Traditionally, adding cells to a mesh, known as H-refinement, was the primary means by which solution accuracy could be improved. The additional resolution enables the capturing of flow phenomena often diffused by coarser variations of the same mesh. Another technique used to improve spatial and temporal accuracy is by performing degree elevation, both for the assumed solution within a given element and for the element itself. In doing so, linear meshes can become curved with the addition of nodes along edges, faces, and in the interior. Fewer elements are then required to accurately represent curved geometry and capture complex flow features of interest.
There are two primary challenges associated with the degree elevation of linear elements: boundary conformance and curving of high aspect ratio cells encountered within the boundary layer region. In this webinar, we will address these challenges by demonstrating the generation of a linear mesh for the Rotor 37 geometry, followed by the elevation of the linear mesh. Because geometry-mesh associativity is known, inserted nodes are properly constrained to the underlying geometry. Additionally, our optimization-based smoothing scheme propagates boundary perturbations into the interior of the mesh, ultimately improving the quality of the resulting high-order mesh and ensuring its validity.
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