Wind and Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Implicit Large Eddy Simulations of a rectangular 5:1 cylinder with a high-order discontinuous Galerkin method

  • Crivellini, Andrea (Department of Industrial Engineering and Mathematical Science, Marche Polytechnic University) ;
  • Nigro, Alessandra (Department of Industrial Engineering and Mathematical Science, Marche Polytechnic University) ;
  • Colombo, Alessandro (Department of Engineering and Applied Sciences, Universita degli Studi di Bergamo) ;
  • Ghidoni, Antonio (Department of Mechanical and Industrial Engineering, Universita degli Studi di Brescia) ;
  • Noventa, Gianmaria (Department of Mechanical and Industrial Engineering, Universita degli Studi di Brescia) ;
  • Cimarelli, Andrea (Department of Engineering "Enzo Ferrari", Universita degli Studi di Modena e Reggio Emilia) ;
  • Corsini, Roberto (Department of Engineering "Enzo Ferrari", Universita degli Studi di Modena e Reggio Emilia)
  • Received : 2021.03.18
  • Accepted : 2021.06.01
  • Published : 2022.01.25
⟨ Previous Next ⟩

Abstract

In this work the numerical results of the flow around a 5:1 rectangular cylinder at Reynolds numbers 3 000 and 40 000, zero angle of attack and smooth incoming flow condition are presented. Implicit Large Eddy Simulations (ILES) have been performed with a high-order accurate spatial scheme and an implicit high-order accurate time integration method. The spatial approximation is based on a discontinuous Galerkin (dG) method, while the time integration exploits a linearly-implicit Rosenbrock-type Runge-Kutta scheme. The aim of this work is to show the feasibility of high-fidelity flow simulations with a moderate number of DOFs and large time step sizes. Moreover, the effect of different parameters, i.e., dimension of the computational domain, mesh type, grid resolution, boundary conditions, time step size and polynomial approximation, on the results accuracy is investigated. Our best dG result at Re=3 000 perfectly agrees with a reference DNS obtained using Nek5000 and about 40 times more degrees of freedom. The Re=40 000 computations, which are strongly under-resolved, show a reasonable correspondence with the experimental data of Mannini et al. (2017) and the LES of Zhang and Xu (2020).

Keywords

Acknowledgement

We acknowledge the european research infrastructure PRACE that, under the project SEPREA (High-order accurate direct numerical simulations of SEParating and REAttaching flow), has provided access to the Joliot-Curie high-performance computing resources at GENCI@CEA (France) used for the Direct Numerical Simulation reported in the present work. Furthermore, we acknowledge the CINECA award under the ISCRA initiative, for the availability of high-performance computing resources and support (ISCRAC ASU-ITIS), Matteo Franciolini for the data of set-up #5 and Pierangelo Conti who provided the grids G1 and G3.

References

  1. Alhawwary, M. and Wang, Z.J. (2018), "Fourier analysis and evaluation of DG, FD and compact difference methods for conservation laws", J. Comput. Phys., 373, 835-862. https://doi.org/10.1016/j.jcp.2018.07.018 .
  2. Bando, K., Naddei, F., de la Llave Plata, M. and Ihme, M. (2018), "Variational multiscale SGS modeling for LES using a highorder discontinuous Galerkin method", In 2018 Annual Research, Center for Turbulence Research, Stanford, 299-312. https://hal.archives-ouvertes.fr/hal-02491834
  3. Bassi, F., Rebay, S., Mariotti, G., Pedinotti, S. and Savini, M. (1997), "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 (Antwerpen, Belgium), 99-108.
  4. Bassi, F., Crivellini, A., Di Pietro, D.A. and Rebay, S. (2006), "An artificial compressibility flux for the discontinuous Galerkin solution of the incompressible Navier-Stokes equations", J. Comput. Phys., 218, 794-815. https://doi.org/10.1016/j.jcp.2006.03.006.
  5. Bassi, F., Botti. L., Colombo, A., Di Pietro, D.A. and Tesini, P. (2012), "On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations", J. Comput. Phys., 231, 45-65. https://doi.org/10.1016/j.jcp.2011.08.018.
  6. Bassi, F., Botti, L., Colombo, A., Ghidoni, A. and Massa, F. (2015), "Linearly implicit Rosenbrock-type Runge-Kutta schemes applied to the Discontinuous Galerkin solution of compressible and incompressible unsteady flows", Comput. Fluids, 118, 305-320. https://doi.org/10.1016/j.compfluid.2015.06.007.
  7. Bassi, F., Botti, L., Colombo, A., Crivellini, A., Franciolini, M., Ghidoni, A., Noventa, G. (2020), "A p-adaptive Matrix-Free Discontinuous Galerkin Method for the Implicit LES of incompressible transitional flows", Flow, Turbulence Combustion, 105, 437-470. https://doi.org/10.1007/s10494-020-00178-2.
  8. Bruno, L., Fransos, D., Coste, N. and Bosco, A. (2010), "3D flow around a rectangular cylinder: A computational study", J. Wind Eng. Ind. Aerod., 98, 263-276. https://doi.org/10.1016/j.jweia.2009.10.005.
  9. Bruno, L., Salvetti, M.V. and Ricciardelli, F. (2014), "Benchmark on the aerodynamics of a rectangular 5: 1 cylinder: An overview after the first four years of activity", J. Wind Eng. Ind. Aerod., 126, 87-106. https://doi.org/10.1016/j.jweia.2014.01.005.
  10. Carton de Wiart, C. and Hillewaert, K. (2012), "DNS and ILES of transitional flows around a SD7003 using a high order Discontinuous Galerkin Method", In: Seventh International Conference on Computational Fluid Dynamics (Big Island, Hawaii), 1-14. http://hdl.handle.net/2268/262495.
  11. Carton de Wiart, C., Hillewaert, K., Bricteux, L. and Winckelmans, G. (2015), "Implicit LES of free and wallbounded turbulent flows based on the discontinuous Galerkin/symmetric interior penalty method", Int. J. Numer. Meth. Fluids, 78, 335-354. https://doi.org/10.1002/fld.4021.
  12. Chiarini, A. and Quadrio, M. (2021), "The turbulent flow over the BARC rectangular cylinder: A DNS study", Flow, Turbulence Combustion. https://doi.org/10.1007/s10494-021-00254-1.
  13. Cimarelli, A., Leonforte, A. and Angeli, D. (2018), "On the structure of the self-sustaining cycle in separating and reattaching flows", J. Fluid Mech., 857, 907-936. https://doi.org/10.1017/jfm.2018.772.
  14. Cimarelli, A., Leonforte, A. De Angelis, E., Crivellini, A. and Angeli, D. (2019a), "On negative turbulence production phenomena in the shear layer of separating and reattaching flows", Phys. Lett. A, 383, 1019-1026. https://doi.org/10.1016/j.physleta.2018.12.026.
  15. Cimarelli, A., Leonforte, A. De Angelis, E., Crivellini, A. and Angeli D. (2019b), "Resolved dynamics and subgrid stresses in separating and reattaching flows", Phys. Fluids, 31, 095101. https://doi.org/10.1063/1.5110036.
  16. Cimarelli, A., Franciolini, M. and Crivellini, A. (2020), "Numerical experiments in separating and reattaching flows", Phys. Fluids, 32, 095119. https://doi.org/10.1063/5.0019049.
  17. Fischer, P., Kruse, J., Mullen, J., Tufo, H., Lottesand, J. and Kerkemeier, S. (2008), "NEK5000: Open source spectral element CFD solver", https://nek5000.mcs.anl.gov/index.php/MainPage.
  18. Franciolini, M., Crivellini, A. and Nigro, A. (2017), "On the efficiency of a matrix-free linearly implicit time integration strategy for high-order Discontinuous Galerkin solutions of incompressible turbulent flows", Comput. Fluids, 159, 276294. https://doi.org/10.1016/j.compfluid.2017.10.008.
  19. Franciolini, M., Botti, L., Colombo, A. and Crivellini, A. (2020), "p-multigrid matrix-free discontinuous Galerkin solution strategies for the under-resolved simulation of incompressible turbulent flows", Comput. Fluids, 206, 104558. https://doi.org/10.1016/j.compfluid.2020.104558.
  20. Gassner, G. and Kopriva, D.A. (2011), "A comparison of the dispersion and dissipation errors of Gauss and GaussLobatto discontinuous Galerkin spectral element methods", SIAM J. Sci. Comput., 33(5), 2560-2579. https://doi.org/10.1137/100807211.
  21. Hesthaven, J. and Warburton, T. (2008), "Nodal discontinuous Galerkin Methods; algorithms, analysis and applications", Texts in Applied Mathematics, 54.
  22. Hughes, T.J.R., Feijo, G.R., Mazzei, L. and Quincy, J.B. (1998), "The variational multiscale method - a paradigm for computational mechanics", Comput. Meth. Appl. Mech. Eng., 166(1), 3-24. https://doi.org/10.1016/S0045-7825(98)00079-6.
  23. Lang, J. and Verwer, J. (2001), "ROS3PAn accurate third-order Rosenbrock solver designed for parabolic problems", BIT Numer. Mathem., 41(4), 731-738. https://doi.org/10.1023/A:1021900219772
  24. Liu, X., Cui, Y. and Liu, Q. (2013), "Wind tunnel study on spanwise correlation of aerodynamic forces on a 5: 1 rectangular cylinder", In: Eighth Asia-Pacific Conference on Wind Engineering (Chennai, India), 211-217. https://doi.org/10.3850/978-981-07-8012-8_289.
  25. Lodato, G. and Chapelier, J.B. (2018), "Evaluation of the spectral element dynamic model for large-eddy simulation on unstructured, deformed meshes", Flow, Turbulence Combustion, 101, 271-294. https://doi.org/10.1007/s10494-018-9935-1.
  26. Mannini, C., Marra, A.M., Pigolotti, L. and Bartoli, G. (2017), "The effects of free-stream turbulence and angle of attack on the aerodynamics of a cylinder with rectangular 5: 1 cross section", J. Wind Eng. Ind. Aerod., 161, 42-58. https://doi.org/10.1016/j.jweia.2016.12.001.
  27. Manzanero, J., Ferrer, E., Rubio, G. and Valero E. (2018), "Dispersion-dissipation analysis for advection problems with nonconstant coefficients: Applications to discontinuous Galerkin formulations", SIAM J. Sci. Comput., 40(2), A747-A768. https://doi.org/10.1137/16M1101143.
  28. Mariotti, A., Salvetti, M.V., Omrani, P.S. and Witteveen, J.A.S (2016), "Stochastic analysis of the impact of freestream conditions on the aerodynamics of a rectangular 5: 1 cylinder", Comput. Fluids, 136, 170-192. https://doi.org/10.1016/j.compfluid.2016.06.008.
  29. Mariotti, A., Siconolfi, L. and Salvetti, M.V. (2017), "Stochastic sensitivity analysis of large-eddy simulation predictions of the flow around a 5: 1 rectangular cylinder", Europ. J. Mech.-B/Fluids, 68, 149-165. https://doi.org/10.1016/j.euromechflu.2016.12.008.
  30. Massa, F.C., Noventa, G., Lorini, M., Bassi, F., Ghidoni, A. (2018), "High-order linearly implicit two-step peer schemes for the discontinuous Galerkin solution of the incompressible NavierStokes equations", Comput. Fluids, 162, 55-71. https://doi.org/10.1016/j.compfluid.2017.12.003.
  31. Mengaldo, G., Mourab, R.C, Giralda B., Peir, J. and Sherwin S.J. (2018), "Spatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit LES", Computers and Fluids, 169, 349364. https://doi.org/10.1016/j.compfluid.2017.09.016
  32. Noventa, G., Massa, F., Rebay, S., Bassi, F., Ghidoni, A. (2020), "Robustness and efficiency of an implicit time-adaptive discontinuous Galerkin solver for unsteady flows", Comput. Fluids, 204, 104529. https://doi.org/10.1016/j.compfluid.2020.104529.
  33. Ribeiro, A.F.P. (2011), "Unsteady RANS modeling of flow past a rectangular 5: 1 cylinder: Investigation of edge sharpness effects", In: Proceedings of the 13th International Conference on Wind Engineering (Amsterdam, The Netherlands).
  34. Ricci, M., Patruno, L., de Miranda, S. and Ubertini F. (2017), "Flow field around a 5: 1 rectangular cylinder using LES: Influence of inflow turbulence conditions, spanwise domain size and their interaction", Comput. Fluids, 149, 181-193. https://doi.org/10.1016/j.compfluid.2017.03.010.
  35. Yoshizawa, A. (1986), "Statistical theory for compressible turbulent shear flows, with the application to sub-grid modeling", Phys. Fluids, 29(7), 2152-2164. https://doi.org/10.1063/1.865552.
  36. Zhang, Z. and Xu, F. (2020), "Spanwise length and mesh resolution effects on simulated flow around a 5: 1 rectangular cylinder", J. Wind Eng. Ind. Aerod., 202, 104186. https://doi.org/10.1016/j.jweia.2020.104186.