Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-27T06:11:05.207Z Has data issue: false hasContentIssue false
  • English
  • Français

High Order Numerical Methods for the Dynamic SGS Model of Turbulent Flows with Shocks

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Computer aspects of numerical algorithms

Published online by Cambridge University Press:  01 February 2016

D. V. Kotov ,
H. C. Yee ,
A. A. Wray ,
A. Hadjadj  and
B. Sjögreen
D. V. Kotov
Affiliation:
Bay Area Environmental Research Institute, 625 2nd St. Ste 209, Petaluma, CA, USA
H. C. Yee*
Affiliation:
NASA-Ames Research Center, Moffett Field, CA94035, USA
A. A. Wray
Affiliation:
NASA-Ames Research Center, Moffett Field, CA94035, USA
A. Hadjadj
Affiliation:
CORIA UMR 6614 & INSA de Rouen, 76800 St-Etienne du Rouvray, France
B. Sjögreen
Affiliation:
Computational Scientist, Lawrence Livermore National Laboratory, USA
*
*Corresponding author. Email addresses:[email protected] (D. V. Kotov), [email protected] (H. C. Yee), [email protected] (A. A. Wray), [email protected] (A. Hadjadj), Sjö[email protected] (B. Sjögreen)
Get access

Abstract

Simulation of turbulent flows with shocks employing subgrid-scale (SGS) filtering may encounter a loss of accuracy in the vicinity of a shock. This paper addresses the accuracy improvement of LES of turbulent flows in two ways: (a) from the SGS model standpoint and (b) from the numerical method improvement standpoint. In an internal report, Kotov et al. ( “High Order Numerical Methods for large eddy simulation (LES) of Turbulent Flows with Shocks”, CTR Tech Brief, Oct. 2014, Stanford University), we performed a preliminary comparative study of different approaches to reduce the loss of accuracy within the framework of the dynamic Germano SGS model. The high order low dissipative method of Yee & Sjögreen (2009) using local flow sensors to control the amount of numerical dissipation where needed is used for the LES simulation. The considered improved dynamics model approaches include applying the one-sided SGS test filter of Sagaut & Germano (2005) and/or disabling the SGS terms at the shock location. For Mach 1.5 and 3 canonical shock-turbulence interaction problems, both of these approaches show a similar accuracy improvement to that of the full use of the SGS terms. The present study focuses on a five levels of grid refinement study to obtain the reference direct numerical simulation (DNS) solution for additional LES SGS comparison and approaches. One of the numerical accuracy improvements included here applies Harten's subcell resolution procedure to locate and sharpen the shock, and uses a one-sided test filter at the grid points adjacent to the exact shock location.

Keywords

High order numerical methodsturbulent flows with shocksGermano SGS modelLES

MSC classification

Secondary: 65Z05: Applications to physics 65M06: Finite difference methods 65M50: Mesh generation and refinement 65M55: Multigrid methods; domain decomposition 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65M99: None of the above, but in this section 65Y99: None of the above, but in this section
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 2 , February 2016 , pp. 273 - 300
Copyright
Copyright © Global-Science Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Adams, N. A. and Stolz, S.. A subgrid-scale deconvolution approach for shock capturing. J. Comput. Phys., 178:391–426, 2002.Google Scholar
[2]Bermejo-Moreno, I., Larsson, J., and Lele, S. K.. LES of canonical shock-turbulence interaction. Annual Research Briefs, Center for Turbulence Research, Stanford, pages 209–222, 2010.Google Scholar
[3]Ciment, M. and Leventhal, S. H.. Higher order compact implicit sehemes for the wave equation. Math. Comput., 29:985–994, 1975.Google Scholar
[4]Ducros, F., Ferrand, V., Nicoud, F., Weber, C., Darracq, D., Gacherieu, C., and Poinsot, T.. Large-eddy simulation of the shock/turbulence interaction. J. Comput. Phys., 152:517–549, 1999.CrossRefGoogle Scholar
[5]Ducros, F., Laporte, F., Soulères, T., Guinot, V., Moinat, P., and Caruelle, B.. High-order fluxes for conservative skew-symmetric-like schemes in structured meshes: Application to compressible flows. J. Comput. Phys., 161:114–139, 2000.Google Scholar
[6]Erlebacher, G., Hussaini, M. Y., Speziale, C. G., and Zang, T. A.. Toward the large eddy simulation of compressible turbulent flows. J. Fluid Mech., 238:155, 1992.CrossRefGoogle Scholar
[7]Germano, M., Piomelli, U., Moin, P., and Cabot, W.. A dynamic subgrid-scale eddy viscosity model. Phys. Fluids, 3(7):1760–1765, 1991.Google Scholar
[8]Grube, N. E. and Martin, M. P.. Assessment of subgrid-scale models and shock-confining filters in large-eddy simulation of highly compressible isotropic turbulence. In 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition, Orlando, Florida, 5-8 January 2009.Google Scholar
[9]Hadjadj, A. and Dubos, S.. Large eddy simulation of supersonic boundary layer at M = 2.4. In Braza, M. and Hourigan, K., editors, Proc. of the IUTAM Symposium on Unsteady Separated Flows and their Control. Springer, 2009. e-ISBN 978-1-4020-9898-7.Google Scholar
[10]Hadjadj, A., Yee, H. C., and Sjögreen, B.. LES of temporally evolving mixing layers by an eighth-order filter scheme. Int. J. Num. Meth. Fluids, 70:1405–1427, 2012.Google Scholar
[11]Harten, A.. ENO schemes with subcell resolution. J. Comput. Phys., 83:148–184, 1989.Google Scholar
[12]Johnsen, E., Larsson, J., Bhagatwala, A.V., Cabot, W. H., Moin, P., Olson, B. J., Rawat, P. S., Shankar, S. K., Sjögreen, B., Yee, H. C., Zhong, X., and Lele, S. K.. Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves. J. Comput. Phys., 229:1213–1237, 2010.Google Scholar
[13]Kotov, D., Yee, H. C., Hadjadj, A., Wray, A., and Sjögreen, B.. High order numerical methods for LES of turbulent flows with shocks. In Proc. of the ICCFD8, Chengdu, Sichuan, China, July 14-18 2014.Google Scholar
[14]Kotov, D., Yee, H. C., Hadjadj, A., Wray, A., and Sjögreen, B.. High-order numerical methods for LES of turbulent flows with shocks. Annual Research Briefs, Center for Turbulence Research, Stanford, pages 89–98, 2014.Google Scholar
[15]Kotov, D., Yee, H. C., and Sjögreen, B.. Performance of improved high-order filter schemes for turbulent flows with shocks. In Proc. of the ASTRONUM-2013, Biarritz, France, July 1-5 2013.Google Scholar
[16]Kotov, D., Yee, H. C., and Sjögreen, B.. Performance of improved high-order filter schemes for turbulent flows with shocks. Annual Research Briefs, Center for Turbulence Research, Stanford, pages 291–302, 2013.Google Scholar
[17]Kotov, D. V., Yee, H. C., Wray, A., and Sjögreen, B.. Numerical dissipation control in high order shock-capturing schemes for LES of low speed flows. In Proc. of the ICOSAHOM 2014, Salt Lake City, Utah, June 23-27 2014.Google Scholar
[18]Larsson, J. and Lele, S. K.. Direct numerical simulation of canonical shock/turbulence interaction. Phys. Fluids, 21(126101), 2009.CrossRefGoogle Scholar
[19]Lee, S., Lele, S. K., and Moin, P.. Interaction of isotropic turbulence with shock waves: Effect of shock strength. J. Fluid Mech., 340:225–247, 1997.Google Scholar
[20]Lilly, D. K.. A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids, 4(3):633–635, 1992.Google Scholar
[21]Lo, S.-C., Blaisdell, G. A., and Lyrintzis, A. S.. High-order shock capturing schemes for turbulence calculations. J. Num. Meth. Fluids, 62(5):473–498, February 2010.Google Scholar
[22]Lombardini, M., Hill, D. J., Pullin, D. I., and Meiron, D. I.. Atwood ratio dependence of Richtmyer-Meshkov flows under reshock conditions using large-eddy simulations. J. Fluid Mech., 670:439–480, 2011.Google Scholar
[23]Lund, T. S.. On the use of discrete fiters for large eddy simulation. Annual Research Briefs, Center for Turbulence Research, Stanford, pages 83–95, 1997.Google Scholar
[24]Olsson, P.. Summation by parts, projections, and stability. I. Math. Comput., 64:1035–1065, 1995.CrossRefGoogle Scholar
[25]Olsson, P. and Oliger, J.. Energy and maximum norm estimates for nonlinear conservation laws. Technical Report 94.01, RIACS, 1994.Google Scholar
[26]Ristorcelli, J. R. and Blaisdell, G. A.. Consistent initial conditions for the DNS of compressible turbulence. Phys. Fluids, 9(4), 1997.Google Scholar
[27]Sagaut, P. and Germano, M.. On the filtering paradigm for LES of flows with discontinuities. J. Turbulence, 6(23):1–9, 2005.Google Scholar
[28]Sandham, N. D., Li, Q., and Yee, H. C.. Entropy splitting for high-order numerical simulation of compressible turbulence. J. Comput. Phys., 178:307–322, 2002.CrossRefGoogle Scholar
[29]Shu, C.-W. and Osher, S.. Efficient implementation of essentially non-oscillatory shock-capturing schemes, II. J. Comput. Phys., 83:32–78, 1989.Google Scholar
[30]Sjögreen, B. and Yee, H. C.. Multiresolution wavelet based adaptive numerical dissipation control for shock-turbulence computation. J. Sci. Comput., 20:211–255, 2004.Google Scholar
[31]Sjögreen, B. and Yee, H. C.. On tenth-order central spatial schemes. In Proc. of the Turbulence and Shear Flow Phenomena 5 (TSFP-5), Munich, Germany, August 27-29 2007.Google Scholar
[32]Sjögreen, B. and Yee, H. C.. On skew-symmetric splitting and entropy conservation schemes for the euler equations. In Proc. of the 8th Euro. Conf. on Numerical Mathematics & Advanced Applications (ENUMATH 2009), Uppsala, Sweden, June 29-July 2 2009. Uppsala University.Google Scholar
[33]Touber, E. and Sandham, N.. Comparison of three large-eddy simulations of shock-induced turbulent separation bubbles. Shock Waves, 19(6):469–478, 2011.Google Scholar
[34]Vinokur, M. and Yee, H. C.. Extension of efficient low dissipative high-order schemes for 3-D curvilinear moving grids. In Frontiers of Computational Fluid dynamics, pages 129–164. World Scientific, 2002.Google Scholar
[35]Wang, W., Shu, C. W., Yee, H. C., and Sjögreen, B.. High order finite difference methods with subcell resolution for advection equations with stiff source terms. J. Comput. Phys., 231:190–214, 2012.CrossRefGoogle Scholar
[36]Yee, H. C., Kotov, D. V., Wang, W., and Shu, C.-W.. Spurious behavior of shock-capturing methods: Problems containing stiff source terms and discontinuities. In Proc. of the ICCFD7, The Big Island, Hawaii, July 9-13 2012. also J. Comput. Phys., 241 (2013) 266291.Google Scholar
[37]Yee, H. C., Sandham, N. D., and Djomehri, M. J.. Low dissipative high order shock-capturing methods using characteristic-based filters. J. Comput. Phys., 150:199–238, 1999.Google Scholar
[38]Yee, H. C. and Sjögreen, B.. Development of low dissipative high order filter schemes for multiscale Navier-Stokes/MHD systems. J. Comput. Phys., 225:910–934, 2007.Google Scholar
[39]Yee, H. C. and Sjögreen, B.. Simulation of Richtmyer-Meshkov instability by sixth-order filter methods. Shock Waves, 17:185–193, 2007.Google Scholar
[40]Yee, H. C. and Sjögreen, B.. High order filter methods for wide range of compressible flow speeds. In Proc. of ICOSAHOM 09, Trondheim, Norway, June 22-26 2013.Google Scholar
[41]Yee, H. C., Sjögreen, B., and Hadjadj, A.. Comparative study of high order schemes for LES of temporal-evolving mixing layers. In Proc. of ASTRONUM-2010, San Diego, Calif., June 13-18 2009.Google Scholar
[42]Yee, H. C., Sjögreen, B., and Hadjadj, A.. Comparative study of three high order schemes for LES of temporally evolving mixing layers. Commun. Comput. Phys., 12:1603–1622, 2012.Google Scholar
[43]Yee, H. C., Vinokur, M., and Djomehri, M. J.. Entropy splitting and numerical dissipation. J. Comput. Phys., 162:33–81, 2000.Google Scholar
[44]Yee, H. C. and Sjögreen, B.. Designing adaptive low dissipative high order schemes for longtime integrations. In Drikakis, D. & Geurts, B., editors, Turbulent Flow Computation. Kluwer Academic, 2002.Google Scholar