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Performance of Low-Dissipation Euler Fluxes and Preconditioned LU-SGS at Low Speeds

Published online by Cambridge University Press:  20 August 2015

Keiichi Kitamura ,
Eiji Shima ,
Keiichiro Fujimoto  and
Z. J. Wang
Keiichi Kitamura*
Affiliation:
JAXA’s Engineering Digital Innovation (JEDI) Center, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuuou, Sagamihara, Kanagawa, 252-5210, Japan
Eiji Shima*
Affiliation:
JAXA’s Engineering Digital Innovation (JEDI) Center, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuuou, Sagamihara, Kanagawa, 252-5210, Japan
Keiichiro Fujimoto*
Affiliation:
JAXA’s Engineering Digital Innovation (JEDI) Center, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuuou, Sagamihara, Kanagawa, 252-5210, Japan JAXA’s Engineering Digital Innovation (JEDI) Center, Japan Aerospace Exploration Agency, 2-1-1 Sengen, Tsukuba, Ibaraki, 305-8505, Japan
Z. J. Wang*
Affiliation:
Department of Aerospace Engineering, Iowa State University, 2271 Howe Hall, Ames, IA 50011, USA
*
Corresponding author.Email:kitamura.keiichi@jaxa.jp
Email:shima.eiji@jaxa.jp
Email:fujimoto.keiichiro@jaxa.jp
Email:zjw@iastate.edu
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Abstract

In low speed flow computations, compressible finite-volume solvers are known to a) fail to converge in acceptable time and b) reach unphysical solutions. These problems are known to be cured by A) preconditioning on the time-derivative term, and B) control of numerical dissipation, respectively. There have been several methods of A) and B) proposed separately. However, it is unclear which combination is the most accurate, robust, and efficient for low speed flows. We carried out a comparative study of several well-known or recently-developed low-dissipation Euler fluxes coupled with a preconditioned LU-SGS (Lower-Upper Symmetric Gauss-Seidel) implicit time integration scheme to compute steady flows. Through a series of numerical experiments, accurate, efficient, and robust methods are suggested for low speed flow computations.

Keywords

65Z0576M1276N99All-speed schemelow-dissipationpreconditioningLU-SGS
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 1 , July 2011 , pp. 90 - 119
Copyright
Copyright © Global Science Press Limited 2011

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References

[1]Kiris, C. C., Kwak, D., Chan, W., and Housman, J. A., High-fidelity simulations of unsteady flow through tubopumps and flowliners, Comput. Fluids., 37 (2008), 536–546.Google Scholar
[2]Tani, N., Tsuda, S., and Yamanishi, N., Numerical study of cavitating inducer in cryogenic fluid, 49th Japan Conference on Propulsion and Power, B14 (2009) (in Japanese).Google Scholar
[3]Tsuboi, N., Fukiba, K., and Shimada, T., Numerical simulation on unsteady compressible low-speed flow using preconditioning method: simulation in combustion chamber of hybrid rocket, 49th Japan Conference on Propulsion and Power, B05 (2009) (in Japanese).Google Scholar
[4]Weiss, J. M., and Smith, W. A., Preconditioning applied to variable and constant densityflows, AIAA J., 33(11) (1995), 2050–2057.Google Scholar
[5]Turkel, E., Preconditioning technique in computational fluid dynamics, Annu. Rev. Fluid. Mech., 31 (1999), 385–416.Google Scholar
[6]Liou, M. S., A sequel to AUSM, part II: AUSM+-up for all speeds, J. Comput. Phys., 214 (2006), 137–170.CrossRefGoogle Scholar
[7]Edwards, J. R., Towards unified CFD simulation of real fluid flows, AIAA Paper, 2001–2524, 2001.Google Scholar
[8]Shima, E., and Kitamura, K., On new simple low-dissipation scheme of AUSM-family for all speeds, AIAA Paper, 2009-0136, 2009.Google Scholar
[9]Li, X. S., and Gu, C. W., An all-speed Roe-type scheme and its asymptotic analysis of low mach number behavior, J. Comput. Phys., 227 (2008), 5144–5159.Google Scholar
[10]Jameson, A., and Turkel, E., Implicit schemes and LU decompositions, Math. Comput., 37 (1981), 385–397.Google Scholar
[11]Yamamoto, S., Preconditioning method for condensate fluid and solid coupling problems in general curvilinear coordinates, J. Comput. Phys., 207 (2005), 240–260.Google Scholar
[12]Xie, F., Song, W., and Han, Z., Numerical study of high-resolution scheme based on preconditioning method, J. Aircraft., 46(2) (2009), 520–525.CrossRefGoogle Scholar
[13]Unrau, D., and Zingg, D. W., Viscous airfoil computations using local preconditioning, AIAA Paper, 97–2027, 1997.Google Scholar
[14]Hauke, G., and Hughes, T. J. R., A comparative study of different sets of variables for solving compressible and incompressible flows, Comput. Methods. Appl. Mech. Engrg., 153 (1998), 1–44.Google Scholar
[15]Shima, E., Kitamura, K., and Fujimoto, K., New gradient calculation method for MUSCL type CFD schemes in arbitrary polyhedra, 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, AIAA Paper, 2010-1081, 2010.Google Scholar
[16]Mavriplis, D. J., Revisiting the least-squares procedure for gradient reconstruction on unstructured meshes, AIAA Paper, 2003–3986, 2003.Google Scholar
[17]Wang, Z. J., A quadtree-based adaptive cartesian/quad grid flow solver for Navier-Stokes equations, Comput. luids., 27(4) (1998), 529–549.Google Scholar
[18]Kitamura, K., Fujimoto, K., Shima, E., Kuzuu, K., and Wang, Z. J., Validation of arbitrary unstructured CFD code for aerodynamic analyses, transactions of the Japan society for aeronautical and space sciences, (accepted for publication).Google Scholar
[19]Roe, P. L., Approximate Riemann solvers, parameter vectors and difference schemes, J. Comput. Phys., 43 (1981), 357–372.Google Scholar
[20]Liou, M. S., A sequel to AUSM: AUSM+, J. Comput. Phys., 129 (1996), 364–382.Google Scholar
[21]Shima, E., Role of CFD in aeronautical engineering (No. 14)-AUSM type upwind schemes-, NAL-SP30, Proceedings of 13th NAL symposium on Aircraft Computational Aerodynamics, 41–46, 1996.Google Scholar
[22]Liu, Y., and Vinokur, M., Upwind algorithms for general thermo-chemical nonequilibrium flows, AIAA Paper, 89–0201, 1989.Google Scholar
[23]Peery, K. M., and Imlay, S. T., Blunt-body flow simulations, AIAA Paper, 88–2904, 1988.Google Scholar
[24]Kitamura, K., Roe, P., and Ismail, F., Evaluation of Euler fluxes for hypersonic flow computations, AIAA Journal, 47(1) (2009), 44–53.Google Scholar
[25]Nichols, R., Tramel, R., and Buning, P., Solver and turbulence model upgrades to OVERFLOW 2 for unsteady and high-speed applications, AIAA-2006-2824, 2006.Google Scholar
[26]Sun, Y., Wang, Z. J., and Liu, Y., Efficient implicit non-linear LU-SGS approach for compressible flow computation using high-order spectral difference method, Commun. Comput. Phys., 5 (2009), 760–778.Google Scholar
[27]Mavriplis, D. J., Jameson, A., and Martinelli, L., Multigrid solution of the Navier-Stokes equations on triangular meshes, AIAA Paper, 89–0120, 1989.Google Scholar
[28]Venkatakrishnan, V., Convergence to steady state solutions of the Euler equations on unstructured grids with limiters, J. Comput. Phys., 118 (1995), 120–130.Google Scholar
[29]Wang, Z. J., A fast nested multi-grid viscous flow solver for adaptive cartesian/quad grids, Int. J.umer. Meth. Fluids., 33 (2000), 657–680.Google Scholar
[30]Liou, M. S., and Edwards, J. R., Numerical speed of sound and its application to schemes of all speeds, NASA TM-1999-09286, 1999; AIAA Paper, 99-3268-CP, 1999.Google Scholar