Space Adaptive Methods/Meshing

Hartmann, R.; Balan, A.; Bassi, F.; Boussuge, J.-F.; de Brauer, A.; Cagnone, J.-S.; Colombo, A.; Couaillier, V.; Coulaud, O.; Crivellini, A.; Franciolini, M.; Ghidoni, A.; Hillewaert, Koen; de la Llave Plata, M.; Manzinali, G.; Naddei, F.; Noventa, G.; Puigt, G.; Vermeire, B. C.; Vincent, Philippe

doi:10.1007/978-3-030-62048-6_4

Request a copy

Contribution to collective works (Parts of books)

Space Adaptive Methods/Meshing

Hartmann, R.; Balan, A.; Bassi, F. et al.

2021 • In Hirsch, Charles; Hillewaert, Koen; Hartmann, Ralf et al. (Eds.) TILDA: Towards Industrial LES/DNS in Aeronautics: Paving the Way for Future Accurate CFD - Results of the H2020 Research Project TILDA, Funded by the European Union, 2015 -2018

Permalink
https://hdl.handle.net/2268/262466

DOI
10.1007/978-3-030-62048-6_4

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

Tilda_Hartmann2021_Chapter_SpaceAdaptiveMethodsMeshing.pdf

Publisher postprint (5.61 MB)

Request a copy

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Abstract :

[en] This chapter describes space adaptive approaches developed by six TILDA partners for the application in scale-resolving simulations. They are designed to provide sufficient spatial resolution in regions where required and to allow a lower resolution elsewhere for efficiency reasons. Adaptation techniques considered include mesh (h-refinement), order refinement of the spatial discretization (p-refinement) or a combination of both (hp-refinement). Furthermore, near-wall local mesh refinement, refinement using feature-based indicators and indicators obtained from the Variational Multiscale Method are considered.

Disciplines :

Aerospace & aeronautics engineering

Author, co-author :

Hartmann, R.

Balan, A.

Bassi, F.

Boussuge, J.-F.

de Brauer, A.

Cagnone, J.-S.

Colombo, A.

Couaillier, V.

Coulaud, O.

Crivellini, A.

More authors (10 more)

Language :

English

Title :

Space Adaptive Methods/Meshing

Publication date :

2021

Main work title :

TILDA: Towards Industrial LES/DNS in Aeronautics: Paving the Way for Future Accurate CFD - Results of the H2020 Research Project TILDA, Funded by the European Union, 2015 -2018

Editor :

Hirsch, Charles

Hillewaert, Koen ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Design of Turbomachines

Hartmann, Ralf

Couaillier, Vincent

Boussuge, Jean-Francois

Chalot, Frederic

Bosniakov, Sergey

Haase, Werner

Publisher :

Springer International Publishing

ISBN/EAN :

978-3-030-62048-6

Pages :

103-190

Additional URL :

https://doi.org/10.1007/978-3-030-62048-6_4

European Projects :

H2020 - 635962 - TILDA - Towards Industrial LES/DNS in Aeronautics – Paving the Way for Future Accurate CFD

Funders :

EC - European Commission

Available on ORBi :

since 11 August 2021

Statistics

Number of views

100 (2 by ULiège)

Number of downloads

1 (1 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

F. Bassi, L. Botti, A. Colombo, A. Crivellini, A. Ghidoni, A. Nigro, S. Rebay, Time integration in the discontinuous Galerkin code MIGALE—unsteady problems, in IDIHOM: Industrialization of High-Order Methods-A Top-Down Approach (Springer, Berlin, 2015), pp. 205–230
F. Bassi, L. Botti, A. Colombo, D.A. Di Pietro, P. Tesini, On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations. J. Comput. Phys. (Elsevier) 231(1), 45–65 (2012)
J. Gottlieb, C. Groth, Assessment of Riemann solvers for unsteady one-dimensional inviscid flows of perfect gases. J. Comput. Phys. (Elsevier) 78(2), 437–458 (1988)
F. Bassi, S. Rebay, G. Mariotti, S. Pedinotti, M. Savini, A high-order accurate discontinuous finite element method for inviscid and viscous turbomachinery flows, in Proceedings of the 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, ed. by R. Decuypere, G. Dibelius (Technologisch Instituut, Antwerpen, Belgium, 1997), pp. 99–108, 5–7 Mar 1997
F. Bassi, L. Botti, A. Colombo, A. Ghidoni, F. Massa, Linearly implicit Rosenbrock-type Runge–Kutta schemes applied to the Discontinuous Galerkin solution of compressible and incompressible unsteady flows. Comput. Fluids (Elsevier) 118, 305–320 (2015)
S. Balay, S. Abhyankar, M.F. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, A. Dener, V. Eijkhout, W.D. Gropp, D. Kaushik, M.G. Knepley, D.A. May, L.C. McInnes, R.T. Mills, T. Munson, K. Rupp, P. Sanan, B.F. Smith, S. Zampini, H. Zhang, H. Zhang, PETSc Web page (2018), http://www.mcs.anl.gov/petsc
J. Lang, J. Verwer, ROS3P—an accurate third-order Rosenbrock solver designed for parabolic problems. BIT 41(4), 731–738 (2001)
R.J. Spiteri, S.J. Ruuth, SIAM, A new class of optimal high-order strong-stability-preserving time discretization methods. J. Numer. Anal. 40(2), 469–491 (2002). ISSN 0036-1429 (Society for Industrial and Applied Mathematics, Philadelphia, PA, USA)
P. Tesini, An h-multigrid approach for high-order discontinuous Galerkin methods. Ph.D. Thesis, Università degli Studi di Bergamo (2008)
A. Ghidoni, E. Pelizzari, S. Rebay, V. Selmin, 3D anisotropic unstructured grid generation. Int. J. Numer. Methods Fluids 51(9–10), 1097–1115 (2006)
L. Krivodonova, J. Xin, J.F. Remacle, N. Chevaugeon, J.E. Flaherty, Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws. Appl. Numer. Math. (Elsevier) 48(3–4), 323–338 (2004)
G. Gassner, M. Staudenmaier, F. Hindenlang, M. Atak, C.D. Munz, A space-time adaptive discontinuous Galerkin scheme. Comput. Fluids 117, 247–261 (2015). https://doi.org/10.1016/j.compfluid.2015.05.002. http://www.sciencedirect.com/science/article/pii/S0045793015001498. ISSN 0045-7930
P.O. Persson, J. Peraire, Sub-cell shock capturing for discontinuous Galerkin methods, in 44th AIAA Aerospace Sciences Meeting and Exhibit (2006), p. 112
G. Karypis, V. Kumar, METIS: Unstructured graph partitioning and sparse matrix ordering system, version 5.0. Technical report (2009), http://www.cs.umn.edu/~metis
M. Langari, Z. Yang, Numerical study of the primary instability in a separated boundary layer transition under elevated free-stream turbulence. Phys. Fluids 25(7), 074106 (2013). https://doi.org/10.1063/1.4816291
Z. Yang, P.R. Voke, Large-eddy simulation of boundary-layer separation and transition at a change of surface curvature. J. Fluid Mech. (Cambridge University Press) 439, 305–333 (2001). https://doi.org/10.1017/S0022112001004633
E. Lamballais, J. Silvestrini, S. Laizet, Direct numerical simulation of flow separation behind a rounded leading edge: Study of curvature effects. Int. J. Heat Fluid Flow 31(3), 295–306 (2010). Sixth International Symposium on Turbulence and Shear Flow Phenomena
M. Franciolini, L. Botti, A. Colombo, A. Crivellini, p-Multigrid matrix-free discontinuous Galerkin solution strategies for the under-resolved simulation of incompressible turbulent flows, arXiv:1809.00866 (2018)
F. Bassi, A. Crivellini, D.D. Pietro, S. Rebay, An artificial compressibility flux for the discontinuous Galerkin solution of the incompressible Navier-Stokes equations. J. Comput. Phys. 218(2), 794–815 (2006). https://doi.org/10.1016/j.jcp.2006.03.006. http://www.sciencedirect. com/science/article/pii/S0021999106001331. ISSN 0021-9991
M.S. Boutilier, S. Yarusevych, Separated shear layer transition over an airfoil at a low Reynolds number. Phys. Fluids (AIP) 24(8), 084105 (2012)
A. Crivellini, V. D’Alessandro, Spalart-Allmaras model apparent transition and RANS simulations of laminar separation bubbles on airfoils. Int. J. Heat Fluid Flow 47, 70–83 (2014). https://doi.org/10.1016/j.ijheatfluidflow.2014.03.002. http://www.sciencedirect.com/science/article/pii/S0142727X14000344. ISSN 0142-727X
M.S.H. Boutilier, S. Yarusevych, Separated shear layer transition over an airfoil at a low Reynolds number. J. Fluid Mech. 24 (2012)
S.H. Peng, M. Strelets, Test case ST12, Boeing rudimentary landing gear. ATAAC (2012)
A. Uranga, P.O. Persson, M. Drela, J. Peraire, Implicit large eddy simulation of transition to turbulence at low Reynolds numbers using a discontinuous Galerkin method. Int. J. Num. Methods Eng. 87, 232–261 (2011)
A. Beck, T. Bolemann, D. Flad, H. Frank, G. Gassner, F. Hindenlang, C. Munz, High order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations. Int. J. Numer. Methods Fluids 76(8), 522–548 (2014)
C. Carton de Wiart, K. Hillewaert, L. Bricteux, G. Winckelmans, Implicit LES of free and wall bounded turbulent flows based on the discontinuous Galerkin/symmetric interior penalty method. Int. J. Numer. Methods Fluids 78(6), 335–354 (2014). https://doi.org/10.1002/fld. 4021
G. Compère, Mesh adaption with large deformations: theory, algorithms and implementation. Ph.D. thesis, Université Catholique de Louvain, École Polytechnique de Louvain, Institut de Mécanique, Matériaux et Génie Civil, Belgium (2009)
P. Frey, About surface remeshingin 9th International Meshing Roundtable (2000), pp. 123–136
P. Laug, Contribution à la génération automatique de maillages de qualité pour la simulation numérique (Université Pierre et Marie Curie, Paris VI, Habilitation à Diriger des Recherches en Mathématiques, 2016)
R. Löhner, Mesh adaptation in fluid mechanics. Eng. Fract. Mech. 50, 819–847 (1995)
O. Zienkiewicz, J. Zhu, The superconvergent patch recovery and a posteriori error estimates. Part 1: the recovery technique. Int. J. Numer. Methods Eng. 33, 1331–1364 (1992)
O. Zienkiewicz, J. Zhu, The superconvergent patch recovery and a posteriori error estimates. Part 2: error estimates and adaptativity. Int. J. Numer. Methods Eng. 33, 1365–1382 (1992)
E.V.F. Fraysse, J. de Vicente, The estimation of truncation error by τ-estimation revisited. J. Comput. Phys. 231, 3457–3482 (2012)
E.V.F. Fraysse, J. Posín, Comparison of mesh adaptation using the adjoint methodology and truncation error estimates. AIAA J. 50, 1920–1932 (2012)
X.D. Zhang, J. Trepanier, R. Camarero, A posteriori error estimation for finite-volume solutions of hyperbolic conservation laws. Comput. Methods Appl. Mech. Eng. 185, 1–19 (2000)
C. Roy, Strategies for driving mesh adaptation in CFD, in 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition (2009). AIAA-2009-1302
C. Roy, Review of discretization error estimators in scientific computing, in 48th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition (2010). AIAA-2010-126
C. Mavriplis, A posteriori error estimators for adaptive spectral element techniques, in Proceedings of the Eighth GAMM-Conference on Numerical Methods in Fluid Mechanics, pp. 333–342 (1990)
J.F.S. Adjerid, K. Devine, L. Krivodonova, A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems. Comput. Methods Appl. Mech. Eng. 191, 1097– 1112 (2002)
L. Krivodonova, J. Flaherty, Error estimation for discontinuous Galerkin solutions of multidimensional hyperbolic problems. Adv. Comput. Math. 19, 57–71 (2003)
R. Becker, R. Rannacher, Optimal control approach to a posteriori error estimation in finite element methods, in Acta Numerica (Cambridge University Press, Cambridge, MA, 2001)
M. Giles, N. Pierce, Adjoint error correction for integral outputs, in Lecture Notes in Computational Science and Engineering: Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics, vol. 25. (Springer, Berlin, 2002)
N.A. Pierce, M.B. Giles, Adjoint and defect error bounding and correction for functional estimates. J. Comput. Phys. 20, 769–794 (2004)
K.J. Fidkowski, D. Darmofal, Review of output-based error estimation and mesh adaptation in computational fluid dynamics. AIAA J. 49, 673–694 (2011)
T. Barth, M. Larson, A posteriori error estimates for higher order Godunov finite volume methods on unstructured meshes, in Finite Volumes for Complex Applications III, ed. by R. Herban, D. Kröner (Hermes Penton, London, 2002), pp. 41–63
D.A. Venditti, D.L. Darmofal, Grid adaptation for functional outputs: application to two-dimensional inviscid flows. J. Comput. Phys. 176, 40–69 (2002)
D.A. Venditti, D.L. Darmofal, Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows. J. Comput. Phys. 187, 22–46 (2003)
J. Lu, An a posteriori Error Control Framework for Adaptive Precision Optimization using Discontinuous Galerkin Finite Element Method. Ph.D. thesis, Massachusetts Institute of Technology (2005). Adjoint problem based error estimation framework
R. Hartmann, P. Houston, Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations. J. Comput. Phys. 183, 508–532 (2002)
R. Hartmann, T. Leicht, Higher order and adaptive DG methods for compressible flows, in VKI LS 2014-03: 37th Advanced VKI CFD Lecture Series: Recent developments in higher order methods and industrial application in aeronautics, Dec. 9–12, 2013, ed. by H. Deconinck (Von Karman Institute for Fluid Dynamics, Rhode Saint Genèse, Belgium, 2014)
J. Krakos, Unsteady adjoint analysis for output sensitivity and mesh adaptation. Ph.D. thesis (Massachusetts Institute of Technology,Cambridge, MA, 2012)
Q. Wang, R. Hu, P. Blonigan, Least squares shadowing sensitivity analysis of chaotic limit cycle oscillations. J. Comput. Phys. 267, 210–224 (2014). ISSN 0021-9991
P. Blonigan, S. Gomez, Q.Wang, Least squares shadowing for sensitivity analysis of turbulent fluid flows, in 52nd Aerospace Sciences Meeting, AIAA SciTech Forum (2014). AIAA 2014-1426
F.J. Geurts BJ, A framework for predicting accuracy limitations in large-eddy simulation. Phys. Fluids 14, L41–L44 (2002)
S. Pope, Turbulent Flows (Cambridge University Press, 2000). ISBN 9780521598866
P. Benard, G. Balarac, V. Moureau, C. Dobrzynski, G. Lartigue, Y. D’Angelo, Mesh adaptation for large-eddy simulations in complex geometries. Int. J. Numer. Methods Fluids 81(12), 719– 740 (2016). Fld.4204
G. Daviller, M. Brebion, P. Xavier, G. Staffelbach, J.D. Müller, T. Poinsot, A mesh adaptation strategy to predict pressure losses in LES of swirled flows. Flow, Turbul. Combust. 99(1), 93–118 (2017). https://doi.org/10.1007/s10494-017-9808-z. ISSN 1573-1987
K. Hillewaert, J. Cagnone, S. Murman, A. Garai, L. Yu, M. Ihme, Assessement of high order DG methods for LES of free stream transonic turbulence, in Proceedings of the Summer Program 2016 (Stanford University, Center for Turbulence Research, 2016)
3rd International Worskhop on High-Order CFD methods, Orlando, Florida, 3–4 Jan 2015. (2015), https://www.grc.nasa.gov/hiocfd
https://qnet-ercoftac.cfms.org.uk/w/index.php/UFR_3-30_Test_Case (2013)
G. Kuru, M. de la Llave Plata, V. Couaillier, R. Abgrall, F. Coquel, An adaptive variational multiscale discontinuous Galerkin method for large eddy simulation, in 54th AIAA Aerospace Sciences Meeting, San Diego, California (AIAA, 2016)
G. Tumolo, L. Bonaventura, M. Restelli, A semi-implicit, semi-Lagrangian, p-adaptive discontinuous Galerkin method for the shallow water equations. J. Comput. Phys. 232(1), 46–67 (2013) (Elsevier)
G. Gassner, C. Altmann, F. Hindenlang, M. Staudenmeier, C. Munz, Explicit discontinuous Galerkin schemes with adaptation in space and time, in36th CFD/ADIGMA course on hp-adaptive and hp-multigrid methods, VKI LS (2009)
R. Hartmann, J. Held, T. Leicht, F. Prill, Error estimation and adaptive mesh refinement for aerodynamic flows, in ADIGMA-A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications (Springer, Berlin, 2010), pp. 339–353
V. Dolejší, hp-DGFEM for nonlinear convection-diffusion problems. Math. Comput. Simul. 87, 87–118 (2013)
F. Naddei, M. de la Llave Plata, V. Couaillier, F. Coquel, A comparison of refinement indicators for p-adaptive simulations of steady and unsteady flows using discontinuous Galerkin methods. J. Comput. Phys. (Elsevier) 376, 508–533 (2019)
M. Breuer, A challenging test case for large-eddy-simulation: high Reynolds number circular cylinder flow. Int. J. Heat Fluid Flow 21(5), 648–654 (2000)
B. Cantwell, D. Coles, An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder. J. Fluid. Mech. 136, 321–374 (1983)
J. Son, T. Hanratty, Velocity gradients at the wall for flow around a cylinder at Reynolds numbers from 5 × 103 to 105 . J. Fluid Mech. 35, 353–368 (1969)
P. Parnaudeau, J. Carlier, D. Heitz, E. Lamballais, Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900. Phys. Fluids 20(8), 085101 (2008)
S. Karabelas, LES of high-Reynolds number flow past a rotating cylinder. Int. J. Heat Fluid Flow 31(4), 518–527 (2010)
H.J. Clercx, C.H. Bruneau, The normal and oblique collision of a dipole with a no-slip boundary. Comput. Fluids (Elsevier) 35(3), 245–279 (2006)
G.H. Keetels, U. D’Ortona, W. Kramer, H.J. Clercx, K. Schneider, G.J. van Heijst, Fourier spectral and wavelet solvers for the incompressible Navier–Stokes equations with volume-penalization: convergence of a dipole–wall collision. J. Comput. Phys. (Elsevier) 227(2), 919– 945 (2007)
M. Lorteau, E. Martin, Stratégie Load-Balancing Pour Ordre Variable. Technical report, ELCI (2017)
D.A. Kopriva, J.H. Kolias, A conservative staggered-grid Chebyshev multidomain method for compressible flows. J. Comput. Phys. 125(1), 244 (1996). ISSN 0021-9991
Y. Sun, Z. Wang, Y. Liu, High-order multidomain spectral difference method for the Navier-Stokes equations on unstructured hexahedral grids. Commun. Comput. Phys. 2(2), 310–333 (2007)
D.A. Kopriva, A conservative staggered-grid Chebyshev multidomain method for compressible flows. II: a semi-structured method. J. Comput. Phys. 128, 29 (1996)
Y. Maday, C. Mavriplis, A. Patera, Nonconforming mortar element methods: application to spectral discretizations, in Domain Decomposition Methods (SIAM, Philadelphia, 1988), pp. 392–418
I. Marter, Handling different h and p refinements in the framework of Spectral Difference method. Master’s thesis (Université Pau et Pays de l’Adour, 2013)
D.A. Kopriva, A staggered-grid multidomain spectral method for the compressible Navier– Stokes equations. J. Comput. Phys. 143(1), 125–158 (1998). ISSN 0021-9991
F. Naddei, M. de la Llave Plata, V. Couaillier, A comparison of refinement indicators for p-adaptive discontinuous Galerkin methods for the Euler and Navier-Stokes equations, in 2018 AIAA Aerospace Sciences Meeting (2018), p. 368
E. Ching, Y. Lv, M. Ihme, Entropy residual as a feature-based adaptation indicator for simulations of unsteady flow, in 54th AIAA Aerospace Sciences Meeting (2016), p. 837
Z.J. Wang, K. Fidkowski, R. Abgrall, F. Bassi, D. Caraeni, A. Cary, H. Deconinck, R. Hartmann, K. Hillewaert, H.T. Huynh et al., High-order CFD methods: current status and perspective. Int. J. Numer. Methods Fluids (Wiley Online Library) 72(8), 811–845 (2013)
H.T. Huynh, A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods, in 18th AIAA Computational Fluid Dynamics Conference (American Institute of Aeronautics and Astronautics. AIAA Paper 2007-4079, Miami, FL, 2007)
B. Vermeire, P. Vincent, On the behaviour of fully-discrete flux reconstruction schemes. Comput. Methods Appl. Mech. Eng. (Elsevier) 315, 1053–1079 (2017)
N. Adams, S. Hickel, S. Franz, Implicit subgrid-scale modeling by adaptive deconvolution. J. Comput. Phys. 200(2), 412–431 (2004)
L. Yanan, Z. Wang, A priori and a posteriori evaluations of subgrid stress models with the Burg-ers’ equation, in 53rd AIAA Aerospace Sciences Meeting. AIAA Paper 2015-1283 (American Institute of Aeronautics and Astronautics, Kissimmee, FL, 2015)
R. Moura, S. Sherwin, J. Peiró, Linear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods. J. Comput. Phys. 298, 695–710 (2015)
P.E. Vincent, A.M. Farrington, F.D. Witherden, A. Jameson, An extended range of stable-symmetric-conservative flux reconstruction correction functions. Comput. Methods Appl. Mech. Eng. 296, 248–272 (2015)
B.C. Vermeire, S. Nadarajah, P.G. Tucker, Implicit large eddy simulation using the high-order correction procedure via reconstruction scheme. Int. J. Numer. Methods Fluids (Wiley Online Library) 82(5), 231–260 (2016)
Z. Wang, K. Fidkowski, R. Abgrall, D. Caraeni, F. Bassi, A. Cary, H. Deconinck, R. Hartmann, K. Hillewaert, H.T. Huynh, N. Kroll, G. May, P. Persson, B. van Leer, M. Visbal, High-order CFD methods: current status and perspective (Wiley Online Library). Int. J. Numer. Methods Fluids 72(8), 811–845 (2013)
M.R. Visbal, R.E. Gordnier, M.C. Galbraith, High-fidelity simulations of moving and flexible airfoils at low Reynolds numbers. Exp. Fluids 46(5), 903–922 (2009). ISSN 0723-4864, 1432-1114
D.J. Garmann, M.R. Visbal, P.D. Orkwis, Comparative study of implicit and subgrid-scale model large-eddy simulation techniques for low-Reynolds number airfoil applications. Int. J. Numer. Methods Fluids 71(12), 1546–1565 (2013)
A. Beck, T. Bolemann, D. Flad, H. Frank, G. Gassner, F. Hindenlang, C. Munz, High-order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations. Int. J. Numer. Methods Fluids 76(8), 522–548 (2014)
B.C. Vermeire, F.D. Witherden, P.E. Vincent, On the utility of GPU accelerated high-order methods for unsteady flow simulations: a comparison with industry-standard tools. J. Comput. Phys. (Elsevier) 334, 497–521 (2017)