Skip to main content
SpringerLink
Log in

A Levelset-Based Sharp-Interface Modified Ghost Fluid Method for High-Speed Multiphase Flows and Multi-Material Hypervelocity Impact

  • Chapter
  • First Online:
Immersed Boundary Method

Part of the book series: Computational Methods in Engineering & the Sciences ((CMES))

Abstract

Multi-material compressible flows are ubiquitous in industrial, defense, and environmental applications. The widely varied range of applications encompasses high-speed multiphase combustion in solid-propellant rocket motors, high-speed manufacturing processes, target–munition interactions, geological impact, and many more. Major challenges in modeling such systems lie in preserving the material interface definition while simultaneously satisfying the interfacial boundary conditions accurately. In this chapter, a levelset-based sharp-interface method is described for general classes of multi-material compressible flows problems. In this framework, the interface definition is retained sharply, while interfacial jump conditions are prescribed through a high-accuracy modified ghost fluid method. The application of the framework is demonstrated for several multi-material flow problems such as shock–particle interactions, shock–droplet interaction, shock-induced void collapse in energetic materials, and shock compaction of metallic powders. The chapter will describe the levelset-based framework for high-speed multiphase flows and shows its application to a broad spectrum of problems of engineering interest.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Artemieva NA, Shuvalov VV (2008) Numerical simulation of high-velocity impact ejecta following falls of comets and asteroids onto the Moon. Sol Syst Res 42(4):329–334

    Article  Google Scholar 

  • Boiko VM et al (1997) Shock wave interaction with a cloud of particles. Shock Waves 7(5):275–285

    Article  MATH  Google Scholar 

  • Burcat’s Thermodynamic Data

    Google Scholar 

  • Bürger D et al (2012) Ballistic impact simulation of an armour-piercing projectile on hybrid ceramic/fiber reinforced composite armours. Int J Impact Eng 43:63–77

    Article  Google Scholar 

  • Chaudhuri A et al (2013) Numerical study of shock-wave mitigation through matrices of solid obstacles. Shock Waves 23(1):91–101

    Article  Google Scholar 

  • Das P et al (2017) A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows. Int J Comput Fluid Dyn 31(6–8):1–23

    Google Scholar 

  • Das P, UdayKumar HS (2019) A sharp-interface method for the simulation of shock-induced vaporization of droplets. J Comp Phys (in press)

    Google Scholar 

  • Das P et al (2018a) Metamodels for interphase heat transfer from mesoscale simulations of Shock-Cylinder Interactions. AIAA Journal 56(10):3975–3987

    Article  Google Scholar 

  • Das P et al (2018b) Strategies for efficient machine learning of surrogate drag models from three-dimensional mesoscale computations of shocked particulate flows. Int J Multiph Flow 108:51–68

    Article  MathSciNet  Google Scholar 

  • Dongmo E, Wenzelburger M, Gadow R (2008) Analysis and optimization of the HVOF process by combined experimental and numerical approaches. Surf Coat Technol 202(18):4470–4478

    Article  Google Scholar 

  • Eakins D, Thadhani NN (2006) Shock-induced reaction in a flake nickel + spherical aluminum powder mixture. J Appl Phys 100(11):113521

    Article  Google Scholar 

  • Eakins DE, Thadhani NN (2008a) The shock-densification behavior of three distinct Ni + Al powder mixtures. Appl Phys Lett 92(11):111903

    Article  Google Scholar 

  • Eakins DE, Thadhani NN (2008b) Mesoscale simulation of the configuration-dependent shock-compression response of Ni + Al powder mixtures. Acta Mater 56(7):1496–1510

    Article  Google Scholar 

  • Eakins DE, Thadhani NN (2009) Shock compression of reactive powder mixtures. Int Mater Rev 54(4):181–213

    Article  Google Scholar 

  • Fedkiw RP et al (1999) A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the Ghost Fluid Method). J Comput Phys 152(2):457–492

    Article  MathSciNet  MATH  Google Scholar 

  • Field John E et al (1992) Hot-spot ignition mechanisms for explosives and propellants. Philos Trans R Soc London Ser A: Phys Eng Sci 339(1654):269–283

    Google Scholar 

  • Gottlieb S, Shu C-W (1998) Total variation diminishing Runge-Kutta schemes. Math Comput Am Math Soc 67(221):73–85

    Article  MathSciNet  MATH  Google Scholar 

  • Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39(1):201–225

    Article  MATH  Google Scholar 

  • Houim RW (2011) Modeling the influence of shock waves on the combustion of aluminum droplets

    Google Scholar 

  • Houim RW, Kuo KK (2013) A ghost fluid method for compressible reacting flows with phase change. J Comput Phys 235:865–900

    Article  MathSciNet  Google Scholar 

  • Huang Y et al (2009) Effect of particle size on combustion of aluminum particle dust in air. Combust Flame 156(1):5–13

    Article  Google Scholar 

  • Jamaluddin AR et al (2011) The collapse of single bubbles and approximation of the far-field acoustic emissions for cavitation induced by shock wave lithotripsy. J Fluid Mech 677:305–341

    Article  MathSciNet  MATH  Google Scholar 

  • Jiang G-S, Shu C-W (1996) Efficient implementation of weighted ENO schemes. J Comput Phys 126(1):202–228

    Article  MathSciNet  MATH  Google Scholar 

  • Khan A, Huang S (1995) Continuum theory of plasticity. Wiley, New York

    MATH  Google Scholar 

  • Liu TG, Khoo BC, Wang CW (2005) The ghost fluid method for compressible gas–water simulation. J Comput Phys 204(1):193–221

    Article  MathSciNet  MATH  Google Scholar 

  • Marusich TD, Ortiz M (1995) Modelling and simulation of high-speed machining. Int J Numer Meth Eng 38(21):3675–3694

    Article  MATH  Google Scholar 

  • Massoni J et al (1999) A mechanistic model for shock initiation of solid explosives. Phys Fluids 11(3):710–736

    Article  MathSciNet  MATH  Google Scholar 

  • Mayer W, Tamura H (1996) Propellant injection in a liquid oxygen/gaseous hydrogen rocket engine. J Propul Power 12(6):1137–1147

    Article  Google Scholar 

  • Mehta Y et al (2016) Shock interaction with three-dimensional face centered cubic array of particles. Phys Rev Fluids 1(5):054202

    Article  MathSciNet  Google Scholar 

  • Meyers MA (1994) Dynamic behavior of materials. Wiley, New York

    Google Scholar 

  • Mousel J (2012) A massively parallel adaptive sharp interface solver with application to mechanical heart valve simulations. Theses and Dissertations

    Google Scholar 

  • Nesterenko VF et al (1994) Controlled high-rate localized shear in porous reactive media. Appl Phys Lett 65(24):3069–3071

    Article  Google Scholar 

  • Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79(1):12–49

    Article  MathSciNet  MATH  Google Scholar 

  • Ponthot JP (2002) Unified stress update algorithms for the numerical simulation of large deformation elasto-plastic and elasto-viscoplastic processes. Int J Plast 18(1):91–126

    Google Scholar 

  • Powell OA et al (2001) Development of hydrocarbon-fueled scramjet engines: the hypersonic technology (HyTech) program. J Propul Power 17(6):1170–1176

    Article  Google Scholar 

  • Rai NK, Kapahi A, Udaykumar HS (2014) Treatment of contact separation in Eulerian high-speed multimaterial dynamic simulations. Int J Numer Meth Eng 100(11):793–813

    Article  MathSciNet  MATH  Google Scholar 

  • Regele JD et al (2014) Unsteady effects in dense, high speed, particle laden flows. Int J Multiph Flow 61:1–13

    Article  Google Scholar 

  • Sambasivan SK, UdayKumar HS (2009) Ghost fluid method for strong shock interactions Part 1: fluid-fluid interfaces. AIAA J 47(12):2907–2922

    Article  Google Scholar 

  • Sambasivan S, Kapahi A, Udaykumar HS (2013) Simulation of high speed impact, penetration and fragmentation problems on locally refined Cartesian grids. J Comput Phys 235:334–370

    Article  MathSciNet  MATH  Google Scholar 

  • Scardovelli R, Zaleski S (2000) Analytical relations connecting linear interfaces and volume fractions in rectangular grids. J Comput Phys 164(1):228–237

    Article  MathSciNet  MATH  Google Scholar 

  • Sethian JA, Smereka P (2003) Level set methods for fluid interfaces. Annu Rev Fluid Mech 35(1):341–372

    Article  MathSciNet  MATH  Google Scholar 

  • Shiv Kumar S, UdayKumar HS (2009) Ghost fluid method for strong shock interactions Part 2: immersed solid boundaries. AIAA j 47(12):2923–2937

    Article  Google Scholar 

  • Shu C-W, Osher S (1989) Efficient implementation of essentially non-oscillatory shock-capturing schemes, II. In: Hussaini PMY , Leer PBV, Rosendale DJV (eds) Upwind and high-resolution schemes. Springer, Berlin, pp 328–374

    Google Scholar 

  • Sussman M, Smereka P, Osher S (1994) A level set approach for computing solutions to incompressible two-phase flow. J Comput Phys 114(1):146–159

    Article  MATH  Google Scholar 

  • Sussman M et al (1998) An improved level set method for incompressible two-phase flows. Comput Fluids 27(5–6):663–680

    Article  MATH  Google Scholar 

  • Tamura S, Horie Y (1998) Discrete meso-dynamic simulation of thermal explosion in shear bands. J Appl Phys 84(7):3574–3580

    Article  Google Scholar 

  • Tarver CM, Chidester SK, Nichols AL (1996) critical conditions for impact- and shock-induced hot spots in solid explosives. J Phys Chem 100(14):5794–5799

    Article  Google Scholar 

  • Thadhani NN (1988) Shock compression processing of powders. Adv Mater Manuf Process 3(4):493–549

    Google Scholar 

  • Unverdi SO, Tryggvason G (1992) A front-tracking method for viscous, incompressible, multi-fluid flows. J Comput Phys 100(1):25–37

    Article  MATH  Google Scholar 

  • Verwer JG, Sommeijer BP, Hundsdorfer W (2004) RKC time-stepping for advection—diffusion—reaction problems. J Comput Phys 201(1):61–79

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge the financial support by the Air Force Office of Scientific Research under grant numbers FA9550-15-1-0332 (Program Officer: Dr. Martin Schmidt) and SA0000506 (Program Officer: Dr. Fariba Fahroo).

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, The University of Iowa, Iowa City, IA, USA

    Pratik Das, Nirmal K. Rai & H. S. Udaykumar

Authors
  1. Pratik Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nirmal K. Rai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. S. Udaykumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. S. Udaykumar .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India

    Somnath Roy

  2. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Ashoke De

  3. Department of Mechanical and Aerospace Engineering, George Washington University, Washington, DC, USA

    Elias Balaras

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Das, P., Rai, N.K., Udaykumar, H.S. (2020). A Levelset-Based Sharp-Interface Modified Ghost Fluid Method for High-Speed Multiphase Flows and Multi-Material Hypervelocity Impact. In: Roy, S., De, A., Balaras, E. (eds) Immersed Boundary Method . Computational Methods in Engineering & the Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-15-3940-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-981-15-3940-4_7

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-3939-8

  • Online ISBN: 978-981-15-3940-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation