Modal explicit filtering for large eddy simulation in discontinuous spectral element method. (English) Zbl 07785510
Summary: Developing a turbulence model that is computationally inexpensive and compatible with the nature of the numerical scheme is a crucial step in expanding the application of spectral element methods for large eddy simulation (LES) in complex geometries. In this paper, an element-level modal low-pass explicit filtering procedure, which operates in the spectral space, is implemented in a discontinuous spectral element method (DSEM). The application of the modal filter is studied for LES without a subgrid-scale (SGS) model. The method is tested for a configuration featuring isotropic turbulence, and its performance is compared with a previously used method – a spectral interpolation-based nodal filter. The modal filter shows superior performance over the nodal filter. The filtering procedure is then applied to a turbulent channel flow at a friction Reynolds number of \(Re_\tau = 544\), and the results are compared with a previous direct numerical simulation (DNS). It is also shown that the filter strength that provides the best comparison with DNS depends only on the polynomial order and is not a function of the grid resolution. An anisotropic version of the modal filter, which damps high-frequency modes in a specific direction, is also introduced and tested for the channel flow. It is observed that filtering in the spanwise direction is the most effective approach based on the comparison of velocity mean and fluctuations with DNS. In general, the modal filter has shown good performance for both isotropic and wall-bounded flows; the calculated channel friction Reynolds number for the modal filter is within 0.26% error with respect to the DNS data, compared to 5.8% error for a case with no filtering.
MSC:
| 76Mxx | Basic methods in fluid mechanics |
| 76Fxx | Turbulence |
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
References:
| [1] | Vasilyev, O. V.; Lund, T. S.; Moin, P., A general class of commutative filters for LES in complex geometries. J. Comput. Phys., 82-104 (1998) · Zbl 0913.76072 |
| [2] | Gullbrand, J.; Chow, F. K., The effect of numerical errors and turbulence models in large-eddy simulations of channel flow, with and without explicit filtering. J. Fluid Mech., 323-341 (2003) · Zbl 1077.76032 |
| [3] | Lund, T.; Kaltenbach, H., Experiments with explicit filtering for LES using a finite-difference method, 91-105 |
| [4] | Lund, T., On the use of discrete filters for large eddy simulation, 83-95 |
| [5] | Winckelmans, G. S.; Wray, A. A.; Vasilyev, O. V.; Jeanmart, H., Explicit-filtering large-eddy simulation using the tensor-diffusivity model supplemented by a dynamic Smagorinsky term. Phys. Fluids, 1385-1403 (2001) · Zbl 1184.76594 |
| [6] | Lilly, D. K., A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A, Fluid Dyn., 633-635 (1992) |
| [7] | Smagorinsky, J., General circulation experiments with the primitive equations, I: the basic experiment. Mon. Weather Rev., 99-164 (1963) |
| [8] | Germano, M.; Piomelli, U.; Moin, P.; Cabot, W. H., A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A, Fluid Dyn., 1760-1765 (1991) · Zbl 0825.76334 |
| [9] | Bardina, J.; Ferziger, J. H.; Reynolds, W. C., Improved subgrid-scale models for large-eddy simulation, 10 |
| [10] | Grinstein, F. F.; Fureby, C., Recent progress on MILES for high Reynolds number flows. J. Fluids Eng., 848-861 (2002) |
| [11] | Margolin, L. G.; Rider, W. J.; Grinstein, F. F., Modeling turbulent flow with implicit LES. J. Turbul., N15 (2006) · Zbl 1273.76213 |
| [12] | Grinstein, F. F.; Margolin, L. G.; Rider, W. J., Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics (2007), Cambridge University Press · Zbl 1135.76001 |
| [13] | Aspden, A.; Nikiforakis, N.; Dalziel, S.; Bell, J., Analysis of implicit LES methods. Commun. Appl. Math. Comput. Sci., 103-126 (2009) · Zbl 1162.76024 |
| [14] | Bogey, C.; Bailly, C., Computation of a high Reynolds number jet and its radiated noise using large eddy simulation based on explicit filtering. Comput. Fluids, 1344-1358 (2006) · Zbl 1177.76372 |
| [15] | Mathew, J.; Lechner, R.; Foysi, H.; Sesterhenn, J.; Friedrich, R., An explicit filtering method for large eddy simulation of compressible flows. Phys. Fluids, 2279-2289 (2003) · Zbl 1186.76355 |
| [16] | Fischer, P.; Mullen, J., Filter-based stabilization of spectral element methods. C. R. Acad. Sci., Ser. 1 Math., 265-270 (2001) · Zbl 0990.76064 |
| [17] | Fischer, P.; Lottes, J.; Siegel, A.; Palmiotti, G., Large eddy simulation of wire wrapped fuel pins, I: hydrodynamics in a periodic array |
| [18] | Sengupta, K., Direct and Large-eddy Simulation of Compressible Flows with Spectral/hp Element Methods (2008), University of Illinois at Chicago, Ph.D. Thesis |
| [19] | Kanchi, H.; Mashayek, F.; Sengupta, K.; Jacobs, G.; Fischer, P., Comparison of LES Studies in Backward-Facing Step Using Chebyshev Multidomain and Legendre Spectral Element Methods (2011), AIAA Paper 2011-3557 |
| [20] | Boyd, J. P., The erfc-log filter and the asymptotics of the Euler and Vandeven sequence accelerations. Proceedings of the Third International Conference on Spectral and High Order Methods. Houst. J. Math., 267-276 (1996) |
| [21] | Boyd, J. P., Two comments on filtering (artificial viscosity) for Chebyshev and Legendre spectral and spectral element methods: preserving boundary conditions and interpretation of the filter as a diffusion. J. Comput. Phys., 283-288 (1998) · Zbl 0920.65046 |
| [22] | Levin, J. G.; Iskandarani, M.; Haidvogel, D. B., A spectral filtering procedure for eddy-resolving simulations with a spectral element ocean model. J. Comput. Phys., 130-154 (1997) · Zbl 0898.76082 |
| [23] | Blackburn, H. M.; Schmidt, S., Spectral element filtering techniques for large-eddy simulation with dynamic estimation. J. Comput. Phys., 610-629 (2003) · Zbl 1047.76520 |
| [24] | Bouffanais, R.; Deville, M. O.; Fischer, P. F.; Leriche, E.; Weill, D., Large-eddy simulation of the lid-driven cubic cavity flow by the spectral element method. J. Sci. Comput., 151-162 (2006) · Zbl 1099.76026 |
| [25] | Lodato, G.; Castonguay, P.; Jameson, A., Discrete filter operators for large-eddy simulation using high-order spectral difference methods. Int. J. Numer. Methods Fluids, 231-258 (2013) · Zbl 1455.76061 |
| [26] | Chaudhuri, A.; Jacobs, G. B.; Don, W.-S.; Abbassi, H.; Mashayek, F., Explicit discontinuous spectral element method with entropy generation based artificial viscosity for shocked viscous flows. J. Comput. Phys., 99-117 (2017) · Zbl 1378.76040 |
| [27] | Gassner, G. J.; Beck, A. D., On the accuracy of high-order discretizations for underresolved turbulence simulations. Theor. Comput. Fluid Dyn., 221-237 (2013) |
| [28] | Flad, D.; Beck, A.; Munz, C.-D., Simulation of underresolved turbulent flows by adaptive filtering using the high order discontinuous Galerkin spectral element method. J. Comput. Phys., 1-12 (2016) · Zbl 1349.76118 |
| [29] | Winters, A. R.; Moura, R. C.; Mengaldo, G.; Gassner, G. J.; Walch, S.; Peiro, J.; Sherwin, S. J., A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations. J. Comput. Phys., 1-21 (2018) · Zbl 1415.76461 |
| [30] | Mullen, J. S.; Fischer, P. F., Filtering techniques for complex geometry fluid flows. Commun. Numer. Methods Eng., 9-18 (1999) · Zbl 0931.76067 |
| [31] | Jacobs, G. B., Numerical Simulation of Two-Phase Turbulent Compressible Flows with a Multidomain Spectral Method (2003), University of Illinois at Chicago, Ph.D. Thesis |
| [32] | Kopriva, D. A.; Kolias, J. H., A conservative staggered-grid Chebyshev multidomain method for compressible flows. J. Comput. Phys., 244-261 (1996) · Zbl 0847.76069 |
| [33] | Kopriva, D. A., A staggered-grid multidomain spectral method for the compressible Navier-Stokes equations. J. Comput. Phys., 125-158 (1998) · Zbl 0921.76121 |
| [34] | Li, D.; Ghiasi, Z.; Komperda, J.; Mashayek, F., The effect of inflow Mach number on the reattachment in subsonic flow over a backward-facing step · Zbl 1507.76078 |
| [35] | Ghiasi, Z.; Komperda, J.; Li, D.; Mashayek, F., Simulation of Supersonic Turbulent Non-Reactive Flow in Ramp-Cavity Combustor Using a Discontinuous Spectral Element Method (2016), AIAA Paper 2016-0617 |
| [36] | Komperda, J.; Ghiasi, Z.; Li, D.; Mashayek, F.; Irannejad, A.; Jaberi, F. A., Simulation of the Cold Flow in a Ramp-Cavity Combustor Using a DSEM-LES/FMDF Hybrid Scheme (2016), AIAA Paper 2016-1938 |
| [37] | Ghiasi, Z.; Li, D.; Komperda, J.; Mashayek, F., Wall resolution study for direct numerical simulation of turbulent channel flow using a multidomain Chebyshev grid · Zbl 1507.76078 |
| [38] | Li, D.; Ghiasi, Z.; Komperda, J.; Mashayek, F., A numerical study of compressibility effects in turbulent mixing layer · Zbl 1461.76297 |
| [39] | Hesthaven, J.; Warburton, T., Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications (2008), Springer Science & Business Media: Springer Science & Business Media Berlin · Zbl 1134.65068 |
| [40] | Corr, P.; Stewart, D.; Hanna, P.; Ming, J.; Smith, F. J., Discrete Chebyshev transform: a natural modification of the DCT. Proceedings of 15th International Conference on Pattern Recognition, 2000, 1142-1145 (2000), IEEE |
| [41] | FFTW documentations: 1d real-even DFTs (DCTs) (2018) |
| [42] | Fischer, P. F.; Kruse, G. W.; Loth, F., Spectral element methods for transitional flows in complex geometries. J. Sci. Comput., 81-98 (2002) · Zbl 1001.76075 |
| [43] | Blaisdell, G. A.; Mansour, N. N.; Reynolds, W. C., Compressibility effects on the growth and structure of homogeneous turbulent shear flow. J. Fluid Mech., 443-485 (1993) · Zbl 0800.76186 |
| [44] | Blaisdell, G. A.; Mansour, N. N.; Reynolds, W. C., Numerical simulation of compressible homogeneous turbulence, Mixing TF-50 · Zbl 0832.76030 |
| [45] | Jacobs, G. B.; Kopriva, D. A.; Mashayek, F., Validation study of a multidomain spectral code for simulation of turbulent flows. AIAA J., 1256-1264 (2005) |
| [46] | Gullbrand, J., Explicit filtering and subgrid-scale models in turbulent channel flow, 31-42 |
| [47] | Lee, M.; Moser, R. D., Direct numerical simulation of turbulent channel flow up to \(\mathit{Re}_\tau \approx 5200\). J. Fluid Mech., 395-415 (2015) |
| [48] | Rai, M. M.; Moin, P., Direct simulations of turbulent flow using finite-difference schemes. J. Comput. Phys., 15-53 (1991) · Zbl 0726.76072 |
| [49] | Kim, J.; Moin, P.; Moser, R. D., Turbulent statistics in fully developed turbulent channel flow at low Reynolds number. J. Fluid Mech., 133-166 (1987) · Zbl 0616.76071 |
| [50] | Ghiasi, Z.; Li, D.; Komperda, J.; Mashayek, F., Near-wall resolution requirement for direct numerical simulation of turbulent flow using multidomain Chebyshev grid. Int. J. Heat Mass Transf., 746-760 (2018) |
| [51] | Lenormand, E.; Sagaut, P.; Ta Phuoc, L., Large eddy simulation of subsonic and supersonic channel flow at moderate Reynolds number. Int. J. Numer. Methods Fluids, 369-406 (2000) · Zbl 0981.76046 |
| [52] | FFT benchmark results (2018) |
| [53] | Advanced Cyberinfrastructure for Education and Research (2018) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
