allows for improvements in prismatic grid generation in computational fluid dynamics, specifically by smoothing poor visibility regions, and by smoothing away small-scale features that have a negligible effect on the overall flow solution. The level set method, coupled with min/max flow, is used to filter out small-scale features based on the grid discretization size, thus smoothing the geometry. Detailed verification studies are employed in this work, showing that the method represents smooth surfaces with an order of accuracy of 2. Validation studies of the approach show asymptotic behavior of the surface area as the grid is refined. Further examples of the approach are presented, including examples of targeted filtering, where certain areas of interest are smoothed further while retaining the small-scale features in others.