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isogeometric analysis; turbulence modeling; spurious oscillations; stabilization techniques; B-splines; backward-facing step
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. \looseness +2
[1] Barrenechea, G. R., John, V., Knobloch, P.: A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations. ESAIM, Math. Model. Numer. Anal. 47 (2013), 1335-1366. DOI 10.1051/m2an/2013071 | MR 3100766 | Zbl 1303.65082
[2] Bastl, B., Brandner, M., Egermaier, J., Horníková, H., Michálková, K., Turnerová, E.: Numerical simulation of lid-driven cavity flow by isogeometric analysis. Acta Polytech., Pr. ČVUT Praha 61 (2021), 33-48. DOI 10.14311/AP.2021.61.0033
[3] Bastl, B., Brandner, M., Egermaier, J., Michálková, K., Turnerová, E.: IgA-Based Solver for turbulence modelling on multipatch geometries. Adv. Eng. Softw. 113 (2017), 7-18. DOI 10.1016/j.advengsoft.2017.06.012
[4] Bazilevs, Y., Calo, V. M., Cottrell, J. A., Hughes, T. J. R., Reali, A., Scovazzi, G.: Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput. Methods Appl. Mech. Eng. 197 (2007), 173-201. DOI 10.1016/j.cma.2007.07.016 | MR 2361475 | Zbl 1169.76352
[5] Bazilevs, Y., Calo, V. M., Tezduyar, T. E., Hughes, T. J. R.: $YZ\beta$ discontinuity capturing for advection-dominated processes with application to arterial drug delivery. Int. J. Numer. Methods Fluids 54 (2007), 593-608. DOI 10.1002/fld.1484 | MR 2333001 | Zbl 1207.76049
[6] Bressan, A., Sangalli, G.: Isogeometric discretizations of the Stokes problem: Stability analysis by the macroelement technique. IMA J. Numer. Anal. 33 (2013), 629-651. DOI 10.1093/imanum/drr056 | MR 3047946 | Zbl 1328.76025
[7] Brooks, N. A., Hughes, T. J. R.: Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 32 (1982), 199-259. DOI 10.1016/0045-7825(82)90071-8 | MR 0679322 | Zbl 0497.76041
[8] Buffa, A., Sangalli, G., Vázquez, R.: Isogeometric analysis in electromagnetics: B-splines approximation. Comput. Methods Appl. Mech. Eng. 199 (2010), 1143-1152. DOI 10.1016/j.cma.2009.12.002 | MR 2594830 | Zbl 1227.78026
[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 \99999DOI99999 10.1016/S0045-7825(02)00318-3 . MR 1912655 | Zbl 1101.76354
[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 \99999DOI99999 10.1016/j.cma.2011.11.002 . MR 2880524 | Zbl 1243.65137
[11] Davidson, P. A.: Turbulence: An Introduction for Scientists and Engineers. Oxford University Press, Oxford (2004). DOI 10.1063/1.2138427 | MR 2077129 | Zbl 1061.76001
[12] Donea, J., Huerta, A.: Finite Element Methods for Flow Problems. John Wiley & Sons, Chichester (2003),\99999DOI99999 10.1002/0470013826 .
[13] Driver, D. M., Seegmiller, H. L.: Features of a reattaching turbulent shear layer in divergent channel flow. AIAA J. 23 (1985), 163-171. DOI 10.2514/3.8890
[14] Elman, H. C., Silvester, D. J., Wathen, A. J.: Finite Elements and Fast Iterative Solvers: With Applications in Incompressible Fluid Dynamics. Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford (2014). DOI 10.1093/acprof:oso/9780199678792.001.0001 | MR 3235759 | Zbl 1304.76002
[15] Falini, A., Špeh, J., Jüttler, B.: Planar domain parameterization with THB-splines. Comput. Aided Geom. Des. 35-36 (2015), 95-108. DOI 10.1016/j.cagd.2015.03.014 | MR 3348885 | Zbl 1417.65066
[16] Hiemstra, R. R., Sangalli, G., Tani, M., Calabrò, F., Hughes, T. J. R.: Fast formation and assembly of finite element matrices with application to isogeometric linear elasticity. Comput. Methods Appl. Mech. Eng. 355 (2019), 234-260. DOI 10.1016/j.cma.2019.06.020 | MR 3975736 | Zbl 1441.74244
[17] Hsu, M.-C., Bazilevs, Y., Calo, V. M., Tezduyar, T. E., Hughes, T. J. R.: Improving stability of stabilized and multiscale formulations in flow simulations at small time steps. Comput. Methods Appl. Mech. Eng. 199 (2010), 828-840. DOI 10.1016/j.cma.2009.06.019 | MR 2581346 | Zbl 1406.76028
[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 \99999DOI99999 10.1016/j.cma.2004.10.008 . MR 2152382 | Zbl 1151.74419
[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 \99999DOI99999 10.1016/j.cma.2008.04.006 . MR 2463659 | Zbl 1194.74114
[20] John, V., Knobloch, P.: On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations. I. A review. Comput. Methods Appl. Mech. Eng. 196 (2007), 2197-2215. DOI 10.1016/j.cma.2006.11.013 | MR 2302890 | Zbl 1173.76342
[21] John, V., Knobloch, P.: On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations. II. Analysis for $P_1$ and $Q_1$ finite elements. Comput. Methods Appl. Mech. Eng. 197 (2008), 1997-2014. DOI 10.1016/j.cma.2007.12.019 | MR 2417168 | Zbl 1194.76122
[22] John, V., Schmeyer, E.: Finite element methods for time-dependent convection-diffusionreaction equations with small diffusion. Comput. Methods Appl. Mech. Eng. 198 (2008), 475-494. DOI 10.1016/j.cma.2008.08.016 | MR 2479278 | Zbl 1228.76088
[23] Kim, J.-Y., Ghajar, A. J., Tang, C., Foutch, G. L.: Comparison of near-wall treatment methods for high Reynolds number backward-facing step flow. Int. J. Comput. Fluid Dyn. 19 (2005), 493-500. DOI 10.1080/10618560500502519 | Zbl 1184.76682
[24] Kuzmin, D., Mierka, O., Turek, S.: On the implementation of the $k-\epsilon$ turbulence model in incompressible flow solvers based on a finite element discretization. Int. J. Comput. Sci. Math. 1 (2007), 193-206. DOI 10.1504/IJCSM.2007.016531 | MR 2396378 | Zbl 1185.76706
[25] Center, Langley Research: NASA Turbulence Modeling Resource: 2DBFS: 2D Backward Facing Step. Available at \brokenlink{{backstep_val.html}} (2021).
[26] Li, R., Wu, Q., Zhu, S.: Proper orthogonal decomposition with SUPG-stabilized isogeometric analysis for reduced order modelling of unsteady convection-dominated convection-diffusion-reaction problems. J. Comput. Phys. 387 (2019), 280-302. DOI 10.1016/ | MR 3924459 | Zbl 1452.76094
[27] Mantzaflaris, A., Jüttler, B.: G+Smo (Geometry plus Simulation Modules) v0.8.1. Available at (2018).
[28] Moukalled, F., Mangani, L., Darwish, M.: The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM and Matlab. Fluid Mechanics and Its Applications 113. Springer, Cham (2016). DOI 10.1007/978-3-319-16874-6 | MR 3382201 | Zbl 1329.76001
[29] Nazarov, M.: Convergence of a residual based artificial viscosity finite element method. Comput. Math. Appl. 65 (2013), 616-626 \99999DOI99999 10.1016/j.camwa.2012.11.003 . MR 3011445 | Zbl 1319.65098
[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 \99999DOI99999 10.1002/fld.3663 . MR 3008293 | Zbl 1430.76314
[31] Nichols, R. H.: Turbulence Models and Their Application to Complex Flows: Revision 4.01. University of Alabama at Birmingham, Birmingham (2014).
[32] Nordanger, K., Holdahl, R., Kvarving, A. M., Rasheed, A., Kvamsdal, T.: Implementation and comparison of three isogeometric Navier-Stokes solvers applied to simulation of flow past a fixed 2D NACA0012 airfoil at high Reynolds number. Comput. Methods Appl. Mech. Eng. 284 (2015), 664-688. DOI 10.1016/j.cma.2014.10.033 | MR 3310302 | Zbl 1425.65118
[33] Group), OpenCFD (ESI: OpenFOAM: User Guide v2112: The open source CFD toolbox. Available at (2019).
[34] Otoguro, Y., Takizawa, K., Tezduyar, T. E.: Element length calculation in B-spline meshes for complex geometries. Comput. Mech. 65 (2020), 1085-1103. DOI 10.1007/s00466-019-01809-w | MR 4077709 | Zbl 1462.76148
[35] Piegl, L., Tiller, W.: The $NURBS$ Books. Monographs in Visual Communication. Springer, Berlin (1997). DOI 10.1007/978-3-642-59223-2 | Zbl 0868.68106
[36] Roos, H.-G., Stynes, M., Tobiska, L.: Robust Numerical Methods for Singularly Perturbed Differential Equations: Convection-diffusion-reaction and Flow Problems. Springer Series in Computational Mathematics. Springer, Berlin (2008). DOI 10.1007/978-3-540-34467-4 | MR 2454024 | Zbl 1155.65087
[37] Shakib, F., Hughes, T. J. R.: A new finite element formulation for computational fluid dynamics. IX. Fourier analysis of space-time Galerkin/least-squares algorithms. Comput. Methods Appl. Mech. Eng. 87 (1991), 35-58. DOI 10.1016/0045-7825(91)90145-V | MR 1103416 | Zbl 0760.76051
[38] Tagliabue, A., Dedè, L., Quarteroni, A.: Isogeometric analysis and error estimates for high order partial differential equations in fluid dynamics. Comput. Fluids 102 (2014), 277-303. DOI 10.1016/j.compfluid.2014.07.002 | MR 3248826 | Zbl 1391.76360
[39] Takizawa, K., Tezduyar, T. E., Otoguro, Y.: Stabilization and discontinuity-capturing parameters for space-time flow computations with finite element and isogeometric discretizations. Comput. Mech. 62 (2018), 1169-1186. DOI 10.1007/s00466-018-1557-x | MR 3876285 | Zbl 1462.76128
[40] Tezduyar, T. E.: Finite element in fluids: Stabilized formulations and moving boundaries and interfaces. Comput. Fluids 36 (2007), 191-206. DOI 10.1016/j.compfluid.2005.02.011 | MR 2288426 | Zbl 1177.76202
[41] Versteeg, H. K., Malalasekera, W.: An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Pearson Education, Harlow (2007).
[42] Wilcox, D. C.: Turbulence Modeling for CFD. DCW Industries, La Canada (2006).
[43] Zhang, H., Craft, T., Iacovides, H.: The formulation of the RANS equations for hypersonic turbulent flows. Proceedings of the 5th World Congress on Mechanical, Chemical, and Material Engineering (MCM'19) Avestia Publishing, Orléans (2019), Article ID 172, 9 pages. DOI 10.11159/htff19.172
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