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Comparison of a spectral method with volume penalization and a finite volume method with body fitted grids for turbulent flows. (English) Zbl 1390.76652

Summary: We consider a turbulent flow past periodic hills at Reynolds number 1400 and compare two numerical methods: a Fourier pseudo-spectral scheme with volume penalization to model the no-slip boundary conditions and a finite volume method with body fitted grids. A detailed comparison of the results is presented for mean velocity profiles and Reynolds stress and confronted with those obtained by M. Breuer et al. [ibid. 38, No. 2, 433–457 (2009; Zbl 1237.76026)]. In addition higher order statistics are performed and their scale-dependence is analyzed using orthogonal wavelets. Moreover, for the Fourier pseudo-spectral scheme, the influence of the Reynolds number is investigated.

MSC:

76M22 Spectral methods applied to problems in fluid mechanics
76F65 Direct numerical and large eddy simulation of turbulence
76M12 Finite volume methods applied to problems in fluid mechanics

Citations:

Zbl 1237.76026

Software:

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References:

[1] Breuer, M.; Peller, N.; Rapp, C.; Manhart, M., Flow over periodic hills - numerical and experimental study in a wide range of Reynolds number, Comput Fluids, 38, 433-457, (2009) · Zbl 1237.76026
[2] Courant, R., Variational methods for the solution of problems of equilibrium and vibrations, Bull Amer Math Soc, 49, 1-23, (1943) · Zbl 0810.65100
[3] Glowinski, R.; Kuznetsov, Y., On the solution of the Dirichlet problem for linear elliptic operators by a distributed Lagrange multiplier method, C R Acad Sci Paris, Sér I, 327, 693-698, (1999) · Zbl 1005.65127
[4] Cheny, Y.; Botella, O., The LS-STAG method: A new immersed boundary/level-set method for the computation of incompressible viscous flows in complex moving geometries with good conservation properties, J Comput Phys, 229, 1043-1076, (2010) · Zbl 1329.76252
[5] Peskin, C. S., Flow patterns around heart valves: a numerical method, J Comput Phys, 10, 2, 252-271, (1972) · Zbl 0244.92002
[6] Angot, P.; Bruneau, C.-H.; Fabrie, P., A penalization method to take into account obstacles in viscous flows, Numer Math, 81, 497, (1999) · Zbl 0921.76168
[7] Peskin, C. S., The immersed boundary method, Acta Numer, 11, 479517, (2002)
[8] Mittal, R.; Iaccarino, G., Immersed boundary methods, Annu Rev Fluid Mech, 37, 23961, (2005)
[9] Schneider, K., Immersed boundary methods for numerical simulation of confined fluid and plasma turbulence in complex geometries: a review, J Plasma Phys, 81, 6, 435810601, (2015)
[10] Canuto, C.; Hussaini, M. Y.; Quarteroni, A.; Zang, T. A., Spectral methods in fluid dynamics, (1988), Springer-Verlag · Zbl 0658.76001
[11] Keetels, G. H.; D’Ortona, U.; Kramer, W.; Clercx, H. J.H.; Schneider, K.; van Heijst, G. J.F., Fourier spectral and wavelet solvers for the incompressible Navier-Stokes equations with volume-penalization: convergence of a dipole-wall collision, J Comput Phys, 227, 2, 919-945, (2007) · Zbl 1301.76062
[12] Schneider, K., Numerical simulation of the transient flow behaviour in chemical reactors using a penalization method, Comput Fluids, 34, 1223-1238, (2005) · Zbl 1095.76041
[13] Kolomenskiy, D.; Schneider, K., A Fourier spectral method for the Navier-Stokes equations with volume penalization for moving solid obstacles, J Comput Phys, 228, 5687-5709, (2009) · Zbl 1169.76045
[14] Fastest - user manual, (2004), Institute of Numerical Methods in Mechanical Engineering. Technische Universität Darmstadt
[15] Chang, P. H.; Liao, C. C.; Hsu, H. W.; Liu, S. H.; Lin, C. A., Simulations of laminar and turbulent flows over periodic hills with immersed boundary method, Comput Fluids, 92, 233-243, (2014) · Zbl 1391.76208
[16] Kadoch, B.; Kolomenskiy, D.; Angot, P.; Schneider, K., A volume penalization method for Navier-Stokes flows and scalar advection-diffusion with moving obstacles, J Comput Phys, 231, 4365-4383, (2012) · Zbl 1244.76074
[17] Benarafa, Y.; Cioni, O.; Ducros, F.; Sagaut, P., RANS LES and coupling for unsteady turbulent flow simulation at high Reynolds number on coarse meshes, Comput Methods Appl Mech Eng, 195, 23-24, 2939-2960, (2006) · Zbl 1176.76050
[18] Lehnhäuser, T.; Schäfer, M., Improved linear interpolation practice for finite-volume schemes on complex grids, Int J Numer Meth Fluids, 38, 7, 625-645, (2002) · Zbl 1017.76053
[19] Hanjalić, K.; Popovac, M.; Hadziabdić, M., A robust near-wall elliptic-relaxation eddy-viscosity turbulence model for CFD, Int J Heat Fluid Flow, 25, 6, 1047-1051, (2004)
[20] Pope, S. B., Turbulent flows, (2000), Cambridge University Press · Zbl 0966.76002
[21] Schneider, K.; Vasilyev, O., Wavelet methods in computational fluid dynamics, Annu Rev Fluid Mech, 42, 473-503, (2010) · Zbl 1345.76085
[22] Bos, W. J.T.; Liechtenstein, L.; Schneider, K., Small scale intermittency in anisotropic turbulence, Phys Rev E, 76, 046310, (2007)
[23] Daubechies, I., Ten lectures on wavelets, Philadelphia: Society for industrial and applied mathematics, 61, 198-202, (1992) · Zbl 0776.42018
[24] Mallat, S., A wavelet tour of signal processing, (1999), Academic Press · Zbl 0998.94510
[25] van yen Nguyen, R.; Kolomenskiy, D.; Schneider, K., Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint, Numer Math, 128, 301-338, (2014) · Zbl 1301.65118
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