Pre-/post-processing & performance
Authors: Kirilov Kaloyan , Sanderson Allen , Kirby Mike 
Published: June 2023

Recent advances in NekMesh – mesh generation and adaptation

High-order mesh generation tools typically adopt the bottom-up approach - first creating a valid linear mesh followed by high-order tools for mesh curving. This poses a significant challenge for the linear mesh generation when very complex geometries are considered. Alternatively, one can produce the linear mesh with a third-party/commercial mesh generator and curve it in-house. NekMesh did have such capability, limited to a projection of only the edge quadrature points on the CAD. Now we present a complete redesign of this pipeline, which does not only projects edge and face nodes to the CAD B-Rep, but also integrates all NekMesh high-order modules for surface and volume optimizations, boundary-layer splitting and untangling into the process.

By implementing this new pipeline, we have achieved the unique capability to produce meshes that exhibit similar surface volume quality to the ones produced with the bottom-up approach, but also with the flexibility, robustness and user-friendly graphical user interface (GUI) of the commercial mesh generator. To demonstrate the capabilities of our new pipeline and showcase the improved mesh quality, we will show various simple and automotive geometries.

The second part of this talk focuses on a posteriori mesh adaptation for compressible flows, specifically highlighting current activities in NekMesh and Nektar++. Initially, we will provide a brief overview of the existing r p adaptation techniques and the new isoparametric h-adaptation. Then, these will be combined in r-p, h-p and h-r-p adaptations, showing the advantages of applying all three adaptation techniques simultaneously.

Exploiting Heterogeneous Systems – GPUs

To exploit parallelism, many codes are being deployed on heterogeneous systems so to make use of GPUs. Those developing codes have two options, write for a specific hardware (CUDA, HIP, SYCL, etc) or utilize a middle layer, Kokkos that encapsulates different hardware. In this talk the lessons learned from working on two different codes that utilize Kokkos and how these lessons can help guide Nektar++ as it transitions to heterogeneous systems.

Non-uniform Knot (NUK) SIAC Post-processing of Flow Fields Produced Through Unstructured Grid Adaptation and Optimization

The post-processing and visualization of 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 other considerations, 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 talk, we demonstrate that the state-of-the-art
adaptive L-SIAC filter, designed for 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.