An isoparametric approach to high-order curvilinear boundary-layer meshing
Comput. Meth. Appl. Mech. Eng., vol. 283, pp. 636–650 (2015)
@article{moxey-2015a,
title = {An isoparametric approach to high-order curvilinear boundary-layer meshing},
author = {Moxey, D. and Green, M. D. and Sherwin, S. J. and Peir{\'o}, J.},
journal = cmame,
volume = {283},
pages = {636--650},
year = {2015},
doi = {10.1016/j.cma.2014.09.019},
url = {http://www.sciencedirect.com/science/article/pii/S004578251400334X},
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 discretisation 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 10^6 and above.}
}
At high Reynolds numbers a mesh has to resolve a thin boundary layer, which means elements stretched heavily in the direction normal to the wall. This paper starts from a valid coarse mesh of high-order prisms against the wall and refines it using the isoparametric mapping those elements already carry, which allows very fine resolution across the layer. It gives conditions under which the refined prismatic or tetrahedral mesh is guaranteed valid, and meshes two aeronautical configurations at Reynolds numbers of a million and above.
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 discretisation 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 10^6 and above.