Non-uniform knot (NUK) SIAC post-processing of flow fields produced through unstructured grid adaptation and optimization

Abstract

As the finite element method (FEM) and the finite volume method (FVM), both their traditional and high-order variants, continue their proliferation into various applied engineering disciplines, adaptive mesh refinement and optimization strategies have increased in their importance when solving real-world computational fluid mechanics applications. The post-processing and visualization of the resulting flow fields present two significant analysis and visualization challenges. The first challenge is the handling of elemental continuity, which is often only C0 continuous (in continuous Galerkin methods) or piecewise discontinuous (in discontinuous Galerkin methods). The second challenge is that, depending on the flow regime and the geometric configurations for which adaptive meshing strategies are used, the meshes generated are often highly anisotropic. The (uniform knot) line-SIAC (L-SIAC) filter has been proposed as a way of handling elemental continuity issues in an accuracy-conserving manner with the added benefit of casting the data in a smooth context even if the representation is element discontinuous. In this paper, we demonstrate that the state-of-the-art adaptive L-SIAC filter, designed for mildly anisotropic meshes, suffers degradation in the quality of the post-processed solution when applied to the types of highly anisotropic meshes produced through adaptive mesh refinement and optimization. Hence, a new Non-Uniform Knot (NUK) L-SIAC filter is proposed that automatically conforms to the underlying mesh anisotropy. We demonstrate that the new filter behaves similarly to the adaptive L-SIAC filter when applied to uniform and mildly anisotropic meshes, and furthermore we show the superiority of the NUK L-SIAC filter when applied to highly anisotropic meshes. The newly formulated filter is applied to 2D canonical scalar fields and used to visualize 2D and 3D fluid flow simulation results.