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A Comparison Study of Numerical Methods for Compressible Two-Phase Flows

  • Jianyu Lin (a1), Hang Ding (a1), Xiyun Lu (a1) and Peng Wang (a2)
Abstract
Abstract

In this article a comparison study of the numerical methods for compressible two-phase flows is presented. Although many numerical methods have been developed in recent years to deal with the jump conditions at the fluid-fluid interfaces in compressible multiphase flows, there is a lack of a detailed comparison of these methods. With this regard, the transport five equation model, the modified ghost fluid method and the cut-cell method are investigated here as the typical methods in this field. A variety of numerical experiments are conducted to examine their performance in simulating inviscid compressible two-phase flows. Numerical experiments include Richtmyer-Meshkov instability, interaction between a shock and a rectangle SF 6 bubble, Rayleigh collapse of a cylindrical gas bubble in water and shock-induced bubble collapse, involving fluids with small or large density difference. Based on the numerical results, the performance of the method is assessed by the convergence order of the method with respect to interface position, mass conservation, interface resolution and computational efficiency.

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Corresponding author
*Corresponding author. Email: linjiany@mail.ustc.edu.cn (J. Y. Lin), hding@ustc.edu.cn (H. Ding), xlu@ustc.edu.cn (X. Y. Lu), wangpei@iapcm.ac.cn (P. Wang)
References
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[1] Abgrall R., How to prevent pressure oscillations in multicomponent flow calculations: A quasi conservative approach, J. Comput. Phys., 125 (1996), pp. 150160.
[2] Shyue K.-M., An efficient shock-capturing algorithm for compressible multicomponent problems, J. Comput. Phys., 142(1) (1998), pp. 208242.
[3] Saurel R. and Abgrall R., A multiphase Godunov method for compressible multifluid and multiphase flows, J. Comput. Phys., 150(2) (1999), pp. 425467.
[4] Allaire G., Clerc S. and Kokh S., A five-equation model for the simulation of interfaces between compressible fluids, J. Comput. Phys., 181(2) (2002), pp. 577616.
[5] Saurel R., Gavrilyuk S. and Renaud F., A multiphase model with internal degrees of freedom: Application to shock-bubble interaction, J. Fluid Mech., 495 (2003), pp. 283321.
[6] Marquina A. and Mulet P., A flux-split algorithm applied to conservative models for multicomponent compressible flows, J. Comput. Phys., 185(1) (2003), pp. 120138.
[7] Chang C.-H. and Liou M.-S., Robust and accurate approach to computing compressible multiphase flow: Stratified flow model and AUSM+-up scheme, J. Comput. Phys., 225(1) (2007), pp. 840873.
[8] Johnsen T. and Colonius E., Implementation of WENO schemes in compressible multicomponent flow problems, J. Comput. Phys., 219(4) (2006), pp. 715732.
[9] Kokh S. and Lagoutière F., An anti-diffusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model, J. Comput. Phys., 229(8) (2010), pp. 27732809.
[10] Shukla R. K., Pantano C. and Freund J. B., An interface capturing method for the simulation of multi-phase compressible flows, J. Comput. Phys., 229(19) (2010), pp. 74117439.
[11] So K. K., Hu X. Y. and Adams N. A., Anti-diffusion interface sharpening technique for two-phase compressible flow simulations, J. Comput. Phys., 231(11) (2012), pp. 43044323.
[12] Tiwari A., Freund J. B. and Pantano C., A diffuse interface model with immiscibility preservation, J. Comput. Phys., 252 (2013), pp. 290309.
[13] Shukla R. K., Nonlinear preconditioning for efficient and accurate interface capturing in simulation of multicomponent compressible flows, J. Comput. Phys., 276 (2014), pp. 508540.
[14] Deligant M., Specklin M. and Khelladi S., A naturally anti-diffusive compressible two phases Kapila model with boundedness preservation coupled to a high order finite volume solver, Comput. Fluids, 114 (2015), pp. 265273.
[15] Fedkiw R. P., Aslam T., Merriman B. and Osher S., A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method), J. Comput. Phys., 152(2) (1999), pp. 457492.
[16] Liu T. G., Khoo B. C. and Yeo K. S., Ghost fluid method for strong shock impacting on material interface, J. Comput. Phys., 190(2) (2003), pp. 651681.
[17] Wang C. W., Liu T. G. and Khoo B. C., A real ghost fluid method for the simulation of multimedium compressible flow, SIAM J. Sci. Comput., 28(1) (2006), pp. 278302.
[18] Sambasivan S. K. and Udaykumar H. S., Ghost fluid method for strong shock interactions part 1: Fluid-fluid interfaces, AIAA J., 47(12) (2009), pp. 29072922.
[19] Terashima H. and Tryggvason G., A front-tracking/ghost-fluid method for fluid interfaces in compressible flows, J. Comput. Phys., 228(11) (2009), pp. 40124037.
[20] Hu X. Y., Khoo B. C., Adams N. A. and Huang F. L., A conservative interface method for compressible flows, J. Comput. Phys., 219(2) (2006), pp. 553578.
[21] Chang C.-H., Deng X. and Theofanous T. G., Direct numerical simulation of interfacial instabilities: A consistent, conservative, all-speed, sharp-interface method, J. Comput. Phys., 242 (2013), pp. 946990.
[22] Nourgaliev R. R., Liou M.-S. and Theofanous T. G., Numerical prediction of interfacial instabilities: Sharp interface method (SIM), J. Comput. Phys., 227(8) (2008), pp. 39403970.
[23] Kim H. and Liou M.-S., Adaptive Cartesian sharp interface method for three-dimensional multiphase flows, AIAA Paper, (2009), pp. 20094153.
[24] Bo W. and Grove J. W., A volume of fluid method based ghost fluid method for compressible multi-fluid flows, Comput. Fluids, 90 (2014), pp. 113122.
[25] Lin J., Shen Y., Ding H., Liu N. and Lu X., Simulation of compressible two-phase flows with topology change of fluid-fluid interface by a robust cut-cell method, preparing.
[26] Roe P. L., Approximate Riemann solvers, parameter vectors and difference schemes, J. Comput. Phys., 43 (1981), pp. 357372.
[27] Hartmann D., Meinke M. and Schröder W., The constrained reinitialization equation for level set methods, J. Comput. Phys., 229(5) (2010), pp. 15141535.
[28] Osher S. and Fedkiw R., Level Set Methods and Dynamic Implicit Surfaces, Springer, 2003.
[29] Harten A., Lax P. D. and Van Leer B., On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev., 25(1) (1983), pp. 3561.
[30] Shu C.-W. and Osher S., Efficient implementation of essentially non-oscillatory shock-capturing schemes, J. Comput. Phys., 77(2) (1988), pp. 439471.
[31] Holmes R. L., Grove J.W. and Sharp D. H., Numerical investigation of Richtmyer–Meshkov instability using front tracking, J. Fluid Mech., 301 (1995), pp. 5164.
[32] Ullah M. A., Mao D.-K and Gao W.-B., Numerical simulations of Richtmyer–Meshkov instabilities using conservative front-tracking method, Appl. Math. Mech., 32(1) (2011), pp. 119132.
[33] Bates K. R., Nikiforakis N. and Holder D., Richtmyer–Meshkov instability induced by the interaction of a shock wave with a rectangular block of SF6 , Phys. Fluids, 19 (2007), 036101.
[34] Johnsen T. and Colonius E., Shock-induced collapse of a gas bubble in shockwave lithotripsy, J. Acoust. Soc. Am., 124(4) (2008), pp. 20112020.
[35] Ball G. J., Howell B. P., Leighton T. G. and Schofield M. J., Shock-induced collapse of a cylindrical air cavity in water: A free-Lagrange simulation, Shock Waves, 10(4) (2000), pp. 265276.
[36] Hu X. Y. and Khoo B. C., An interface interaction method for compressible multifluids, J. Comput. Phys., 198(1) (2004), pp. 3564.
[37] Nourgaliev R. R. and Dinh T. N., Adaptive characteristics-based matching for compressible multifluid dynamics, J. Comput. Phys., 213(2) (2006), pp. 500529.
[38] Hawker N. A. and Ventikos Y., Interaction of a strong shockwave with a gas bubble in a liquid medium: A numerical study, J. Fluid Mech., 701 (2012), pp. 5997.
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Advances in Applied Mathematics and Mechanics
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  • EISSN: 2075-1354
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