UDNS or LES, That Is the Question
Affiliation(s)
1 Paul Scherrer Institut, Laboratory for Thermal-Hydraulics (LTH), Villigen PSI, Switzerland. 2 école Polytechnique Fédérale de Lausanne, School of Engineering, Lausanne, Switzerland. 3 Université de Lille 1, Laboratoire de Mécanique, Boulevard Paul Langevin, Villeneuve d'Ascq Cedex, France.
1 Paul Scherrer Institut, Laboratory for Thermal-Hydraulics (LTH), Villigen PSI, Switzerland. 2 école Polytechnique Fédérale de Lausanne, School of Engineering, Lausanne, Switzerland. 3 Université de Lille 1, Laboratoire de Mécanique, Boulevard Paul Langevin, Villeneuve d'Ascq Cedex, France.
ABSTRACT
In the framework of the spectral element method, a comparison is carried out on turbulent first-and second-order statistics generated by large eddy simulation (LES), under-resolved (UDNS) and fully resolved direct numerical simulation (DNS). The LES is based on classical models like the dynamic Smagorinsky approach or the approximate deconvolution method. Two test problems are solved: the lid-driven cubical cavity and the differentially heated cavity. With the DNS data as benchmark solutions, it is shown that the numerical results produced by the UDNS calculation are of the same accuracy, even in some cases of better quality, as the LES computations. The conclusion advocates the use of UDNS and calls for improvement of the available algorithms.
In the framework of the spectral element method, a comparison is carried out on turbulent first-and second-order statistics generated by large eddy simulation (LES), under-resolved (UDNS) and fully resolved direct numerical simulation (DNS). The LES is based on classical models like the dynamic Smagorinsky approach or the approximate deconvolution method. Two test problems are solved: the lid-driven cubical cavity and the differentially heated cavity. With the DNS data as benchmark solutions, it is shown that the numerical results produced by the UDNS calculation are of the same accuracy, even in some cases of better quality, as the LES computations. The conclusion advocates the use of UDNS and calls for improvement of the available algorithms.
KEYWORDS
Spectral Element Method, Under-Resolved Direct Numerical Simulation, Large Eddy Simulation, Lid-Driven Cavity, Differentially Heated Cavity
Spectral Element Method, Under-Resolved Direct Numerical Simulation, Large Eddy Simulation, Lid-Driven Cavity, Differentially Heated Cavity
Cite this paper
Bosshard, C. , Deville, M. , Dehbi, A. and Leriche, E. (2015) UDNS or LES, That Is the Question. Open Journal of Fluid Dynamics, 5, 339-352. doi: 10.4236/ojfd.2015.54034.
Bosshard, C. , Deville, M. , Dehbi, A. and Leriche, E. (2015) UDNS or LES, That Is the Question. Open Journal of Fluid Dynamics, 5, 339-352. doi: 10.4236/ojfd.2015.54034.
References
[1] Berselli, L.C., Iliescu, T. and Layton, W.J. (2006) Mathematics of Large Eddy Simulation of Turbulent Flows. Springer, Berlin. [2] Deville, M.O. and Gatski, T.B. (2012) Mathematical Modeling for Complex Fluids and Flows. Springer, Berlin.
http://dx.doi.org/10.1007/978-3-642-25295-2 [3] Sagaut, P. (2006) Large Eddy Simulation for Incompressible Flows. Springer, Berlin. [4] Deville, M.O., Fischer, P.F. and Mund, E.H. (2002) High-Order Methods for Incompressible Fluid Flow. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511546792 [5] Germano, M., Piomelli, U., Moin, P. and Cabot, W.H. (1991) A Dynamic Subgrid-Scale Eddy Viscosity Model. Physics of Fluids A: Fluid Dynamics, 3, 1760-1765.
http://dx.doi.org/10.1063/1.857955 [6] Lilly, D.K. (1992) A Proposed Modification of the Germano Subgrid-Scale Closure Method. Physics of Fluids A: Fluid Dynamics, 4, 633-635.
http://dx.doi.org/10.1063/1.858280 [7] Boyd, J.P. (1998) Two Comments on Filtering for Chebyshev and Legendre Spectral and Spectral Element Methods. Journal of Computational Physics, 143, 283-288.
http://dx.doi.org/10.1006/jcph.1998.5961 [8] Fischer, P.F. and Mullen, J. (2001) Filter-Based Stabilization of Spectral Element Methods. Comptes Rendus de l’Académie des Sciences, Series I, Mathematics, 332, 265-270.
http://dx.doi.org/10.1016/S0764-4442(00)01763-8 [9] Blackburn, H.M. and Schmidt, S. (2003) Spectral Element Filtering Techniques for Large Eddy Simulation with Dynamic Estimation. Journal of Computational Physics, 186, 610-629.
http://dx.doi.org/10.1016/S0021-9991(03)00088-3 [10] Bosshard, C., Dehbi, A., Deville, M., Leriche, E., Puragliesi, R. and Soldati, A. (2013) Large Eddy Simulation of the Differentially Heated Cubic Cavity Flow by the Spectral Element Method. Computers & Fluids, 86, 210-227.
http://dx.doi.org/10.1016/j.compfluid.2013.07.007 [11] Leriche, E. (2006) Direct Numerical Simulation of Lid Driven Cavity at High Reynolds Numbers. Journal of Scientific Computing, 27, 335-345.
http://dx.doi.org/10.1007/s10915-005-9032-1 [12] Leriche, E. and Gavrilakis, S. (2000) Direct Numerical Simulation of the Flow in a Lid-Driven Cubical Cavity. Physics of Fluids, 12, 1363-1376.
http://dx.doi.org/10.1063/1.870387 [13] Puragliesi, R. (2010) Numerical Investigation of Particle-Laden Thermally Driven Turbulent Flows in Enclosure. PhD Thesis, No. 4600, EPF Lausanne, écublens. [14] Bouffanais, R., Deville, M.O. and Leriche, E. (2007) Large-Eddy Simulation of the Flow in a Lid-Driven Cubical Cavity. Physics of Fluids, 19, Article ID: 055108.
http://dx.doi.org/10.1063/1.2723153 [15] Habisreutinger, M.A., Bouffanais, R., Leriche, E. and Deville, M.O. (2007) A Coupled Approximate Deconvolution and Dynamic Mixed Scale Model for Large-Eddy Simulation. Journal of Computational Physics, 224, 241-266.
http://dx.doi.org/10.1016/j.jcp.2007.02.010 [16] Puragliesi, R., Dehbi, A., Leriche, E., Soldati, A. and Deville, M.O. (2011) DNS of Buoyancy-Driven Flows and Lagrangian Particle Tracking in a Square Cavity at High Rayleigh Numbers. International Journal of Heat and Fluid Flow, 32, 915-931.
http://dx.doi.org/10.1016/j.ijheatfluidflow.2011.06.007 [17] Stolz, S. and Adams, N.A. (1999) An Approximate Deconvolution Procedure for Large-Eddy Simulation. Physics of Fluids, 11, 1699-1701.
http://dx.doi.org/10.1063/1.869867 [18] Stolz, S., Adams, N.A. and Kleiser, L. (2001) An Approximate Deconvolution Model for Large-Eddy Simulation with Application to Incompressible Wall-Bounded Flows. Physics of Fluids, 13, 997-1015.
http://dx.doi.org/10.1063/1.1350896 [19] Bouffanais, R. (2007) Simulation of shear-driven flows: transition with a free surface and confined turbulence. PhD Thesis, No. 3837, EPF Lausanne, écublens. [20] Bosshard, C. (2012) Large Eddy Simulation of Particle Dynamics inside a Differentially Heated Cavity. PhD Thesis, No. 5297, EPF Lausanne, écublens. [21] Dubois-Pèlerin, Y., Van Kemenade, V. and Deville, M.O. (1999) An Object-Oriented Toolbox for Spectral Element Analysis. Journal of Scientific Computing, 14, 1-29.
http://dx.doi.org/10.1023/A:1025677921253 [22] Speculoos. Spectral Element Analysis Software for the Numerical Solution of Partial Differential Equations; 1998- 2013.
http://sourceforge.net/projects/openspeculoos/ [23] Zang, Y., Street, R.L. and Koseff, J.R. (1993) A Dynamic Mixed Subgrid-Scale Model and Its Application to Turbulent Recirculating Flows. Physics of Fluids A: Fluid Dynamics, 5, 3186-3196.
http://dx.doi.org/10.1063/1.858675 [24] Domaradzki, J.A. and Adams, N.A. (2002) Direct Modelling of Subgrid Scales of Turbulence in Large Eddy Simulations. Journal of Turbulence, 3, 024.
http://dx.doi.org/10.1088/1468-5248/3/1/024 [25] Domaradzki, J.A., Loh, K.C. and Yee, P.P. (2002) Large Eddy Simulations Using the Subgrid-Scale Estimation Model and Truncated Navier-Stokes Dynamics. Theoretical and Computational Fluid Dynamics, 15, 421-450.
http://dx.doi.org/10.1007/s00162-002-0056-y
[1] Berselli, L.C., Iliescu, T. and Layton, W.J. (2006) Mathematics of Large Eddy Simulation of Turbulent Flows. Springer, Berlin. [2] Deville, M.O. and Gatski, T.B. (2012) Mathematical Modeling for Complex Fluids and Flows. Springer, Berlin.
http://dx.doi.org/10.1007/978-3-642-25295-2 [3] Sagaut, P. (2006) Large Eddy Simulation for Incompressible Flows. Springer, Berlin. [4] Deville, M.O., Fischer, P.F. and Mund, E.H. (2002) High-Order Methods for Incompressible Fluid Flow. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511546792 [5] Germano, M., Piomelli, U., Moin, P. and Cabot, W.H. (1991) A Dynamic Subgrid-Scale Eddy Viscosity Model. Physics of Fluids A: Fluid Dynamics, 3, 1760-1765.
http://dx.doi.org/10.1063/1.857955 [6] Lilly, D.K. (1992) A Proposed Modification of the Germano Subgrid-Scale Closure Method. Physics of Fluids A: Fluid Dynamics, 4, 633-635.
http://dx.doi.org/10.1063/1.858280 [7] Boyd, J.P. (1998) Two Comments on Filtering for Chebyshev and Legendre Spectral and Spectral Element Methods. Journal of Computational Physics, 143, 283-288.
http://dx.doi.org/10.1006/jcph.1998.5961 [8] Fischer, P.F. and Mullen, J. (2001) Filter-Based Stabilization of Spectral Element Methods. Comptes Rendus de l’Académie des Sciences, Series I, Mathematics, 332, 265-270.
http://dx.doi.org/10.1016/S0764-4442(00)01763-8 [9] Blackburn, H.M. and Schmidt, S. (2003) Spectral Element Filtering Techniques for Large Eddy Simulation with Dynamic Estimation. Journal of Computational Physics, 186, 610-629.
http://dx.doi.org/10.1016/S0021-9991(03)00088-3 [10] Bosshard, C., Dehbi, A., Deville, M., Leriche, E., Puragliesi, R. and Soldati, A. (2013) Large Eddy Simulation of the Differentially Heated Cubic Cavity Flow by the Spectral Element Method. Computers & Fluids, 86, 210-227.
http://dx.doi.org/10.1016/j.compfluid.2013.07.007 [11] Leriche, E. (2006) Direct Numerical Simulation of Lid Driven Cavity at High Reynolds Numbers. Journal of Scientific Computing, 27, 335-345.
http://dx.doi.org/10.1007/s10915-005-9032-1 [12] Leriche, E. and Gavrilakis, S. (2000) Direct Numerical Simulation of the Flow in a Lid-Driven Cubical Cavity. Physics of Fluids, 12, 1363-1376.
http://dx.doi.org/10.1063/1.870387 [13] Puragliesi, R. (2010) Numerical Investigation of Particle-Laden Thermally Driven Turbulent Flows in Enclosure. PhD Thesis, No. 4600, EPF Lausanne, écublens. [14] Bouffanais, R., Deville, M.O. and Leriche, E. (2007) Large-Eddy Simulation of the Flow in a Lid-Driven Cubical Cavity. Physics of Fluids, 19, Article ID: 055108.
http://dx.doi.org/10.1063/1.2723153 [15] Habisreutinger, M.A., Bouffanais, R., Leriche, E. and Deville, M.O. (2007) A Coupled Approximate Deconvolution and Dynamic Mixed Scale Model for Large-Eddy Simulation. Journal of Computational Physics, 224, 241-266.
http://dx.doi.org/10.1016/j.jcp.2007.02.010 [16] Puragliesi, R., Dehbi, A., Leriche, E., Soldati, A. and Deville, M.O. (2011) DNS of Buoyancy-Driven Flows and Lagrangian Particle Tracking in a Square Cavity at High Rayleigh Numbers. International Journal of Heat and Fluid Flow, 32, 915-931.
http://dx.doi.org/10.1016/j.ijheatfluidflow.2011.06.007 [17] Stolz, S. and Adams, N.A. (1999) An Approximate Deconvolution Procedure for Large-Eddy Simulation. Physics of Fluids, 11, 1699-1701.
http://dx.doi.org/10.1063/1.869867 [18] Stolz, S., Adams, N.A. and Kleiser, L. (2001) An Approximate Deconvolution Model for Large-Eddy Simulation with Application to Incompressible Wall-Bounded Flows. Physics of Fluids, 13, 997-1015.
http://dx.doi.org/10.1063/1.1350896 [19] Bouffanais, R. (2007) Simulation of shear-driven flows: transition with a free surface and confined turbulence. PhD Thesis, No. 3837, EPF Lausanne, écublens. [20] Bosshard, C. (2012) Large Eddy Simulation of Particle Dynamics inside a Differentially Heated Cavity. PhD Thesis, No. 5297, EPF Lausanne, écublens. [21] Dubois-Pèlerin, Y., Van Kemenade, V. and Deville, M.O. (1999) An Object-Oriented Toolbox for Spectral Element Analysis. Journal of Scientific Computing, 14, 1-29.
http://dx.doi.org/10.1023/A:1025677921253 [22] Speculoos. Spectral Element Analysis Software for the Numerical Solution of Partial Differential Equations; 1998- 2013.
http://sourceforge.net/projects/openspeculoos/ [23] Zang, Y., Street, R.L. and Koseff, J.R. (1993) A Dynamic Mixed Subgrid-Scale Model and Its Application to Turbulent Recirculating Flows. Physics of Fluids A: Fluid Dynamics, 5, 3186-3196.
http://dx.doi.org/10.1063/1.858675 [24] Domaradzki, J.A. and Adams, N.A. (2002) Direct Modelling of Subgrid Scales of Turbulence in Large Eddy Simulations. Journal of Turbulence, 3, 024.
http://dx.doi.org/10.1088/1468-5248/3/1/024 [25] Domaradzki, J.A., Loh, K.C. and Yee, P.P. (2002) Large Eddy Simulations Using the Subgrid-Scale Estimation Model and Truncated Navier-Stokes Dynamics. Theoretical and Computational Fluid Dynamics, 15, 421-450.
http://dx.doi.org/10.1007/s00162-002-0056-y