Abstract
The generation of high-order curvilinear meshes for complex three-dimensional geometries is presently a challenging topic, particularly for meshes used in simulations at high Reynolds numbers where a thin boundary layer exists near walls and elements are highly stretched in the direction normal to flow. In this paper, we present a conceptually simple but very effective and modular method to address this issue. We propose an isoparametric approach, whereby a mesh containing a valid coarse discretization comprising of high-order triangular prisms near walls is refined to obtain a finer prismatic or tetrahedral boundary-layer mesh. The validity of the prismatic mesh provides a suitable mapping that allows one to obtain very fine mesh resolutions across the thickness of the boundary layer. We describe the method in detail for a high-order approximation using modal basis functions, discuss the requirements for the splitting method to produce valid prismatic and tetrahedral meshes and provide a sufficient criterion of validity in both cases. By considering two complex aeronautical configurations, we demonstrate how highly stretched meshes with sufficient resolution within the laminar sublayer can be generated to enable the simulation of flows with Reynolds numbers of 106 and above.
Highlights
The use of high-order methods in complex aeronautical geometries and their associated flows is attracting attention due to their low dispersion and diffusion errors and their potential to achieve exponential convergence [1]
The generation of high-order curvilinear meshes for complex three-dimensional geometries is presently a challenging topic, for meshes used in simulations at high Reynolds numbers where a thin boundary layer exists near walls and elements are highly stretched in the direction normal to flow
We propose an isoparametric approach, whereby a mesh containing a valid coarse discretization comprising of high-order triangular prisms near walls is refined to obtain a finer prismatic or tetrahedral boundary-layer mesh
Summary
The use of high-order methods in complex aeronautical geometries and their associated flows is attracting attention due to their low dispersion and diffusion errors and their potential to achieve exponential convergence [1]. There are some issues with this approach, the most serious being that there is no guarantee of obtaining a valid mesh at the end of the procedure These methods are all relatively expensive, meaning that when either high polynomial orders or large numbers of elements are desired for very thin boundary layer resolution, long generation times are required. In this article we propose a method which adopts a different approach to the generation procedure outlined above and that helps to address the problem of generating high-order meshes for high Reynolds number flows. We outline the spacing function used to determine the sizes of sub-elements in Section 2.5, and show how this can be varied between elements to provide a spatially-aware refinement procedure
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