High-order mesh generation for CFD solvers

Transcription

1 High-order mesh generation for CFD solvers M. Turner, D. Moxey, S. Sherwin, J. Peiró Department of Aeronautics, Imperial College London DiPaRT 2015 Annual Meeting, Bristol, UK 17 th November 2015

2 Overview Motivation The spectral/hp element method Challenges: mesh generation Some results Conclusions 2

3 Motivation Primary research goal is to investigate challenging external aerodynamics cases: High Reynolds numbers Complex three-dimensional geometries Large resolution requirements Transient dynamics Using high-order spectral/hp element method 3

4 Spectral/hp element method map from reference element st tensor product expansion Primarily tensor-product bases 4

5 Why high-order methods? Rotation of Gaussian bump in linear advection equation 5

6 Why high-order methods? Very good numerical properties: should therefore be better at tracking long-time transient structures Discrete operators are dense and have rich structure: computationally efficient & scale well but... Lots of specialised knowledge required One big challenge: mesh generation 6

7 High-order mesh generation (in theory) 7

8 High-order mesh generation Curving coarse meshes leads to invalid elements Most existing MG packages cannot deal with this 8

9 MG pipeline to date For complex geometries: Use commercial mesh generator for coarse straight-sided mesh (prism boundary, tet interior) Manipulate the mesh to make it high order Try to fix broken elements Pray 9

10 NACA 0012 wing tip Re = O(10 6 ) Strong wingtip vortex difficult to capture with RANS 10

11 Existing workflow Linear mesh from Star-CCM+ Convert to high-order Output high order mesh

12 NACA 0012 example Simulations at Re = 1.2m Highly unsteady, vortex dominated SVV-LES formulation of incompressible NS Lombard, Moxey, Hoessler, Dhandapani, Taylor and Sherwin to appear in AIAA J. (2015)

13 NACA 0012 example (a) (b) Exp. (c) Nektar LES. Uzun Fig.-2 9 SVV-iLES computed streamlines and normalized time-averaged axial velocity at the crossflow plane x/c = downstream of the trailing edge in b) compared against experi Cp Exp. - Chow et al. (AIAA 1997) 0.5 SVV-iLES - P= x/c Exp. - Chow et al. (AIAA 1997) SVV-iLES - P= Cp -0.5 (c).-0.5 Cp Cp mental results from Chow et al.[1], in -1(a) and previous LES results by by Uzun et al.[5], in Exp. - Chow et al. (AIAA 1997) SVV-iLES -0.5 P=3 SVV-iLES - P=5 SVV-iLES - P= (a) 0.5 x/c Exp. - Chow et al. (AIAA 1997) SVV-iLES - P=3 SVV-iLES - P=5 SVV-iLES - P= x/c 0 (b) x/c 1

14 NACA 0012 example Vortex core streamwise velocity Streamwise distance (x/c) Lombard, Moxey, Hoessler, Dhandapani, Taylor and Sherwin to appear in AIAA J. (2015) 14

15 More complex geometries 15

16 Towards a better MG solution Single step process from CAD to flow solution As few user parameters as possible CAD Flow solution Linear mesh generation High-order manipulation Mesh optimisation + correction CFD / solvers 16

17 Construct an octree 17

18 Smooth the octree 18

19 Relate geometry to mesh sizing δ(r) 19

20 Propagate mesh specification 20

21 Our process OpenCascade for CAD handling Modified version of Triangle for surface meshing Modified version of TetGen for the interior volume Our own system for high-order manipulation Linear elastic PDE solver for mesh deformation Encapsulated inside Nektar++ spectral/hp element framework 21

22 Result CAD Flow solution Without leaving Nektar++ and only 4 user parameters for meshing 22 P = 6 Re = 10,000

23 More complex geometries 23

24 Nektar++ high-order framework Framework for spectral(/hp) element method: Dimension independent, supports CG/DG/HDG Mixed elements (quads/tris, hexes, prisms, tets, pyramids) using hierarchical modal and classical nodal formulations Solvers for (in)compressible Navier-Stokes, advection-diffusionreaction, shallow water equations,... Parallelised with MPI, tested scaling up to ~10k cores 24

25 Thanks for