Accurate boundary-conforming curvilinear hexahedral mesh generation

Develop computational geometry methods to generate accurate, boundary-conforming curvilinear hexahedral meshes suitable for high-order CFD simulations using hexahedral elements.

Background

The paper emphasizes that nekCRF and its underlying solver nekRS achieve optimal performance with hexahedral elements. For complex geometries, accurate boundary-conforming curvilinear hexahedral meshes are required to preserve geometric fidelity and support high-order spectral element discretizations.

The authors note that generating such meshes is challenging and currently unsolved, highlighting overset grids as a partial mitigation. They contrast this with the greater geometric flexibility of unstructured simplicial or hybrid meshes, which face performance trade-offs on modern architectures, underscoring the importance of resolving the hexahedral mesh generation problem.

References

For optimal performance, the code supports only hexahedral elements, although geometric modeling can be challenging as the generation of accurate, boundary-conforming curvilinear hexahedral meshes remains an open problem.

— nekCRF: A next generation high-order reactive low Mach flow solver for direct numerical simulations  (2409.06404 - Kerkemeier et al., 2024) in Section 1 (Introduction)