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Variable High-Order Multiblock Overlapping Grid Methods for Mixed Steady and Unsteady Multiscale Viscous Flows, Part II: Hypersonic Nonequilibrium Flows

Published online by Cambridge University Press:  03 June 2015

Andrea Lani ,
Björn Sjögreen ,
H. C. Yee  and
William D. Henshaw
Andrea Lani*
Affiliation:
NASA Ames /Stanford Centre for Turbulence Research, Palo Alto, CA, USA
Björn Sjögreen*
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA, USA
H. C. Yee*
Affiliation:
MS 258-5, NASA Ames Research Center, Moffett Field, CA, USA
William D. Henshaw*
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA, USA
*
Corresponding author.Email:alani0@stanford.edu
Email:Sjögreen2@llnl.gov
Email:helen.m.yee@nasa.gov
Email:henshaw@llnl.gov
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Abstract

The variable high-order multiblock overlapping (overset) grids method of Sjögreen & Yee [CiCP, Vol. 5, 2009] for a perfect gas has been extended to nonequilibrium flows. This work makes use of the recently developed high-order well-balanced shock-capturing schemes and their filter counterparts [Wang et al., J. Comput. Phys., 2009, 2010] that exactly preserve certain non-trivial steady state solutions of the chemical nonequilibrium governing equations. Multiscale turbulence with strong shocks and flows containing both steady and unsteady components is best treated by mixing of numerical methods and switching on the appropriate scheme in the appropriate subdomains of the flow fields, even under the multiblock grid or adaptive grid refinement framework. While low dissipative sixth- or higher-order shock-capturing filter methods are appropriate for unsteady turbulence with shocklets, second- and third- order shock-capturing methods are more effective for strong steady or nearly steady shocks in terms of convergence. It is anticipated that our variable high-order overset grid framework capability with its highly modular design will allow for an optimum synthesis of these new algorithms in such a way that the most appropriate spatial discretizations can be tailored for each particular region of the flow. In this paper some of the latest developments in single block high-order filter schemes for chemical nonequilibrium flows are applied to overset grid geometries. The numerical approach is validated on a number of test cases characterized by hypersonic conditions with strong shocks, including the reentry flow surrounding a 3D Apollo-like NASA Crew Exploration Vehicle that might contain mixed steady and unsteady components, depending on the flow conditions.

Keywords

65Z0565M0665M5065M5565M6065M9965Y99
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 2 , February 2013 , pp. 583 - 602
Copyright
Copyright © Global Science Press Limited 2013

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References

[1]Barnhardt, M. and Candler, G., Detached Eddy Simulation of the reentry-F flight experiment, 46th AIAA Aerospace Sciences Meeting, 7-10 January, Reno (Nevada), AIAA 2008625, 2008.CrossRefGoogle Scholar
[2]Brown, D. L., Henshaw, W. D., and Quinlan, D. J., Overture: Object-oriented Tools for Solving PDEs in Complex Geometries.Google Scholar
[3]Chesshire, G. and Henshaw, W., Composite Overlapping Meshes for the Solution of Partial Differential Equations, J. Comput. Phys., Vol. 90, No. 1(1990), pp. 1–64.CrossRefGoogle Scholar
[4]Ducros, F., Laporte, F., Souleres, 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., Vol. 161(2000), pp. 114–139.Google Scholar
[5]Sjögreen, B. and Yee, H., On Skew-Symmetric Splitting of the Euler Equations, Proceedings of the EUNUMATH-09 Conference, June 29 – July 2 2009.Google Scholar
[6]Hadjadj, A., Yee, H. C., and Sjögreen, B., LES of temporally evolving mixing layers by high order filter schemes, AIAA-ASM meeting, Jan. 9-12, 2012 Nashville, TN; to appear, International J. Num. Meth. Fluids.Google Scholar
[7]Henshaw, W. D., Ogen: An Overlapping Grid Generator for Overture, Research Report UCRL-MA-132237, Lawrence Livermore National Laboratory, 1998.Google Scholar
[8]Hirschfelder, J. O., Curtiss, C. F., and Bird, R. B., Molecular theory of gases and liquids, John Wiley and Sons, New York, 1967.Google Scholar
[9]Jiang, G. S. and Shu, C. W., Efficient Implementation of Weighted ENO Schemes, J. Comput. Phys., Vol. 126(1996), pp. 202–228.CrossRefGoogle Scholar
[10]Lani, A., Yee, H. C., and Sjögreen, B., High order simulation of hypersonic nonequilibrium flows on overset grids, CTR Annual Research Briefs 2010.Google Scholar
[11]MacLean, M., Mundy, E., Wadhams, T., Holden, M., Barnhardt, M., and Candler, G., Exper-imental and numerical study of laminar and turbulent base flow on spherical capsule, 47th AIAA Aerospace Sciences Meeting, 5-8 January, Orlando (Florida), AIAA 2009-783, 2009.Google Scholar
[12]Magin, T. and Degrez, G., Transport Algorithms for Partially Ionized and Unmagnetized Plasmas, J. Comput. Phys., Vol. 198(2004), pp. 424–449.Google Scholar
[13]Park, C., Review of Chemical-Kinetic Problems of Future NASA Mission, I: Earth Entries, J. of Thermophys. Heat Transfer, Vol. 7, July-Sept (1993), pp. 385–398.Google Scholar
[14]Olsson, P. and Oliger, J., Energy and Maximum Norm Estimates for Nonlinear Conservation Laws, Tech. rep., RIACS Tech. Report 91.01, 1994.Google Scholar
[15]Olsson, P., Summation by Parts, Projections and Stability, I, Math. Comp., Vol. 64(1995), pp. 1035–1065.Google Scholar
[16]Sinha, K., Barnhardt, M., and Candler, G., Detached Eddy Simulation of hypersonic Base Flows with application to Fire II experiments, 38th AIAA Fluid Dynamics Conference and Exhibit, 28 June – 1 July, Portland (Oregon), AIAA 2004-2633-853, 2004.CrossRefGoogle Scholar
[17]Sjögreen, B. and Yee, H. C., Multiresolution Wavelet Based Adaptive Numerical Dissipation Control for Shock-Turbulence Computation, Riacs technical report tr01.01, NASA Ames re-search center, Oct 2000, also J. Scient. Comput., Vol. 20(2004), pp. 211–255.CrossRefGoogle Scholar
[18]Sjögreen, B., Yee, H. C., Djomehri, J., Lazanoff, A., and Henshaw, W. D., Parallel Performance of ADPDIS3D – A High Order Multiblock Overlapping Grid Solver for Hypersonic Turbulence, Parallel CFD, Moffett Field (CA), May 18-22 2009.Google Scholar
[19]Sjögreen, B. and Yee, H. C., Variable High Order Multiblock Overlapping Grid Methods for Mixed Steady and Unsteady Multiscale Viscous Flow, Comm. Comput. Phys., Vol. 5, No. 2-4 (2009), pp. 730–744.Google Scholar
[20]Stuart, A. and Humphries, A., Dynamical Systems and Numerical Analysis, Cambridge Monographs on Appl. and Comput. Math., 1998.Google Scholar
[21]Abeele, D. V., An Efficient Computational Model for Inductively Coupled Air Plasma Flows under Thermal and Chemical Non-Equilibrium, Ph.D. thesis, Katholieke Universiteit Leu-ven, Chaussée de Waterloo, 72, 1640 Rhode-St-Genèse, Belgium, Nov. 2000.Google Scholar
[22]Vinokur, M. and Yee, H., Extension of Efficient Low Dissipative High Order Schemes for 3-D Curvilinear Moving Grids, Tech. rep., NASA TM 209598, June 2000, also appear at the Proceedings of the Frontiers of Computational Fluid Dynamics, 2002, World Scientific, Caughey, D.A. & Hafez, M. editors., pp. 129–164.Google Scholar
[23]Yee, H. C., A class of high-resolution explicit and implicit shock-capturing methods, VKI lecture series 1989-04, NASA TM-101088, March 1989.Google Scholar
[24]Yee, H. C., Sandham, N. S. and Djomehri, M., Low Dissipative High Order Shock-Capturing Methods Using Characteristic-Based Filters, J. Comput. Phys., Vol. 150, 1999, pp. 199–238.Google Scholar
[25]Yee, H. C., Vinokur, M. and Djomehri, M., Entropy Splitting and Numerical Dissipation, J. Comput. Phys., Vol. 162(2000), pp. 33–81.Google Scholar
[26]Yee, H. C. and Sjögreen, B., Designing Adaptive Low Dissipative High Order Schemes for Long-Time Integrations, In Turbulent Flow Computation, edited by Geurts, E. D. D. B., Kluwer Academic Publisher, 2002, also RIACS Technical Report TR01-28, Dec. 2001.Google Scholar
[27]Yee, H. C. and Sjögreen, B., Nonlinear Filtering and Limiting in High Order Methods for Ideal and Non-ideal MHD, J.Sci.Comp, Vol. 27(2006), pp. 507–521.Google Scholar
[28]Yee, H. C. and Sjögreen, B., Development of Low Dissipative High Order Filter Schemes for Multiscale Navier-Stokes/MHD Systems, J. Comput. Phys., Vol. 225(2007), pp. 910–934.Google Scholar
[29]Yee, H. C., Sjögreen, B., and Barone, M., High order numerical schemes for hypersonic flow simulations, VKI Lecture Series: Course on hypersonic entry and cruise vehicles, Von Karman Institute for Fluid Dynamics, Stanford University, Palo Alto (CA), 30 June – 3 July 2008.Google Scholar
[30]Yee, H. C. and Sjögreen, B., High Order Filter Methods for Wide Range of Compressible Flow Speeds, Proceedings of ICOSAHOM 09, International Conference on Spectral and High Order Methods, Trondheim, Norway, Jun 22-26 2009.Google Scholar
[31]Yee, H. C., Sjögreen, B., and Hadjadj, A., Comparative study of high order schemes for LES of temporally evolving mixing layers, Extended version of the paper for the Proceedings of ASTRONUM-2010, June 13-18, 2010, San Diego, Calif; AIAA-ASM meeting, Jan. 9-12, 2012 Nashville, TN.Google Scholar
[32]Yee, H. C. and Sjögreen, B., Local Flow Sensors in Controlling Numerical Dissipations for a Wide Spectrum of Flow Speed and Shock Strength, in preparation.Google Scholar
[33]Wang, W., Shu, C. W., Yee, H. C., and Sjögreen, B., High-order well balanced schemes and applications to non-equilibrium flows, J. Comput. Phys., Vol. 228(2009), pp. 6682–6702.Google Scholar
[34]Wang, W., Yee, H. C., Sjögreen, B., Magin, T., and Shu, C. W., Construction of low dissipative high-order well balanced filter schemes for non-equilibrium flows, J. Comput. Phys., Vol. 230(2011) pp. 4316–4335.Google Scholar