Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T13:47:00.710Z Has data issue: false hasContentIssue false
  • English
  • Français

Extension and Comparative Study of AUSM-Family Schemes for Compressible Multiphase Flow Simulations

Published online by Cambridge University Press:  03 June 2015

Keiichi Kitamura ,
Meng-Sing Liou  and
Chih-Hao Chang
Keiichi Kitamura*
Affiliation:
NASA Glenn Research Center, Cleveland, OH 44135, USA Research Fellow of Japan Society for the Promotion of Science (JSPS), JAXA’s Engineering Digital Innovation (JEDI) Center, 3-1-1 Yoshinodai, Chuo, Sagamihara, Japan; Previously at Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603 Japan; Currently at Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
Meng-Sing Liou*
Affiliation:
NASA Glenn Research Center, Cleveland, OH 44135, USA
Chih-Hao Chang*
Affiliation:
Theofanous & Co Inc. Santa Barbara, CA 93109, USA
*
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
Get access

Abstract

Several recently developed AUSM-family numerical flux functions (SLAU, SLAU2, AUSMM+-up2, and AUSMPW+) have been successfully extended to compute compressible multiphase flows, based on the stratified flow model concept, by following two previous works: one by M.-S. Liou, C.-H. Chang, L. Nguyen, and T.G. Theofanous [AIAA J. 46:2345-2356, 2008], in which AUSM+-up was used entirely, and the other by C.-H. Chang, and M.-S. Liou [J. Comput. Phys. 225:840-873, 2007], in which the exact Riemann solver was combined into AUSM+-up at the phase interface. Through an extensive survey by comparing flux functions, the following are found: (1) AUSM+-up with dissipation parameters of Kp and Ku equal to 0.5 or greater, AUSMPW+, SLAU2, AUSM+-up2, and SLAU can be used to solve benchmark problems, including a shock/water-droplet interaction; (2) SLAU shows oscillatory behaviors [though not as catastrophic as those of AUSM+ (a special case of AUSM+-up with Kp = Ku = 0)] due to insufficient dissipation arising from its ideal-gas-based dissipation term; and (3) when combined with the exact Riemann solver, AUSM+-up (Kp = Ku = 1), SLAU2, and AUSMPW+ are applicable to more challenging problems with high pressure ratios.

Keywords

76T1076M1276N99Multiphase flowtwo-fluid modelAUSM-familystratified flow model
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 3 , September 2014 , pp. 632 - 674
Copyright
Copyright © Global Science Press Limited 2014

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]Peery, K.M., and Imlay, S.T., Blunt-Body Flow Simulations, AIAA Paper 88–2904,1988.Google Scholar
[2]Pandolfi, M., and D’Ambrosio, D., Numerical Instabilities in Upwind Methods: Analysis and Cures for the Carbuncle Phenomenon, J. Comput. Phys., Vol. 166, No. 2, 2001, pp. 271301. doi:10.1006/jcph.2000.6652.Google Scholar
[3]Liou, M.S., Mass Flux Schemes and Connection to Shock Instability, J. Comput. Phys., Vol. 160, 2000, pp. 623–648.CrossRefGoogle Scholar
[4]Kitamura, K., Roe, P., and Ismail, F., Evaluation of Euler Fluxes for Hypersonic Flow Computations, AIAA J., Vol. 47, 2009, pp. 44–53.Google Scholar
[5]Gnoffo, P.A., Multidimensional, Inviscid Flux Reconstruction for Simulation of Hypersonic Heating on Tetrahedral Grids, AIAA Paper 2009–599, 2009.Google Scholar
[6]Candler, G.V., Mavriplis, D.J., and Trevino, L., Current Status and Future Prospects for the Numerical Simulation of Hypersonic Flows, AIAA Paper 2009–153,2009.Google Scholar
[7]Kitamura, K., Shima, E., Nakamura, Y., and Roe, P., Evaluation of Euler Fluxes for Hypersonic Heating Computations, AIAA J., Vol. 48, 2010, pp. 763–776. doi:10.2514/1.41605.CrossRefGoogle Scholar
[8]Kitamura, K., Shima, E., and Roe, P., Carbuncle Phenomena and Other Shock Anomalies in Three Dimensions, AIAA J., Vol. 50, 2012, pp. 2655–2669. doi:10.2514/1.J051227.CrossRefGoogle Scholar
[9]Turkel, E., Preconditioning Technique in Computational Fluid Dynamics, Annual Review of Fluid Mechanics, Vol. 31,1999, pp. 385–416.Google Scholar
[10]Weiss, J.M., and Smith, W.A., Preconditioning Applied to Variable and Constant Density Flows, AIAA J., Vol. 33, No.11,1995, pp. 2050–2057.CrossRefGoogle Scholar
[11]Liou, M.-S., A Sequel to AUSM, Part II: AUSM+-up for All Speeds, J. Comput. Phys., Vol. 214, 2006, pp. 137–170.Google Scholar
[12]Shima, E., and Kitamura, K., Parameter-Free Simple Low-Dissipation AUSM-Family Scheme for All Speeds, AIAA J., Vol. 49, No. 8, 2011, pp. 1693–1709. doi:10.2514/1.55308.Google Scholar
[13]Hosangadi, A., Sachdev, J., and Sankaran, V., Improved Flux Formulations for Unsteady Low Mach Number Flows, ICCFD7-2202, Seventh International Conference on Computational Fluid Dynamics (ICCFD7), Big Island, Hawaii, July 9–13, 2012.Google Scholar
[14]Kitamura, K., Shima, E., Fujimoto, K., and Wang, Z.J., Performance of Low-Dissipation Euler Fluxes and Preconditioned LU-SGS at Low Speeds, Commun. Comput. Phys., Vol. 10, No. 1, 2011, pp. 90–119.Google Scholar
[15]Kitamura, K., and Shima, E., Improvements of Simple Low-dissipation AUSM against Shock Instabilities in consideration of Interfacial Speed of Sound, V European Conference on Computational Fluid Dynamics, ECCOMAS CFD 2010, 2010.Google Scholar
[16]Liou, M.-S., Chang, C.-H., Nguyen, L., and Theofanous, T. G., How to Solve Compressible Multifluid Equations: A Simple, Robust, and Accurate Method, AIAA J., Vol. 46, 2008, pp. 2345–2356.Google Scholar
[17]Chang, C.-H., and Liou, M.-S, A Robust and Accurate Approach to Computing Compressible Multiphase Flow: Stratified Flow Model and AUSM+-up Scheme, J. Comput. Phys., Vol. 225, 2007, pp. 840–873.Google Scholar
[18]Chang, C.-H., and Liou, M.-S., A New Approach to the Simulation of Compressible Multi-phase Flows with AUSM+ Scheme, AIAA Paper 2003–4107,2003.Google Scholar
[19]Niu, Y.-Y., Lin, Y.-C., and Chang, C.-H., A Further Work on Multi-Phase Two-Fluid Approach for Compressible Multi-Phase Flows, Int. J. Numer. Meth. Fluids, Vol. 58, 2008, pp. 879–896.Google Scholar
[20]Paillère, H., Corre, C., and Cascales, J.R.G., On the Extension of the AUSM+ Scheme to Compressible Two-Fluid Models, Comput. Fluids, Vol. 32, 2003, pp. 891–916.Google Scholar
[21]Stewart, H.B., and Wendroff, B., Two-Phase Flow: Models and Methods, J. Comput. Phys., Vol. 56,1984, pp. 363–409.Google Scholar
[22]Liou, M.-S., A Sequel to AUSM: AUSM+, J. Comput. Phys., Vol. 129,1996, pp. 364–382.Google Scholar
[23]Kitamura, K., and Shima, E., Towards shock-stable and accurate hypersonic heating computations: A new pressure flux for AUSM-family schemes, J. Comput. Phys., Vol. 245, 2013, pp. 62–83. doi: 10.1016/j.jcp.2013.02.046.Google Scholar
[24]Kim, S.S., Kim, C., Rho, O.H., Hong, S.K., Methods for the Accurate Computations of Hypersonic Flows I. AUSMPW+ Scheme, J. Comput. Phys., Vol. 174, 2001, pp. 38–80.CrossRefGoogle Scholar
[25]Godunov, S.K., A Finite Difference Method for the Numerical Computation of Discontinuous Solutions of the Equations of Fluid Dynamics, Matematicheskii Sbornik/Izdavaemyi Moskovskim Matematicheskim Obshchestvom, Vol. 47, No. 3,1959, pp. 271–306.Google Scholar
[26]Osher, S., and Sethian, J.A., Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations, J. Comput. Phys., Vol. 79,1988, pp. 12–49.Google Scholar
[27]Sussman, M., Smereka, P., and Osher, S., A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow, J. Comput. Phys., Vol. 114,1994, pp. 146–159.Google Scholar
[28]Kim, H., and Liou, M.-S., Accurate Adaptive Level Set Method and Sharpening Technique for Three Dimensional Deforming Interfaces, Comput. Fluids, Vol. 44, 2011, pp. 111–129.Google Scholar
[29]Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S., and Jan, Y.-J., A Front-Tracking Method for the Computations of Multiphase Flow, J. Comput. Phys., Vol. 169, 2001, pp. 708–759.Google Scholar
[30]Terashima, H., and Tryggvason, G., A Front-Tracking/Ghost-Fluid Method for Fluid Interfaces in Compressible Flows, J. Comput. Phys., Vol. 228, 2009, pp. 4012–4037.Google Scholar
[31]Hirt, C.W., and Nichols, B.D., Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comput. Phys., Vol. 39, No. 1, 1981, pp. 201–225. doi:10.1016/0021-9991(81)90145-5.Google Scholar
[32]Ii, S., Sugiyama, K., Takeuchi, S., Takagi, S., Matsumoto, Y., and Xiao, F., An Interface Capturing Method with a Continuous Function: The THINC Method with Multi-Dimensional Reconstruction, J. Comput. Phys., Vol. 231, 2012, pp. 2328–2358.Google Scholar
[33]Goncalves, E., and Patella, R. F., Numerical Simulation of Cavitating Flows with Homogeneous Models, Comput. Fluids, Vol. 38, 2009, pp. 1682–1696.Google Scholar
[34]Edwards, J. R., Franklin, R. K., and Liou, M.-S., Low-Diffusion Flux-Splitting Methods for Real Fluid Flows with Phase Transitions, AIAA J., Vol. 38, 2000, pp. 1624–1633.Google Scholar
[35]Ihm, S.-W., and Kim, C., Computations of Homogeneous-Equilibrium Two-Phase Flows with Accurate and Efficient Shock-Stable Schemes, AIAA J., Vol. 46, 2008, pp. 3012–3037.Google Scholar
[36]Saurel, R., and Lemetayer, O., A Multiphase Model for Compressible Flows with Interfaces, Shocks, Detonation Waves and Cavitation, J. Fluid Mech., Vol. 431, 2001, pp. 239–271.Google Scholar
[37]Toumi, I., An Upwind Numerical Method for Two-Fluid Two-Phase Flow Methods, Nuclear Sci. Eng., Vol. 123,1996, pp. 147–168.Google Scholar
[38]Saurel, R., and Abgrall, R., A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows, J. Comput. Phys., Vol. 150,1999, pp. 425–467.Google Scholar
[39]Chang, C.-H., Sushchikh, S., Nguyen, L., Liou, M.-S., and Theofanous, T., Hyperbolicity, Discontinuities, and Numerics of the Two-Fluid Model, 5th Joint ASME/JSME Fluids Engineering Summer Conference, American Society of Mechanical Engineers, Fluid Engineering Div., Paper FEDSM 2007–37338,2007.Google Scholar
[40]Shukla, R.K., Pantano, C., and Freund, J.B., An Interface Capturing Method for the Simulation of Multi-Phase Compressible Flows, J. Comput. Phys., Vol. 229, 2010, pp. 7411–7439.Google Scholar
[41]So, K.K., Hu, X.Y., and Adams, N.A., Anti-Diffusion Interface Sharpening Technique for Two-Phase Compressible Flow Simulations, J. Comput. Phys., Vol. 231, 2012, pp. 4304–4323.Google Scholar
[42]Kiris, C.C., Kwak, D., Chan, W., and Housman, J.A., High-Fidelity Simulations of Unsteady Flow through Turbopumps and Flowliners, Comput. Fluids, Vol. 37, 2008, pp. 536–546.Google Scholar
[43]Van Leer, B., Towards the Ultimate Conservative Difference Scheme. V. A Second-Order Sequel to Godunov’s Method, J. Comput. Phys., Vol. 32,1979, pp. 101–136.Google Scholar
[44]Van Albada, G.D., Van Leer, B., and Roberts, W.W. Jr., A Comparative Study of Computational Methods in Cosmic Gas Dynamics, Astron. Astrophys., Vol. 108,1982, pp. 76–84.Google Scholar
[45]Gottlieb, S., and Shu, C.-W., Total Variation Diminishing Runge-Kutta Schemes, Math. Comput., Vol. 67,1998, pp. 73–85.Google Scholar
[46]Stuhmiller, J., The Influence of Interfacial Pressure Forces on the Character of Two-Phase Flow Model Equations, Int. J. Multiphase Flow, Vol. 3,1977, pp. 551–60.Google Scholar
[47]Harlow, F., and Amsden, A., Fluid Dynamics, Technical Report LA-4700, Los Alamos National Laboratory, 1971.Google Scholar
[48]Jolgam, S., Ballil, A., Nowakowski, A., and Nicolleau, F., On Equations of State for Simulations of Multiphase Flows, Proc. World Congress on Engineering 2012, Vol. III, WCE 2012, July 4–6, 2012, London, U.K.Google Scholar
[49]Private communication with Chongam Kim, Seoul National University, Republic of Korea, August 11, 2012.Google Scholar
[50]Kitamura, K., and Liou, M.-S., Comparative Study of AUSM-Family Schemes in Compressible Multiphase Flow Simulations, ICCFD7-3702, Seventh International Conference on Computational Fluid Dynamics (ICCFD7), Big Island, Hawaii, July 9–13, 2012.Google Scholar
[51]Toro, E.F., The Riemann Problem for the Euler Equations, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, Third Edition, Springer-Verlag, Telos, 2009, pp. 115–162. doi:10.1007/b7976-l_4.Google Scholar
[52]Terashima, H., Kawai, S., and Yamanishi, N., High-Resolution Numerical Method for Supercritical Flows with Large Density Variations, AIAA J., Vol. 49, No. 12, 2011, pp. 2658–2672.CrossRefGoogle Scholar
[53]Roe, P.L., Characteristic-based Schemes for the Euler Equations, Ann. Rev. Fluid Mech., Vol. 18, pp. 337–365.Google Scholar
[54]Chakravathy, S.R., and Osher, S., High Resolution Applications of the Osher Upwind Scheme for the Euler Equations, Proc. AIAA 6th Computational Fluid Dynamics Conference, AIAA Paper 83-1943, pp. 363–373,1983.Google Scholar
[55]Ransom, V.H., Numerical Benchmark Tests, edited by Hewitt, G. F., Delhay, J. M., and Zuber, N., Vol. 3, Multiphase Science and Technology, Hemisphere, Washington, DC, 1987, pp. 465–467.Google Scholar
[56]Liu, T.G., Khoo, B.C., and Yeo, K.S., Ghost fluid method for strong shock impacting on material interface, J. Comput. Phys., Vol. 190, 2003, pp. 651–681.CrossRefGoogle Scholar
[57]Liu, T.G., Khoo, B.C., and Wang, C.W., The ghost fluid method for compressible gas-water simulation, J. Comput. Phys., Vol. 204, 2005, pp. 193–221.Google Scholar
[58]Nonomura, T., Kitamura, K., and Fujii, K., A Simple Interface Sharpening Technique with a Hyperbolic Tangent Function Applied to Compressible Two-Fluid Modeling, J. Comput. Phys., Vol. 258, 2014, pp. 95–117. doi: 10.1016/j.jcp.2013.10.021.Google Scholar
[59]Theofanous, T., and Chang, C.-H., On the Computation of Multiphase Interactions in Transonic and Supersonic Flows, AIAA 2008–1233,2008.Google Scholar