Book contents
3 - Mesh Generation
Published online by Cambridge University Press: 05 June 2016
Summary
Introduction
Unless the boundary element method (see Brebbia and Wrobel 1980), mesh less methods such as lattice-Boltzman (see Derksen and Van den Akker 1999), smooth particle hydrodynamics (Marongiu et al. 2007, 2010) or vortex methods (see Chapter 4) are used, then a volume mesh is needed. Indeed, ‘meshless’ methods can need a background mesh, but more for data structure purposes. There are wide ranges of meshing techniques and some of these are discussed here. Securing a mesh for numerical simulation can be an extremely time consuming task. Notably, it is hard to assess, ahead of making a simulation, if a mesh is adequate and hence mesh development can be an iterative process. Currently, the process of subsequent mesh refinement tends to be highly manual. Although adaptive refinement has been developed for some years, this approach is seldom used. A critical element of the mesh refinement process is finding an adequate heuristic that detects the mesh zones that need improvement. Such aspects are briefly discussed in Chapter 7. As with most other areas of CFD, there are a wide range of methods and concepts. Figure 3.1 attempts to summarize these. In this chapter, an overview of the concepts in this figure will be given. First, different mesh types will be described along with their applicability. The care that is needed to consider how a particular mesh will work with a particular solver is outlined. The mesh generation techniques are given along with methods for grid control. Parameters for quantifying grid quality are described. Optimal mesh forms for turbulent flow computations are discussed. Both the fields of RANS and eddy-resolving simulations are addressed along with hybrids of these. Finally, adaptive and moving meshes are considered.
Mesh Types, Applicability and Solver Compatibility
Basic Mesh Types
The mesh or grid types used in CFD can crudely be broadly classified as: structured Cartesian (or related variants such as cylindrical polar coordinates); modified structured Cartesian (trimmed cell, immersed boundary); structured curvilinear and unstructured.
Figure 3.2, gives examples of these grids for a divergent duct. The grids in frames (I–III), although amenable to solution in structured flow solvers, can of course be used in unstructured. Notably, with unstructured grids (see Frame (IV)), the element labelling does not need to follow a clear order (see Figure 3.3b).
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- Advanced Computational Fluid and Aerodynamics , pp. 67 - 147Publisher: Cambridge University PressPrint publication year: 2016
References
, , , & 2008a. On the use of embedded meshes in the LES of external flows. Flow, Turbulence and Combustion, 80, 393–403.Google Scholar
, , & 2008b. Optimal unstructured meshing for large eddy simulations, Quality and Reliability of Large-Eddy Simulations, 93–103, Springer.
& 2013. Multiblock structured mesh generation for turbomachinery flows, Proc. 22nd International Meshing Roundtable, Orlando, Florida, 13–16 Oct 2013. Editors: Sarrate J, Staten M. Springer. pp. 165–182.
1995. Computational fluid dynamics: The basics with applications, McGraw-Hill.
, & 2005. LES prediction of flow and acoustic field of a coaxial jet, 11th AIAA/CEAS Aeroacoustics Conference, 23–25 May, Monterey, California, AIAA Paper No. AIAA-2005-2884.
, 1994. Aspects of unstructured grids and finite-volume solvers for the Euler and Navier-Stokes equations, VKI Series 1994-04, Computational Fluid Dynamics.
, & . 2002. LNS – An approach towards embedded LES, 40th Aerospace Sciences Meeting and Exhibit, Reno/NV, AIAA Paper No. AIAA-2002-0427.
& 1994. A space-time coupled p-version least-squares finite element formulation for unsteady fluid dynamics problems. International Journal of Numerical Methods in Engineering, 37, 3545–3569.Google Scholar
& 1989. Local adaptive mesh refinement for shock hydrodynamics. Journal of Computational Physics, 82, 64–89.Google Scholar
1977. Multilevel adaptive solutions to boundary value problems. Mathematics of computation, 31(138), 333–390.Google Scholar
1980. Multilevel adaptive computations in fluid dynamics. AIAA Journal, 18(10), 1164–42172.Google Scholar
& 1980. Steady and unsteady potential problems using the boundary element method. Recent Advances in Numerical Methods in Fluids, Vol. 1, 1–25, Pineridge Press Ltd.
2002 (March). Hexing the tet. Communications in Numerical Methods in Engineering, 18(3), 223–227.Google Scholar
& 1988. An experimental and theoretical study of transient free-convection flow between horizontal concentric cylinders. International Journal of Heat and Mass Transfer, 31(2), 273–284.Google Scholar
, & 1975. Computers vs. wind tunnels for aerodynamic flow simulations. Astronaut. Aeronaut, 13, 12–35.Google Scholar
& , 1990. Composite overlapping meshes for the solution of partial differential equations. Journal of Computational Physics, 90, 1–64.Google Scholar
1984. Development of a computer program for the prediction of flow in a rotating cavity. International Journal for Numerical Methods in Fluids, 4, 667–683.Google Scholar
. . 1989. Constrained Delaunay Triangulations. Algorithmica, Vol. 4, 97–108, Springer.
. . 1993. Guaranteed-quality mesh generation for curved surfaces. Proceedings of the Ninth Annual Symposium on Computational Geometry, 274–280.
& 2003. Accuracy of higher-order finite difference schemes on non-uniform grids. AIAA Journal, 41(8), 1609–1611.Google Scholar
, & 1991. Calculation of laminar recirculating flows using a local non-staggered grid refinement system. International Journal for Numerical Methods in Fluids, 12, 535–557.Google Scholar
& 1972. False diffusion in numerical fluid mechanics. University of New South Wales, School of Mechanical and Industrial Engineering, Report 1972/FMT/1.
& 1994. Three-dimensional adaptive grid-embedding Euler technique. AIAA Journal, 32(6), 1167–1174.Google Scholar
, . & . 2009. Using level sets as the basis for a scalable, parallel geometry engine and mesh generation system. 47th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper No. AIAA-2009-0372.
2012. Recent improvements in the zonal detached eddy simulation (ZDES) formulation. Theoretical and Computational Fluid Dynamics, 26, 523–550.Google Scholar
& 1988. Space conservation law in finite volume calculations of fluid flow. International Journal for Numerical Methods in Fluids, 8, 1037–1050.Google Scholar
2010. Some limitations of turbomachinery CFD. Proceedings of ASME Turbo Expo 2010: Power for Land, Sea and Air, GT2010-22540.
& 1999. Large eddy simulations of stirred tank flow. Engineering Turbulence Modelling and Experiments, 257–266, Elsevier Science Ltd.
& 1989. Multilevel convergence acceleration for viscous and turbulent transonic flows computed with cell-vertex method. Proceedings of the Fourth Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado, 1–15.
2004. A 2D combined advancing front-Delaunay mesh generation scheme. Finite Elements in Analysis and Design, 40, 967–989.Google Scholar
& 1977. Computational methods for fluid dynamics, Springer.
1997. Computational techniques for fluid dynamics: Fundamental and general techniques, Vol. 1, Springer.
, & 1998. 3D Delaunay mesh generation coupled with advancing-front approach. Computer Methods in Applied Mechanics and Engineering, 157, (1–2), 115–131.Google Scholar
& 1993. A three-dimensional moving mesh method for the calculation of unsteady transonic flows. Recent Developments and Applications in Aeronautical CFD, p. 13
& 2009. Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering, 79(11), 1309–1331.Google Scholar
& 1965. Numerical calculation of time dependent viscous incompressible flow with free surface physics. The Physics of Fluids, 8(12), 2182–2189.Google Scholar
, & 2007a. Unstructured mesh methods for the solution of the unsteady compressible flow equations with moving boundary components. Philos. Trans. R. Soc. A, Math. Phys. Eng. Sci., 365 (1859), 2531–2552.Google Scholar
, , ., . & . 2007b. A method for time accurate turbulent compressible fluid flow simulation with moving boundary components employing local remeshing. International Journal for Numerical Methods in Fluids, 53(8), 1243–1266.Google Scholar
& 1998. A method for computing compressible, highly stratified flows in astrophysics based on operator splitting. International Journal for Numerical Methods in Fluids, 28, 1–22.Google Scholar
& 2011. Reconstructing high-order surfaces for meshing, Engineering with Computers, 28(4), 361–373, Springer.Google Scholar
1986. Computer Modelling of flows with a free surface. PhD Thesis, University of London.
1995. Mesh generation using vector fields, Journal of Computational Physics, 119, 142–148.Google Scholar
2008. Remarks on mesh quality. 45th AIAA Aerospace Sciences Meeting and Exhibit, 7–10 January, 2007, Reno, NV, AIAA Paper No. AIAA-2008-933
. & . 1988. Generation of three-dimensional unstructured grids by the advancing-front method. International Journal for Numerical Methods in Fluids, Vol. 8, 1135–1149.Google Scholar
. 1996. Progress in grid generation via the advancing front technique. Engineering with Computers, Vol. 12, 186–210, Springer.
& 2014. The prospect of using LES and DES in engineering design and the research required to get there, Philosophical Transactions of the Royal Society (Series A: Mathematical, Physical and Engineering Sciences, A 372, 20130329. (doi:10.1098/rsta.2013.0329).
, & 2006. Fast dynamic grid deformation based on Delaunay graph mapping. Journal of Computational Physics, 211(2), 405–423.Google Scholar
& 1984. The pressure correction method and the use of a multigrid technique for laminar source sink flow between co-rotating discs. Numerical Analysis Report No. 95, Department of Mathematics, The University of Manchester.
2011. Automated blocking for structured CFD gridding with an application to turbomachinery secondary flows. 20th AIAA Computational Fluid Dynamics Conference, Honolulu, Hawaii, AIAA Paper Number AIAA-2011-3049.
& 2010. Spatially non-uniform time-step adaptation for functional outputs in unsteady flow problems. 48th AIAA Aerospace Sciences Meeting, AIAA Paper Number AIAA-2010-121.
, & 2007. Numerical simulation of the flow in a Pelton turbine using the meshless method smoothed particle hydrodynamics: a new simple solid boundary treatment. Proc. Inst. Mech. Eng. A, Journal of Power Energy, 221(6), 849–856.Google Scholar
, , . & . 2010. Free surface flows simulations in Pelton turbines using an hybrid SPH-ALE method. Journal of Hydraulic Research, 48(S1), 40–49.Google Scholar
2014. CFD modeling of tail planes, 1st year PhD Report, School of Engineering, Cambridge University.
1999. Directional agglomeration multigrid techniques for high-Reynolds-number viscous flows. AIAA Journal, 37(10), 1222–1230.Google Scholar
& 1985. Finite difference simulation of non-linear ship waves. Journal of Fluid Mechanics, 157, 327–357.Google Scholar
1999. Algorithm developments for an unstructured viscous flow solver. PhD thesis, University of Oxford.
& 2000. Inter-grid boundary definition method for overset unstructured grid approach. AIAA Journal, 38(11), 2077–2084.Google Scholar
& 1988. Fronts propagating with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations. J Comput Phys, 79, 12–49.Google Scholar
, . & . 2013. Inverse design of 3D multistage transonic fans at dual operating points. Proceedings of ASME Turbo Expo. ASME Paper GT2013-95062.
& . 2009. Curved mesh generation and mesh refinement using lagrangian solid mechanics. Proceedings of 47th AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2009-949.
. 2006. Mesh size functions for implicit geometries and PDE-based gradient limiting. Engineering with Computers, 22(2), 95–109.Google Scholar
2014. Large-eddy simulations in 2030 and beyond. Philosophical Transactions of the Royal Society (Series A: Mathematical, Physical and Engineering Sciences), A 372, 20130320. (doi:10.1098/rsta.2013.0320).
, . & . 2013. Computational fluid mechanics and heat transfer, CRC Press.
& 2001. A parallel multiblock mesh movement scheme for complex aeroelastic applications. 39th Aerospace Sciences Meeting and Exhibit. January AIAA Paper No AIAA-2001-716.
2008. An investigation into methods to aid the simulation of turbulent separation control. PhD Thesis, School of Engineering, The University of Warwick.
& 1997. Hexahedral mesh generation by medial surface subdivision: Part II solids with flat and concave edges. International Journal for Numerical Methods in Engineering, 40(1), 111–136.Google Scholar
, & 1995. Hexahedral mesh generation by medial surface subdivision: Part I solids with convex edges. International Journal for Numerical Methods in Engineering, 38(19), 3335–3359.Google Scholar
2004. Topmaker: A technique for automatic multi-block topology generation using the medial axis, NASA/CR-213044.
1976. Computational fluid dynamics, Hermosa.
1994. Perspective: a method for uniform reporting of grid refinement studies. Journal of Fluids Engineering, 116, 405–413.Google Scholar
& 1986. Algebraic Multigrid, 210, Arbeitspapiere der GMD.
1995. Algorithm for Quality 2-dimensional Mesh Generation. Journal of Algorithms 18(3), 548–585.Google Scholar
& 1981. Study of coating flow by finite element method. Journal of Computational Physics, 42, 53–73.Google Scholar
2013. Final year 4A2, CFD, report, School of Engineering, Cambridge University.
1994. Curvature flow and entropy conditions applied to grid generation. Journal of Computational Physics, 115(2), 440–454.Google Scholar
, , & 1993. Multigrid computation for turbulent recirculating flows in complex geometries. Numerical. Heat Transfer, A23, 79–98.Google Scholar
1996. Automatic grid generation for compressible Navier-Stokes solvers in aerodynamic design for complex geometries. Doctor of Engineering Thesis, University of Manchester Institute of Science and Technology (UMIST).
& 1992. A one equation turbulence model for aerodynamic flows. Recherche Aérospatiale, 1, 5–21.Google Scholar
2001. Young-person's guide to detached-eddy simulation grids. NASA/CR-2001–211032.
& . 1997 (April). A comparison of sequential delaunay triangulation algorithms, Computational Geometry, 7(5–6), 361–385.Google Scholar
, & 2007. High-order multidomain spectral difference method for the Navier-Stokes equations on unstructured hexahedral grids. Communications in Computational Physics, 2(2), 310–333.Google Scholar
& 1991. 2D finite element mesh generation by medial axis subdivision. Advances in Engineering Software and Workstations, 13(5), 313–324.Google Scholar
, & 1975. Finite element methods for the solution of some incompressible non-Newtonian fluid mechanics problems with free surfaces. Computer Methods in Applied Mechanics and Engineering, 6, 154.4270.Google Scholar
& 1989. A multigrid adaptive method for incompressible flows. Journal of Computational Physics, 82, 94–121.Google Scholar
1997. Numerical precision and dissipation errors in rotating flows. International Journal for Numerical Methods in Heat Fluid Flow, 7(7), 647–658.Google Scholar
2006. Turbulence modelling of problem aerospace flows. International Journal for Numerical Methods in Fluids, 51, 261–283.Google Scholar
2013. Unsteady computational fluid dynamics in aeronautics, Springer.
& 2001. Introduction to grid and mesh generation for CFD, Published by NAFEMS (Ref. R0079).
& 2000. A Cartesian cut cell method for incompressible viscous flow. Applied Mathematical Modeling, 24, 591–606.Google Scholar
, , , , , & 2013. Les for turbines: methodologies, cost and future outlooks, Proceedings of ASME Turbo Expo 2013, San Antonio, Texas, 3–7 June. ASME Paper No. GT2013-94416.
& 2002. Grid adaptation for functional outputs: Application to two-dimensional inviscid flows. Journal of Computational Physics, 176(1), 40–69.Google Scholar
2014. High-order CFD tools for aircraft design, Proceedings Royal Society, A 372, 20130318. (doi:10.1098/rsta.2013.0318).
& 2010. Finite volume distance field and its application to medial axis transforms. International Journal of Numerical Methods in Engineering, 82(1), 114–134.Google Scholar
& 2011. Fast equal and biased distance fields for medial axis transform with meshing in mind. Applied Mathematical Modelling, 35, 5804–5819.
, & 2010. Level sets for CFD in aerospace engineering. Progress in Aerospace Sciences – Invited Paper, 46(7), 274–283.Google Scholar
, & 2012. Novel applications of BEM based level set approach. International Journal of Boundary Element Methods, 36, 907–912.Google Scholar
, , , & 1997. Cartesian cut cell method for compressible flows, Part B: Moving body problems. The Aeronautical Journal, Paper No. 2120, February, 57–65.
& . 2003. A novel approach of three-dimensional hybrid grid methodology: part I. Grid generation. Computer Methods in Applied Mechanics and Engineering, 192, 4147–4171.Google Scholar