Consistent streamline residual-based artificial viscosity stabilization for numerical simulation of incompressible turbulent flow by isogeometric analysis

Bohumír Bastl; Marek Brandner; Kristýna Slabá; Eva Turnerová

Applications of Mathematics (2022)

  • Volume: 67, Issue: 6, page 805-829
  • ISSN: 0862-7940

Abstract

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In this paper, we propose a new stabilization technique for numerical simulation of incompressible turbulent flow by solving Reynolds-averaged Navier-Stokes equations closed by the SST k - ω turbulence model. The stabilization scheme is constructed such that it is consistent in the sense used in the finite element method, artificial diffusion is added only in the direction of convection and it is based on a purely nonlinear approach. We present numerical results obtained by our in-house incompressible fluid flow solver based on isogeometric analysis (IgA) for the benchmark problem of a wall bounded turbulent fluid flow simulation over a backward-facing step. Pressure coefficient and reattachment length are compared to experimental data acquired by Driver and Seegmiller, to the computational results obtained by open source software OpenFOAM and to the NASA numerical results.

How to cite

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Bastl, Bohumír, et al. "Consistent streamline residual-based artificial viscosity stabilization for numerical simulation of incompressible turbulent flow by isogeometric analysis." Applications of Mathematics 67.6 (2022): 805-829. <http://eudml.org/doc/298534>.

@article{Bastl2022,
abstract = {In this paper, we propose a new stabilization technique for numerical simulation of incompressible turbulent flow by solving Reynolds-averaged Navier-Stokes equations closed by the SST $k$-$\omega $ turbulence model. The stabilization scheme is constructed such that it is consistent in the sense used in the finite element method, artificial diffusion is added only in the direction of convection and it is based on a purely nonlinear approach. We present numerical results obtained by our in-house incompressible fluid flow solver based on isogeometric analysis (IgA) for the benchmark problem of a wall bounded turbulent fluid flow simulation over a backward-facing step. Pressure coefficient and reattachment length are compared to experimental data acquired by Driver and Seegmiller, to the computational results obtained by open source software OpenFOAM and to the NASA numerical results. },
author = {Bastl, Bohumír, Brandner, Marek, Slabá, Kristýna, Turnerová, Eva},
journal = {Applications of Mathematics},
keywords = {isogeometric analysis; turbulence modeling; spurious oscillations; stabilization techniques; B-splines; backward-facing step},
language = {eng},
number = {6},
pages = {805-829},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Consistent streamline residual-based artificial viscosity stabilization for numerical simulation of incompressible turbulent flow by isogeometric analysis},
url = {http://eudml.org/doc/298534},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Bastl, Bohumír
AU - Brandner, Marek
AU - Slabá, Kristýna
AU - Turnerová, Eva
TI - Consistent streamline residual-based artificial viscosity stabilization for numerical simulation of incompressible turbulent flow by isogeometric analysis
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 6
SP - 805
EP - 829
AB - In this paper, we propose a new stabilization technique for numerical simulation of incompressible turbulent flow by solving Reynolds-averaged Navier-Stokes equations closed by the SST $k$-$\omega $ turbulence model. The stabilization scheme is constructed such that it is consistent in the sense used in the finite element method, artificial diffusion is added only in the direction of convection and it is based on a purely nonlinear approach. We present numerical results obtained by our in-house incompressible fluid flow solver based on isogeometric analysis (IgA) for the benchmark problem of a wall bounded turbulent fluid flow simulation over a backward-facing step. Pressure coefficient and reattachment length are compared to experimental data acquired by Driver and Seegmiller, to the computational results obtained by open source software OpenFOAM and to the NASA numerical results.
LA - eng
KW - isogeometric analysis; turbulence modeling; spurious oscillations; stabilization techniques; B-splines; backward-facing step
UR - http://eudml.org/doc/298534
ER -

References

top
  1. Barrenechea, G. R., John, V., Knobloch, P., 10.1051/m2an/2013071, ESAIM, Math. Model. Numer. Anal. 47 (2013), 1335-1366. (2013) Zbl1303.65082MR3100766DOI10.1051/m2an/2013071
  2. Bastl, B., Brandner, M., Egermaier, J., Horníková, H., Michálková, K., Turnerová, E., 10.14311/AP.2021.61.0033, Acta Polytech., Pr. ČVUT Praha 61 (2021), 33-48. (2021) DOI10.14311/AP.2021.61.0033
  3. Bastl, B., Brandner, M., Egermaier, J., Michálková, K., Turnerová, E., 10.1016/j.advengsoft.2017.06.012, Adv. Eng. Softw. 113 (2017), 7-18. (2017) DOI10.1016/j.advengsoft.2017.06.012
  4. Bazilevs, Y., Calo, V. M., Cottrell, J. A., Hughes, T. J. R., Reali, A., Scovazzi, G., 10.1016/j.cma.2007.07.016, Comput. Methods Appl. Mech. Eng. 197 (2007), 173-201. (2007) Zbl1169.76352MR2361475DOI10.1016/j.cma.2007.07.016
  5. Bazilevs, Y., Calo, V. M., Tezduyar, T. E., Hughes, T. J. R., 10.1002/fld.1484, Int. J. Numer. Methods Fluids 54 (2007), 593-608. (2007) Zbl1207.76049MR2333001DOI10.1002/fld.1484
  6. Bressan, A., Sangalli, G., 10.1093/imanum/drr056, IMA J. Numer. Anal. 33 (2013), 629-651. (2013) Zbl1328.76025MR3047946DOI10.1093/imanum/drr056
  7. Brooks, N. A., Hughes, T. J. R., 10.1016/0045-7825(82)90071-8, Comput. Methods Appl. Mech. Eng. 32 (1982), 199-259. (1982) Zbl0497.76041MR0679322DOI10.1016/0045-7825(82)90071-8
  8. Buffa, A., Sangalli, G., Vázquez, R., 10.1016/j.cma.2009.12.002, Comput. Methods Appl. Mech. Eng. 199 (2010), 1143-1152. (2010) Zbl1227.78026MR2594830DOI10.1016/j.cma.2009.12.002
  9. Burman, E., Ern, A., Nonlinear diffusion and discrete maximum principle for stabilized Galerkin approximations of the convection-diffusion-reaction equation, Comput. Methods Appl. Mech. Eng. 191 (2002), 3833-3855 9999DOI99999 10.1016/S0045-7825(02)00318-3 . (2002) Zbl1101.76354MR1912655
  10. Collier, N., Pardo, D., Dalcin, L., Paszynski, M., Calo, V. M., The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers, Comput. Methods Appl. Mech. Eng. 213-216 (2012), 353-361 9999DOI99999 10.1016/j.cma.2011.11.002 . (2012) Zbl1243.65137MR2880524
  11. Davidson, P. A., 10.1063/1.2138427, Oxford University Press, Oxford (2004). (2004) Zbl1061.76001MR2077129DOI10.1063/1.2138427
  12. Donea, J., Huerta, A., Finite Element Methods for Flow Problems, John Wiley Sons, Chichester (2003),9999DOI99999 10.1002/0470013826 . (2003) 
  13. Driver, D. M., Seegmiller, H. L., 10.2514/3.8890, AIAA J. 23 (1985), 163-171. (1985) DOI10.2514/3.8890
  14. Elman, H. C., Silvester, D. J., Wathen, A. J., 10.1093/acprof:oso/9780199678792.001.0001, Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford (2014). (2014) Zbl1304.76002MR3235759DOI10.1093/acprof:oso/9780199678792.001.0001
  15. Falini, A., Špeh, J., Jüttler, B., 10.1016/j.cagd.2015.03.014, Comput. Aided Geom. Des. 35-36 (2015), 95-108. (2015) Zbl1417.65066MR3348885DOI10.1016/j.cagd.2015.03.014
  16. Hiemstra, R. R., Sangalli, G., Tani, M., Calabrò, F., Hughes, T. J. R., 10.1016/j.cma.2019.06.020, Comput. Methods Appl. Mech. Eng. 355 (2019), 234-260. (2019) Zbl1441.74244MR3975736DOI10.1016/j.cma.2019.06.020
  17. Hsu, M.-C., Bazilevs, Y., Calo, V. M., Tezduyar, T. E., Hughes, T. J. R., 10.1016/j.cma.2009.06.019, Comput. Methods Appl. Mech. Eng. 199 (2010), 828-840. (2010) Zbl1406.76028MR2581346DOI10.1016/j.cma.2009.06.019
  18. Hughes, T. J. R., Cottrell, J. A., Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Eng. 194 (2005), 4135-4195 9999DOI99999 10.1016/j.cma.2004.10.008 . (2005) Zbl1151.74419MR2152382
  19. Hughes, T. J. R., Reali, A., Sangalli, G., Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: Comparison of p -method finite elements with k -method NURBS, Comput. Methods Appl. Mech. Eng. 197 (2008), 4104-4124 9999DOI99999 10.1016/j.cma.2008.04.006 . (2008) Zbl1194.74114MR2463659
  20. John, V., Knobloch, P., 10.1016/j.cma.2006.11.013, Comput. Methods Appl. Mech. Eng. 196 (2007), 2197-2215. (2007) Zbl1173.76342MR2302890DOI10.1016/j.cma.2006.11.013
  21. John, V., Knobloch, P., 10.1016/j.cma.2007.12.019, Comput. Methods Appl. Mech. Eng. 197 (2008), 1997-2014. (2008) Zbl1194.76122MR2417168DOI10.1016/j.cma.2007.12.019
  22. John, V., Schmeyer, E., 10.1016/j.cma.2008.08.016, Comput. Methods Appl. Mech. Eng. 198 (2008), 475-494. (2008) Zbl1228.76088MR2479278DOI10.1016/j.cma.2008.08.016
  23. Kim, J.-Y., Ghajar, A. J., Tang, C., Foutch, G. L., 10.1080/10618560500502519, Int. J. Comput. Fluid Dyn. 19 (2005), 493-500. (2005) Zbl1184.76682DOI10.1080/10618560500502519
  24. Kuzmin, D., Mierka, O., Turek, S., 10.1504/IJCSM.2007.016531, Int. J. Comput. Sci. Math. 1 (2007), 193-206. (2007) Zbl1185.76706MR2396378DOI10.1504/IJCSM.2007.016531
  25. Center, Langley Research, NASA Turbulence Modeling Resource: 2DBFS: 2D Backward Facing Step, Available at https://turbmodels.larc.nasa.gov/backstepval.html (2021). (2021) 
  26. Li, R., Wu, Q., Zhu, S., 10.1016/j.jcp.2019.02.051, J. Comput. Phys. 387 (2019), 280-302. (2019) Zbl1452.76094MR3924459DOI10.1016/j.jcp.2019.02.051
  27. Mantzaflaris, A., Jüttler, B., G+Smo (Geometry plus Simulation Modules) v0.8.1, Available at https://github.com/gismo (2018). (2018) 
  28. Moukalled, F., Mangani, L., Darwish, M., 10.1007/978-3-319-16874-6, Fluid Mechanics and Its Applications 113. Springer, Cham (2016). (2016) Zbl1329.76001MR3382201DOI10.1007/978-3-319-16874-6
  29. Nazarov, M., Convergence of a residual based artificial viscosity finite element method, Comput. Math. Appl. 65 (2013), 616-626 9999DOI99999 10.1016/j.camwa.2012.11.003 . (2013) Zbl1319.65098MR3011445
  30. Nazarov, M., Hoffman, J., Residual-based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods, Int. J. Numer. Methods Fluids 71 (2013), 339-357 9999DOI99999 10.1002/fld.3663 . (2013) Zbl1430.76314MR3008293
  31. Nichols, R. H., Turbulence Models and Their Application to Complex Flows: Revision 4.01, University of Alabama at Birmingham, Birmingham (2014). (2014) 
  32. Nordanger, K., Holdahl, R., Kvarving, A. M., Rasheed, A., Kvamsdal, T., 10.1016/j.cma.2014.10.033, Comput. Methods Appl. Mech. Eng. 284 (2015), 664-688. (2015) Zbl1425.65118MR3310302DOI10.1016/j.cma.2014.10.033
  33. Group), OpenCFD (ESI, OpenFOAM: User Guide v2112: The open source CFD toolbox, Available at https://www.openfoam.com/documentation/guides/latest/doc/index.html (2019). (2019) 
  34. Otoguro, Y., Takizawa, K., Tezduyar, T. E., 10.1007/s00466-019-01809-w, Comput. Mech. 65 (2020), 1085-1103. (2020) Zbl1462.76148MR4077709DOI10.1007/s00466-019-01809-w
  35. Piegl, L., Tiller, W., 10.1007/978-3-642-59223-2, Monographs in Visual Communication. Springer, Berlin (1997). (1997) Zbl0868.68106DOI10.1007/978-3-642-59223-2
  36. Roos, H.-G., Stynes, M., Tobiska, L., 10.1007/978-3-540-34467-4, Springer Series in Computational Mathematics. Springer, Berlin (2008). (2008) Zbl1155.65087MR2454024DOI10.1007/978-3-540-34467-4
  37. Shakib, F., Hughes, T. J. R., 10.1016/0045-7825(91)90145-V, Comput. Methods Appl. Mech. Eng. 87 (1991), 35-58. (1991) Zbl0760.76051MR1103416DOI10.1016/0045-7825(91)90145-V
  38. Tagliabue, A., Dedè, L., Quarteroni, A., 10.1016/j.compfluid.2014.07.002, Comput. Fluids 102 (2014), 277-303. (2014) Zbl1391.76360MR3248826DOI10.1016/j.compfluid.2014.07.002
  39. Takizawa, K., Tezduyar, T. E., Otoguro, Y., 10.1007/s00466-018-1557-x, Comput. Mech. 62 (2018), 1169-1186. (2018) Zbl1462.76128MR3876285DOI10.1007/s00466-018-1557-x
  40. Tezduyar, T. E., 10.1016/j.compfluid.2005.02.011, Comput. Fluids 36 (2007), 191-206. (2007) Zbl1177.76202MR2288426DOI10.1016/j.compfluid.2005.02.011
  41. Versteeg, H. K., Malalasekera, W., An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Pearson Education, Harlow (2007). (2007) 
  42. Wilcox, D. C., Turbulence Modeling for CFD, DCW Industries, La Canada (2006). (2006) 
  43. Zhang, H., Craft, T., Iacovides, H., 10.11159/htff19.172, Proceedings of the 5th World Congress on Mechanical, Chemical, and Material Engineering (MCM'19) Avestia Publishing, Orléans (2019), Article ID 172, 9 pages. (2019) DOI10.11159/htff19.172

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