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A Sharp Interface Method for Compressible Multi-Phase Flows Based on the Cut Cell and Ghost Fluid Methods

Part of: Optics, electromagnetic theory - General

Published online by Cambridge University Press:  11 July 2017

Xiao Bai  and
Xiaolong Deng
Xiao Bai*
Affiliation:
School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China Building 9, East Zone, ZPark II, No. 10 East Xibeiwang Road, Haidian District, Beijing Computational Science Research Center, Beijing 100193, China
Xiaolong Deng*
Affiliation:
Building 9, East Zone, ZPark II, No. 10 East Xibeiwang Road, Haidian District, Beijing Computational Science Research Center, Beijing 100193, China
*
*Corresponding author. Email:baixiao@csrc.ac.cn (X. Bai), xiaolong.deng@csrc.ac.cn (X. L. Deng)
*Corresponding author. Email:baixiao@csrc.ac.cn (X. Bai), xiaolong.deng@csrc.ac.cn (X. L. Deng)
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Abstract

A new sharp interface method with the combination of Ghost Fluid Method (GFM) and Cut Cell scheme is developed to study compressible multi-phase flows with clear interfaces. Straight-line cutting is applied on the cells passed by the interface. A new real-ghost mixing method is presented and applied around the cut cells to deal with very small cut cells. A cut face reconstruction method similar to volume of fluid is applied to deal with topological change problems. A high order Level Set (LS) method is applied to evolve the free interface, with the Level Set velocities from exact Riemann solver on the cut faces. Various 1D and 2D numerical examples are tested to show the robustness and ability of the present method in wide flow variable domains. This method benefits from cut cell on the sharp interface description, shows good conservation performance, and does not have the topological change difficulty of the full cut cell method presented in Chang, Deng & Theofanous, J. Comput. Phys., 242 (2013), pp. 946–990.

Keywords

Compressible multi-phase flowscut cell methodlevel set methodghost fluid methodinterfacial dynamics

MSC classification

Secondary: 78A48: Composite media; random media
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 5 , October 2017 , pp. 1052 - 1075
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Hirt, C. W. and Nichols, B. D., Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys., 39 (1981), pp. 201–225.CrossRefGoogle Scholar
[2] Rider, W. J. and Kothe, D. B., Reconstructing volume tracking, J. Comput. Phys., 141 (1998), pp. 112–152.Google Scholar
[3] Osher, S. and Sethain, J. A., Front propagating with curvature dependent speed: algorithm based on Hamilton-Jaccobi formulation, J. Comput. Phys., 79 (1988), pp. 12–49.Google Scholar
[4] Osher, S. and Fedkiw, R. P., Level Set methods: an overview and some recent results, J. Comput. Phys., 169 (2001), pp. 463–502.Google Scholar
[5] Osher, S. and Fedkiw, R. P., Level Set Methods and Dynamic Implicit Surfaces, Springer, 2002.Google Scholar
[6] Sussman, M., Fatemi, E., Smereka, P., Osher, S. and Sethain, J. A., An improved Level Set method for imcompressible two-phase flows, Comput. Fluids, 27 (1998), pp. 663–680.Google Scholar
[7] Jacqmin, D., Calculation of two-phase Navier-Stokes flows using phase-field modeling, J. Comput. Phys., 155 (1999), pp. 96–127.CrossRefGoogle Scholar
[8] Yang, X. F., Feng, J. J., Liu, C. and Shen, J., Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method, J. Comput. Phys., 218 (2006), pp. 417–428.Google Scholar
[9] Chern, I. L., Glimm, J., McBryan, O., Plohr, B. and Yanvi, S., Front tracking for gas dynamics, J. Comput. Phys., 62 (1986), pp. 83–110.Google Scholar
[10] Glimm, J., Graham, M. J., Grove, J., Li, X. L., Smith, T. M., Tan, D., Tangerman, F. and Zhang, Q., Front tracking in two and three dimensions, Comput. Math. Appl., 35 (1998), pp. 1–11.Google Scholar
[11] Nourgaliev, R. R., Liou, M.-S., and Theofanous, T. G., Numerical prediction of interfacial instabilities: Sharp interface method (SIM), J. Comput. Phys., 227 (2008), pp. 3940–3970.CrossRefGoogle Scholar
[12] Chang, C.-H., Deng, X. L. and Theofanous, T. G., Direct numerical simulation of interfacial instabilities: A consistent, conservative, all-speed, sharp-interface method, J. Comput. Phys., 242 (2013), pp. 946–990.Google Scholar
[13] 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 (1999), pp. 457–492.Google Scholar
[14] Caiden, R., Fedkiw, R. P. and Anderson, C., A numerical method for two-phase flow consisting of separate compressible and incompressible regions, J. Comput. Phys., 166 (2001), pp. 1–27.CrossRefGoogle Scholar
[15] Fedkiw, R. P., Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method, J. Comput. Phys., 175 (2002), pp. 200–224.CrossRefGoogle Scholar
[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 (2003), pp. 651–681.Google Scholar
[17] Liu, T. G., Khoo, B. C. and Wang, C. W., The ghost fluid method for compressible gas-water simulation, J. Comput. Phys., 204 (2005), pp. 193–221.Google Scholar
[18] 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 (2006), pp. 278–302.CrossRefGoogle Scholar
[19] Hu, X. Y. and Khoo, B. C., An interface interaction method for compressible multifluids, J. Comput. Phys., 198 (2004), pp. 35–64.CrossRefGoogle Scholar
[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 (2006), pp. 553–578.Google Scholar
[21] Liou, M. S., A sequel to AUSM: AUSM+-up for all speed, J. Comput. Phys., 214 (2006), pp. 137–170.Google Scholar
[22] 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., 225 (2007), pp. 840–873.Google Scholar
[23] Jameson, A., Solution of the Euler equations for two dimensional flow by a multigrid method, Appl. Math. Comput., 13 (1983), pp. 327–355.Google Scholar
[24] Sommeijer, B. P., Van Der Houwen, P. J. and Kok, J., Time integration of three-dimendional numerical transport models, Appl. Numer. Math., 16 (1994), pp. 201–225.Google Scholar
[25] Nourgaliev, R. R. and Theofanous, T. G., High-fidelity interface tracking in compressible flows: Unlimited anchored adaptived Level Set, J. Comput. Phys., 224 (2007), pp. 836–866.Google Scholar
[26] Zhao, H.-K., Chan, T., Merriman, B. and Osher, S., A variational level set approach to multiphase motion, J. Comput. Phys., 127 (1996), pp. 179–195.CrossRefGoogle Scholar
[27] Sussman, M., Smereka, P. and Osher, S., A Level Set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys., 114 (1994), pp. 146–159.CrossRefGoogle Scholar
[28] Sussman, M., Almgren, A. S., Bell, J. B., Colella, P., Howell, L. H. and Welcome, M. L., An adaptive Level Set approach for incompressible two-phase flow, J. Comput. Phys., 148 (1999), pp. 81–124.CrossRefGoogle Scholar
[29] Peng, D. P., Merriman, B., Osher, S., Zhao, H. and Kang, M., A PDE-based fast local Level Set method, J. Comput. Phys., 155 (1999), pp. 410–438.Google Scholar
[30] Nourgaliev, R. R., Dinh, T. N. and Theofanous, T. G., Adaptive characteristics-based matching for compressible multifluid dynamics, J. Comput. Phys., 213 (2006), pp. 500–529.Google Scholar
[31] Li, J., Calcul d’interface affine par morceaux (Piecewise linear interface calculation), C. R. Acad. Sci. Paris, Sér. IIb (Paris), 320 (1995), pp. 391–396.Google Scholar
[32] Youngs, D. L., An interface tracking method for a 3D Eulerian hydrodynamics code, Technical report, AWRE, Technical Report 44/92/35.Google Scholar
[33] Saurel, R. and Abgrall, R., A simple method for compressible multifluid flows, SIAM J. Sci. Comput., 21 (1999), pp. 1115–1145.Google Scholar
[34] Richtmyer, R. D., Taylor instability in shock acceleration of compressible fluids, Commun. Pure Appl. Math., 13 (1960), pp. 297–313.Google Scholar
[35] Meshkov, E. E., Instability of the interface of two gases accelerated by a shock wave, Fluid Dyn., 43 (1969), pp. 101–104.Google Scholar
[36] Meshkov, E. E., Instability of a shock wave accelerated interface between two gases, NASA Tech. Trans., TT F-13 (1970), pp. 074.Google Scholar
[37] Holmes, R. L., A Numerical Investigation of the Richtmyer-Meshkov Instability Using Front-Tracking, Ph. D. dissertation, State University of New York at Stony Broke, USA 1994.Google Scholar
[38] 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. 51–64.CrossRefGoogle Scholar
[39] Ullah, M. A., Gao, W. B. and Mao, D. K., Numerical simulations of Richtmyer-Meshkov instabilities using conservative front-tracking method, Appl. Math. Mech., 32 (2011), pp. 119–132.Google Scholar
[40] Movahed, P. and Johnsen, E., A solution-adaptive method for efficient compressible multifluid simulations, with application to the Richtmyer-Meshkov instability, J. Comput. Phys., 239 (2013), pp. 166–186.Google Scholar
[41] Haas, J. F. and Sturtevant, B., Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities, J. Fluid Mech., 181 (1987), pp. 41–76.Google Scholar
[42] Quirk, J. J. and Karni, S., On the dynamics of a shock-bubble interaction, J. Fluid Mech., 318 (1996), pp. 129–163.CrossRefGoogle Scholar
[43] Ullah, M. A., Gao, W. B. and Mao, D. K., Towards front-tracking based on conservation in two space dimensions III, tracking interfaces, J. Comput. Phys., 242 (2013), pp. 268–303.CrossRefGoogle Scholar
[44] Shyue, K. M., A wave-propagation based volume tracking method for compressible multicomponent flow in two space dimensions, J. Comput. Phys., 215 (2006), pp. 219–244.CrossRefGoogle Scholar
[45] Terashima, H. and Tryggvason, G., A front-tracking/ghost-fluid method for fluid interface in compressible flows, J. Comput. Phys., 228 (2009), pp. 4012–4037.Google Scholar
[46] Grove, J. W. and Menikoff, R., The anomalous reflection of a shock wave at a material interface, J. Fluid Mech., 219 (1990), pp. 313–336.Google Scholar
[47] Bo, W. and Grove, J. W., A volume of fluid based ghost fluid method for compressible multi-fluid flows, Comput. Fluids, 90 (2014), pp. 113–122.Google Scholar
[48] Bourne, N. K. and Field, J. E., Shock-induced collapse of single cavities in liquids, J. Fluid Mech., 244 (1992), pp. 225–240.Google Scholar
[49] Shukla, R. K., Nonlinear preconditioning for efficient and accurate interface capturing in simulation of multicomponent compressible flows, J. Comput. Phys., 276 (2014), pp. 508–540.Google Scholar
[50] Hu, X. Y., Adams, N. A. and Iaccarino, G., On the HLLC Riemann solver for interface interaction in compressible multi-fluid flow, J. Comput. Phys., 228 (2009), pp. 6572–6589.Google Scholar
[51] Grove, J. W. and Menikoff, R., The anomalous reflection of a shock wave at a material interface, J. Fluid Mech., 219 (1990), pp. 313–336.CrossRefGoogle Scholar
[52] Shukla, R. K., Pantano, C. and Freund, J. B., An interface caputing method for simulation of multi-phase compressible flows, J. Comput. Phys., 229 (2010), pp. 7411–7439.Google Scholar