Mesh generation in curvilinear domains using high‐order elements

The ability to construct suitable computational meshes is currently a significant limiting factor in the development of compact high‐order algorithms in very complex geometries. Compact high‐order algorithms such as spectral element or p ‐type finite element techniques offer the potential of high accuracy if the solution is smooth and a well‐behaved mapping exists between the local sub‐domains and a standard region. In this paper we address the problem of coupling high‐order algorithms with unstructured mesh generation and CAD representation techniques. We present three complementary strategies to alleviate the problem of generation of elemental regions with singular elemental mappings. The first strategy investigates the influence of an anisometric parametric surface representation on the quality of high‐order unstructured meshes. We show that a straightforward splitting of a standard linear mesh for use in a high‐order method can lead to the generation of distorted, possibly invalid, meshes even for simple computational domains such as cubes. The second strategy uses hybrid meshes applying prismatic elements near curvilinear boundaries. In the third and final strategy we investigate the use of curvature driven surface discretization to incorporate higher‐order information about the surface into the mesh generation. Using the computational reconstruction of the arterial bypass graft as an example computational domain we demonstrate how the combination of all three strategies leads to a valid high‐order discretization of the computational domain.