Compressible, multiphase semi-implicit method with moment of fluid interface representation

Jemison, Matthew; Sussman, Mark; Arienti, Marco

doi:10.1016/j.jcp.2014.09.005

Compressible, multiphase semi-implicit method with moment of fluid interface representation

Journal Article · Tue Sep 16 00:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2014.09.005· OSTI ID:1145652

Jemison, Matthew ^[1]; Sussman, Mark ^[1]; Arienti, Marco ^[2]

Florida State Univ., Tallahassee, FL (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

A unified method for simulating multiphase flows using an exactly mass, momentum, and energy conserving Cell-Integrated Semi-Lagrangian advection algorithm is presented. The deforming material boundaries are represented using the moment-of-fluid method. Our new algorithm uses a semi-implicit pressure update scheme that asymptotically preserves the standard incompressible pressure projection method in the limit of infinite sound speed. The asymptotically preserving attribute makes the new method applicable to compressible and incompressible flows including stiff materials; enabling large time steps characteristic of incompressible flow algorithms rather than the small time steps required by explicit methods. Moreover, shocks are captured and material discontinuities are tracked, without the aid of any approximate or exact Riemann solvers. As a result, wimulations of underwater explosions and fluid jetting in one, two, and three dimensions are presented which illustrate the effectiveness of the new algorithm at efficiently computing multiphase flows containing shock waves and material discontinuities with large “impedance mismatch.”

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1145652

Report Number(s):: SAND--2014-4016J; PII: S0021999114006317

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 279; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (53)

On finite-difference approximations and entropy conditions for shocks Harten, A.; Hyman, J. M.; Lax, P. D. Communications on Pure and Applied Mathematics, Vol. 29, Issue 3 https://doi.org/10.1002/cpa.3160290305	journal	May 1976
Coupled ghost fluid/two-phase level set method for curvilinear body-fitted grids Huang, Juntao; Carrica, Pablo M.; Stern, Frederick International Journal for Numerical Methods in Fluids, Vol. 55, Issue 9 https://doi.org/10.1002/fld.1499	journal	January 2007
Interface reconstruction with least-square fit and split Eulerian-Lagrangian advection Scardovelli, Ruben; Zaleski, Stephane International Journal for Numerical Methods in Fluids, Vol. 41, Issue 3 https://doi.org/10.1002/fld.431	journal	January 2003
An Adaptive Level Set Approach for Incompressible Two-Phase Flows Sussman, Mark; Almgren, Ann S.; Bell, John B. Journal of Computational Physics, Vol. 148, Issue 1 https://doi.org/10.1006/jcph.1998.6106	journal	January 1999
A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) Fedkiw, Ronald P.; Aslam, Tariq; Merriman, Barry Journal of Computational Physics, Vol. 152, Issue 2 https://doi.org/10.1006/jcph.1999.6236	journal	July 1999
A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows Sussman, Mark; Puckett, Elbridge Gerry Journal of Computational Physics, Vol. 162, Issue 2 https://doi.org/10.1006/jcph.2000.6537	journal	August 2000
The Constrained Interpolation Profile Method for Multiphase Analysis Yabe, Takashi; Xiao, Feng; Utsumi, Takayuki Journal of Computational Physics, Vol. 169, Issue 2, p. 556-593 https://doi.org/10.1006/jcph.2000.6625	journal	May 2001
Riemann-Problem and Level-Set Approaches for Homentropic Two-Fluid Flow Computations Koren, B.; Lewis, M. R.; van Brummelen, E. H. Journal of Computational Physics, Vol. 181, Issue 2 https://doi.org/10.1006/jcph.2002.7150	journal	September 2002
Dynamic fragmentation of laser shock-melted tin: experiment and modelling Rességuier, T.; Signor, L.; Dragon, A. International Journal of Fracture, Vol. 163, Issue 1-2 https://doi.org/10.1007/s10704-009-9378-8	journal	July 2009
Numerical Approximation of the Euler-Poisson-Boltzmann Model in the Quasineutral Limit Degond, P.; Liu, H.; Savelief, D. Journal of Scientific Computing, Vol. 51, Issue 1 https://doi.org/10.1007/s10915-011-9495-1	journal	May 2011
A Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase Flows Jemison, Matthew; Loch, Eva; Sussman, Mark Journal of Scientific Computing, Vol. 54, Issue 2-3 https://doi.org/10.1007/s10915-012-9614-7	journal	June 2012
Numerical calculation of almost incompressible flow Harlow, Francis H.; Amsden, Anthony A. Journal of Computational Physics, Vol. 3, Issue 1 https://doi.org/10.1016/0021-9991(68)90007-7	journal	August 1968
The next generation CIP as a conservative semi-Lagrangian solver for solid, liquid and gas Yabe, T.; Ogata, Y.; Takizawa, K. Journal of Computational and Applied Mathematics, Vol. 149, Issue 1 https://doi.org/10.1016/S0377-0427(02)00535-6	journal	December 2002
A 2D unstructured multi-material Cell-Centered Arbitrary Lagrangian–Eulerian (CCALE) scheme using MOF interface reconstruction Galera, Stéphane; Breil, Jérôme; Maire, Pierre-Henri Computers & Fluids, Vol. 46, Issue 1 https://doi.org/10.1016/j.compfluid.2010.09.038	journal	July 2011
A parallelized, adaptive algorithm for multiphase flows in general geometries Sussman, Mark Computers & Structures, Vol. 83, Issue 6-7 https://doi.org/10.1016/j.compstruc.2004.06.006	journal	February 2005
An embedded level set method for sharp-interface multiphase simulations of Diesel injectors Arienti, M.; Sussman, M. International Journal of Multiphase Flow, Vol. 59 https://doi.org/10.1016/j.ijmultiphaseflow.2013.10.005	journal	February 2014
Unified formulation for compressible and incompressible flows by using multi-integrated moments I: one-dimensional inviscid compressible flow Xiao, Feng Journal of Computational Physics, Vol. 195, Issue 2 https://doi.org/10.1016/j.jcp.2003.10.014	journal	April 2004
The pressure-corrected ICE finite element method for compressible flows on unstructured meshes Martineau, Richard C.; Berry, Ray A. Journal of Computational Physics, Vol. 198, Issue 2 https://doi.org/10.1016/j.jcp.2004.01.034	journal	August 2004
The ghost fluid method for compressible gas–water simulation Liu, T. G.; Khoo, B. C.; Wang, C. W. Journal of Computational Physics, Vol. 204, Issue 1 https://doi.org/10.1016/j.jcp.2004.10.012	journal	March 2005
A second order primitive preconditioner for solving all speed multi-phase flows Kadioglu, Samet Y.; Sussman, Mark; Osher, Stanley Journal of Computational Physics, Vol. 209, Issue 2 https://doi.org/10.1016/j.jcp.2005.03.020	journal	November 2005
Unified formulation for compressible and incompressible flows by using multi-integrated moments II: Multi-dimensional version for compressible and incompressible flows Xiao, Feng; Akoh, Ryosuke; Ii, Satoshi Journal of Computational Physics, Vol. 213, Issue 1 https://doi.org/10.1016/j.jcp.2005.08.002	journal	March 2006
CIP/multi-moment finite volume method for Euler equations: A semi-Lagrangian characteristic formulation Ii, S.; Xiao, F. Journal of Computational Physics, Vol. 222, Issue 2 https://doi.org/10.1016/j.jcp.2006.08.015	journal	March 2007
Interface reconstruction with least-squares fit and split advection in three-dimensional Cartesian geometry Aulisa, E.; Manservisi, S.; Scardovelli, R. Journal of Computational Physics, Vol. 225, Issue 2 https://doi.org/10.1016/j.jcp.2007.03.015	journal	August 2007
Multi-material interface reconstruction on generalized polyhedral meshes Ahn, Hyung Taek; Shashkov, Mikhail Journal of Computational Physics, Vol. 226, Issue 2 https://doi.org/10.1016/j.jcp.2007.06.033	journal	October 2007
Adaptive solution techniques for simulating underwater explosions and implosions Kadioglu, Samet Y.; Sussman, Mark Journal of Computational Physics, Vol. 227, Issue 3 https://doi.org/10.1016/j.jcp.2007.10.019	journal	January 2008
Reconstruction of multi-material interfaces from moment data Dyadechko, Vadim; Shashkov, Mikhail Journal of Computational Physics, Vol. 227, Issue 11 https://doi.org/10.1016/j.jcp.2007.12.029	journal	May 2008
Adaptive moment-of-fluid method Ahn, Hyung Taek; Shashkov, Mikhail Journal of Computational Physics, Vol. 228, Issue 8 https://doi.org/10.1016/j.jcp.2008.12.031	journal	May 2009
A method for avoiding the acoustic time step restriction in compressible flow Kwatra, Nipun; Su, Jonathan; Grétarsson, Jón T. Journal of Computational Physics, Vol. 228, Issue 11 https://doi.org/10.1016/j.jcp.2009.02.027	journal	June 2009
Conservative Volume-of-Fluid method for free-surface simulations on Cartesian-grids Weymouth, G. D.; Yue, Dick K. -P. Journal of Computational Physics, Vol. 229, Issue 8 https://doi.org/10.1016/j.jcp.2009.12.018	journal	April 2010
A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction Galera, Stéphane; Maire, Pierre-Henri; Breil, Jérôme Journal of Computational Physics, Vol. 229, Issue 16 https://doi.org/10.1016/j.jcp.2010.04.019	journal	August 2010
An unconditionally stable fully conservative semi-Lagrangian method Lentine, Michael; Grétarsson, Jón Tómas; Fedkiw, Ronald Journal of Computational Physics, Vol. 230, Issue 8 https://doi.org/10.1016/j.jcp.2010.12.036	journal	April 2011
Numerically stable fluid–structure interactions between compressible flow and solid structures Grétarsson, Jón Tómas; Kwatra, Nipun; Fedkiw, Ronald Journal of Computational Physics, Vol. 230, Issue 8 https://doi.org/10.1016/j.jcp.2011.01.005	journal	April 2011
A new volume-of-fluid method with a constructed distance function on general structured grids Wang, Zhaoyuan; Yang, Jianming; Stern, Frederick Journal of Computational Physics, Vol. 231, Issue 9 https://doi.org/10.1016/j.jcp.2012.01.022	journal	May 2012
FIVER: A finite volume method based on exact two-phase Riemann problems and sparse grids for multi-material flows with large density jumps Farhat, Charbel; Gerbeau, Jean-Frédéric; Rallu, Arthur Journal of Computational Physics, Vol. 231, Issue 19 https://doi.org/10.1016/j.jcp.2012.05.026	journal	August 2012
A hybrid level set-volume constraint method for incompressible two-phase flow Wang, Y.; Simakhina, S.; Sussman, M. Journal of Computational Physics, Vol. 231, Issue 19 https://doi.org/10.1016/j.jcp.2012.06.014	journal	August 2012
Direct numerical simulation of interfacial instabilities: A consistent, conservative, all-speed, sharp-interface method Chang, Chih-Hao; Deng, Xiaolong; Theofanous, Theo G. Journal of Computational Physics, Vol. 242 https://doi.org/10.1016/j.jcp.2013.01.014	journal	June 2013
Fully conservative leak-proof treatment of thin solid structures immersed in compressible fluids Grétarsson, Jón Tómas; Fedkiw, Ron Journal of Computational Physics, Vol. 245 https://doi.org/10.1016/j.jcp.2013.02.017	journal	July 2013
A monolithic mass tracking formulation for bubbles in incompressible flow Aanjaneya, Mridul; Patkar, Saket; Fedkiw, Ronald Journal of Computational Physics, Vol. 247 https://doi.org/10.1016/j.jcp.2013.03.048	journal	August 2013
The Symmetric Moment-of-Fluid interface reconstruction algorithm Hill, Ryan N.; Shashkov, Mikhail Journal of Computational Physics, Vol. 249 https://doi.org/10.1016/j.jcp.2013.04.037	journal	September 2013
Positivity-preserving Lagrangian scheme for multi-material compressible flow Cheng, Juan; Shu, Chi-Wang Journal of Computational Physics, Vol. 257 https://doi.org/10.1016/j.jcp.2013.09.047	journal	January 2014
Time-resolved proper orthogonal decomposition of liquid jet dynamics Arienti, Marco; Soteriou, Marios C. Physics of Fluids, Vol. 21, Issue 11 https://doi.org/10.1063/1.3263165	journal	November 2009
Spherical cap bubbles and skirt formation Hnat, J. G. Physics of Fluids, Vol. 19, Issue 2 https://doi.org/10.1063/1.861445	journal	January 1976
Numerical solution of the Navier-Stokes equations Chorin, Alexandre Joel Mathematics of Computation, Vol. 22, Issue 104 https://doi.org/10.1090/S0025-5718-1968-0242392-2	journal	January 1968
Volume of fluid interface reconstruction methods for multi-material problems Benson, David J. Applied Mechanics Reviews, Vol. 55, Issue 2 https://doi.org/10.1115/1.1448524	journal	March 2002
The Characteristics-Based Matching (CBM) Method for Compressible Flow With Moving Boundaries and Interfaces Nourgaliev, R. R.; Dinh, T. N.; Theofanous, T. G. Journal of Fluids Engineering, Vol. 126, Issue 4 https://doi.org/10.1115/1.1778713	journal	July 2004
Optimum Configuration of an Expanding-Contracting-Nozzle for Thrust Enhancement by Bubble Injection Singh, Sowmitra; Choi, Jin-Keun; Chahine, Georges Journal of Fluids Engineering, Vol. 134, Issue 1 https://doi.org/10.1115/1.4005687	journal	January 2012
Shock-induced collapse of a gas bubble in shockwave lithotripsy Johnsen, Eric; Colonius, Tim The Journal of the Acoustical Society of America, Vol. 124, Issue 4 https://doi.org/10.1121/1.2973229	journal	October 2008
Interaction of lithotripter‐generated shock waves with air bubbles Philipp, A.; Delius, M.; Scheffczyk, C. The Journal of the Acoustical Society of America, Vol. 93, Issue 5 https://doi.org/10.1121/1.406853	journal	May 1993
A Stable and Efficient Method for Treating Surface Tension in Incompressible Two-Phase Flow Sussman, Mark; Ohta, Mitsuhiro SIAM Journal on Scientific Computing, Vol. 31, Issue 4 https://doi.org/10.1137/080732122	journal	January 2009
A Robust Front Tracking Method: Verification and Application to Simulation of the Primary Breakup of a Liquid Jet Bo, Wurigen; Liu, Xingtao; Glimm, James SIAM Journal on Scientific Computing, Vol. 33, Issue 4 https://doi.org/10.1137/10079135X	journal	January 2011
A Simple Method for Compressible Multifluid Flows Saurel, Richard; Abgrall, Rémi SIAM Journal on Scientific Computing, Vol. 21, Issue 3 https://doi.org/10.1137/S1064827597323749	journal	January 1999
Aerobreakup of Newtonian and Viscoelastic Liquids Theofanous, T. G. Annual Review of Fluid Mechanics, Vol. 43, Issue 1 https://doi.org/10.1146/annurev-fluid-122109-160638	journal	January 2011
Spherical Solutions of an Underwater Explosion Bubble Wardlaw, Andrew B.; Mair, Hans U. Shock and Vibration, Vol. 5, Issue 2 https://doi.org/10.1155/1998/690105	journal	January 1998

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Compressible, multiphase semi-implicit method with moment of fluid interface representation

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