Skip to main content
×
×
Home

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

  • Xiao Bai (a1) (a2) and Xiaolong Deng (a2)
Abstract
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.

Copyright
Corresponding author
*Corresponding author. Email: baixiao@csrc.ac.cn (X. Bai), xiaolong.deng@csrc.ac.cn (X. L. Deng)
References
Hide All
[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. 201225.
[2] Rider W. J. and Kothe D. B., Reconstructing volume tracking, J. Comput. Phys., 141 (1998), pp. 112152.
[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. 1249.
[4] Osher S. and Fedkiw R. P., Level Set methods: an overview and some recent results, J. Comput. Phys., 169 (2001), pp. 463502.
[5] Osher S. and Fedkiw R. P., Level Set Methods and Dynamic Implicit Surfaces, Springer, 2002.
[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. 663680.
[7] Jacqmin D., Calculation of two-phase Navier-Stokes flows using phase-field modeling, J. Comput. Phys., 155 (1999), pp. 96127.
[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. 417428.
[9] Chern I. L., Glimm J., McBryan O., Plohr B. and Yanvi S., Front tracking for gas dynamics, J. Comput. Phys., 62 (1986), pp. 83110.
[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. 111.
[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. 39403970.
[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. 946990.
[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. 457492.
[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. 127.
[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. 200224.
[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. 651681.
[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. 193221.
[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. 278302.
[19] Hu X. Y. and Khoo B. C., An interface interaction method for compressible multifluids, J. Comput. Phys., 198 (2004), pp. 3564.
[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. 553578.
[21] Liou M. S., A sequel to AUSM: AUSM+-up for all speed, J. Comput. Phys., 214 (2006), pp. 137170.
[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. 840873.
[23] Jameson A., Solution of the Euler equations for two dimensional flow by a multigrid method, Appl. Math. Comput., 13 (1983), pp. 327355.
[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. 201225.
[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. 836866.
[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. 179195.
[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. 146159.
[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. 81124.
[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. 410438.
[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. 500529.
[31] Li J., Calcul d’interface affine par morceaux (Piecewise linear interface calculation), C. R. Acad. Sci. Paris, Sér. IIb (Paris), 320 (1995), pp. 391396.
[32] Youngs D. L., An interface tracking method for a 3D Eulerian hydrodynamics code, Technical report, AWRE, Technical Report 44/92/35.
[33] Saurel R. and Abgrall R., A simple method for compressible multifluid flows, SIAM J. Sci. Comput., 21 (1999), pp. 11151145.
[34] Richtmyer R. D., Taylor instability in shock acceleration of compressible fluids, Commun. Pure Appl. Math., 13 (1960), pp. 297313.
[35] Meshkov E. E., Instability of the interface of two gases accelerated by a shock wave, Fluid Dyn., 43 (1969), pp. 101104.
[36] Meshkov E. E., Instability of a shock wave accelerated interface between two gases, NASA Tech. Trans., TT F-13 (1970), pp. 074.
[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.
[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. 5164.
[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. 119132.
[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. 166186.
[41] Haas J. F. and Sturtevant B., Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities, J. Fluid Mech., 181 (1987), pp. 4176.
[42] Quirk J. J. and Karni S., On the dynamics of a shock-bubble interaction, J. Fluid Mech., 318 (1996), pp. 129163.
[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. 268303.
[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. 219244.
[45] Terashima H. and Tryggvason G., A front-tracking/ghost-fluid method for fluid interface in compressible flows, J. Comput. Phys., 228 (2009), pp. 40124037.
[46] Grove J. W. and Menikoff R., The anomalous reflection of a shock wave at a material interface, J. Fluid Mech., 219 (1990), pp. 313336.
[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. 113122.
[48] Bourne N. K. and Field J. E., Shock-induced collapse of single cavities in liquids, J. Fluid Mech., 244 (1992), pp. 225240.
[49] Shukla R. K., Nonlinear preconditioning for efficient and accurate interface capturing in simulation of multicomponent compressible flows, J. Comput. Phys., 276 (2014), pp. 508540.
[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. 65726589.
[51] Grove J. W. and Menikoff R., The anomalous reflection of a shock wave at a material interface, J. Fluid Mech., 219 (1990), pp. 313336.
[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. 74117439.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Advances in Applied Mathematics and Mechanics
  • ISSN: 2070-0733
  • EISSN: 2075-1354
  • URL: /core/journals/advances-in-applied-mathematics-and-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 66 *
Loading metrics...

Abstract views

Total abstract views: 266 *
Loading metrics...

* Views captured on Cambridge Core between 11th July 2017 - 18th January 2018. This data will be updated every 24 hours.