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Implementation of the ghost fluid method for free surface flows in polyhedral finite volume framework. (English) Zbl 1390.76529

Summary: This paper presents an extension of the ghost fluid method to arbitrary polyhedral finite volume framework for free surface flow simulations, primarily intended for marine hydrodynamics applications. Two immiscible, incompressible fluids are implicitly coupled via interface jump conditions, allowing the formulation of a single set of equations for both fluids. The jump conditions at the free surface are discretised with one sided extrapolates, using a compact computational stencil in second-order accurate, collocated polyhedral finite volume method. The free surface is captured using the volume-of-fluid method with an additional compressive term. Even though the volume-of-fluid method is used, density and dynamic pressure exhibit sharp distribution at the interface due to jump conditions. The paper also demonstrates how the conditionally averaged equations with segregated solution algorithms cause spurious velocities at the free surface, which are resolved by the present approach since the ghost fluid method relocates the pressure-density coupling inside the pressure equation. The method is implemented in OpenFOAM computational continuum mechanics software, and the verification and validation is performed on two sets of test cases: free surface flow over a ramp and a steady resistance simulation of a container ship free to sink and trim.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids

Software:

OpenFOAM; ComFLOW
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[1] Tuković, Z.; Jasak, H., A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow, Comput Fluids, 55, 70-84, (2012) · Zbl 1291.76223
[2] Dieter-Kissling, K.; Marschall, H.; Bothe, D., Numerical method for coupled interfacial surfactant transport on dynamic surface meshes of general topology, Comput Fluids, 109, 168-184, (2015) · Zbl 1390.76052
[3] Tryggvason, G.; Bunner, B.; Esmaeeli, A.; Juric, D.; Al-Rawahi, N.; Tauber, W., A front-tracking method for computations of multiphase flow, J Comput Phys, 169, 708-759, (2001) · Zbl 1047.76574
[4] Stern, F.; Yang, J.; Wang, Z.; Sadat-Hosseini, H.; Mousaviraad, M.; Bhushan, S.; Xing, T., Computational ship hydrodynamics: nowadays and way forward, Proceedings of the 29th ONR symposium on naval hydrodynamics, 1-73, (2012)
[5] Luppes, R.; Düz, B.; van der Heiden, H.; van der Plas, P.; Veldman, A., Numerical simulations of two-phase flow with COMFLOW: past and recent developments, Proceedings of the ECCOMAS 2012 conference, 1-16, (2012)
[6] Carrica, P. M.; Wilson, R. V.; Noack, R. W.; Stern, F., Ship motions using single-phase level set with dynamic overset grids, Comput Fluids, 36, 1415-1433, (2007) · Zbl 1194.76197
[7] Carrica, P. M.; Wilson, R. V.; Stern, F., An unsteady single-phase level set method for viscous free surface flows, Int J Numer Meth Fluids, 53, 229-256, (2007) · Zbl 1227.76049
[8] Fedkiw, R. P.; Aslam, T.; Xu, S., The ghost fluid method for deflagration and detonation discontinuities, J Comput Phys, 154, 2, 393-427, (1999) · Zbl 0955.76071
[9] Kang, M.; Fedkiw, R. P.; Liu, X.-D., A boundary condition capturing method for multiphase incompressible flow, J Sci Comput, 15, 3, 323-360, (2000) · Zbl 1049.76046
[10] Desjardins, O.; Moureau, V.; Pitsch, H., An accurate conservative level set/ghost fluid method for simulating turbulent atomization, J Comput Phys, 227, 18, 8395-8416, (2008) · Zbl 1256.76051
[11] Huang, J.; Carrica, P. M.; Stern, F., Coupled ghost fluid/two-phase level set method for curvilinear body-fitted grids, Int J Numer Meth Fluids, 44, 867-897, (2007) · Zbl 1388.76253
[12] Bo, W.; Grove, J. W., A volume of fluid method based ghost fluid method for compressible multi-fluid flows, Comput Fluids, 90, 113-122, (2014) · Zbl 1391.76524
[13] Kaneda, M.; Haruna, T.; Suga, K., Ghost-fluid-based boundary treatment in lattice Boltzmann method and its extension to advancing boundary, Appl Therm Eng, 72, 1, 126-134, (2014)
[14] Lalanne, B.; Villegas, L. R.; Tanguy, S.; Risso, F., On the computation of viscous terms for incompressible two-phase flows with level set/ghost fluid method, J Comput Phys, 301, 289-307, (2015) · Zbl 1349.76352
[15] Larsson, L.; Stern, F.; Visonneau, M., Numerical ship hydrodynamics: an assessment of the Gothenburg 2010 workshop, (2013), Springer
[16] Tryggvason, G.; Scardovelli, R.; Zaleski, S., Direct numerical simulations of gas-liquid multiphase flows, (2011), Cambridge University Press · Zbl 1226.76001
[17] Ubbink, O.; Issa, R. I., A method for capturing sharp fluid interfaces on arbitrary meshes, J Comput Phys, 153, 26-50, (1999) · Zbl 0955.76058
[18] Ubbink, O., Numerical prediction of two fluid systems with sharp interfaces, (1997), Imperial College of Science, Technology & Medicine London, [Ph.D. thesis]
[19] Rusche, H., Computational fluid dynamics of dispersed two-phase flows at high phase fractions, (2002), Imperial College of Science, Technology & Medicine London, [Ph.D. thesis]
[20] Kissling, K.; Springer, J.; Jasak, H.; Schütz, S.; Urban, K.; Piesche, M., A coupled pressure based solution algorithm based on the volume-of-fluid approach for two or more immiscible fluids, Proceedings of Vth European conference on computational fluid dynamics, ECCOMAS CFD, (2010)
[21] Sethian, J. A., Level set methods: evolving interfaces in geometry, fluid mechanics, computer vision and materials science, (1996), Cambridge University Press · Zbl 0859.76004
[22] Sussman, M.; Smereka, P.; Osher, S., A level set approach for computing solutions to incompressible two-phase flow, J Comput Phys, 114, 146-159, (1994) · Zbl 0808.76077
[23] Olsson, E.; Kreiss, G., A conservative level set method for two phase flow, J Comput Phys, 210, 1, 225-246, (2005) · Zbl 1154.76368
[24] Olsson, E.; Kreiss, G.; Zahedi, S., A conservative level set method for two phase flow ii, J Comput Phys, 225, 1, 785-807, (2007) · Zbl 1256.76052
[25] Jacobsen, N. G.; Fuhrman, D. R.; Fredsøe, J., A wave generation toolbox for the open-source CFD library: openfoam®, Int J Numer Meth Fluids, 70, 9, 1073-1088, (2012) · Zbl 1412.76004
[26] Higuera, P.; Lara, J.; Losada, I. J., Realistic wave generation and active wave absorption for Navier-Stokes models: application to openfoam®, Coast Eng, 71, 102-118, (2013)
[27] Higuera, P.; Lara, J.; Losada, I. J., Simulating coastal engineering processes with openfoam®, Coast Eng, 71, 119-134, (2013)
[28] Paulsen, B. T.; Bredmose, H.; Bingham, H. B., An efficient domain decomposition strategy for wave loads on surface piercing circular cylinders, Coast Eng, 86, 57-76, (2014)
[29] Paulsen, B. T.; Bredmose, H.; Bingham, H. B.; Jacobsen, N. G., Forcing of a bottom-mounted circular cylinder by steep regular water waves at finite depth, J Fluid Mech, 755, 1-3, (2014)
[30] Osher, S.; Fedkiw, R., Level set methods and dynamic implicit surfaces, (2003), Springer · Zbl 1026.76001
[31] Sussman, M.; Fatemi, E., An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow, SIAM J Sci Comput, 20, 4, 1165-1191, (1999) · Zbl 0958.76070
[32] Gómez, P.; Hernández, J.; López, J., On the reinitialization procedure in a narrow-band locally refined level set method for interfacial flows, Int J Numer Methods Eng, 63, 1478-1512, (2005) · Zbl 1086.76559
[33] Sun, Y.; Beckermann, C., Sharp interface tracking using the phase-field equation, J Comput Phys, 220, 626-653, (2007) · Zbl 1228.76110
[34] Sun, Y.; Beckermann, C., A two-phase diffusive-interface model for Hele-Shaw flows with large property contrasts, Physica D, 237, 3089-3098, (2008) · Zbl 1407.76035
[35] Wang S, Glimm J, Samulyak R, Jiao X, Diao C. An embedded boundary method for two phase incompressible flow. arXiv e-prints1304.5514; 2013. http://adsabs.harvard.edu/abs/2013arXiv1304.5514W
[36] Johansen, H.; Colella, P., A Cartesian grid embedding boundary method for poisson’s equation on irregular domains, J Comput Phys, 147, 60-85, (1998) · Zbl 0923.65079
[37] Crockett, R. K.; Colella, P.; Graves, D. T., A Cartesian grid embedded boundary method for solving the Poisson and heat equations with discontinuous coefficients in three dimensions, J Comput Phys, 230, 613-628, (2010)
[38] Jasak, H., Error analysis and estimation for the finite volume method with applications to fluid flows, (1996), Imperial College of Science, Technology & Medicine London, [Ph.D. thesis]
[39] Queutey, P.; Visonneau, M., An interface capturing method for free-surface hydrodynamic flows, Comput Fluids, 36, 1481-1510, (2007) · Zbl 1194.76163
[40] Menter, F. R.; Kuntz, M.; Langtry, R., Ten years of industrial experience with the SST turbulence model, Turbul Heat Mass Transf, 4, 625-632, (2003)
[41] Weller, H. G.; Tabor, G.; Jasak, H.; Fureby, C., A tensorial approach to computational continuum mechanics using object oriented techniques, Comput Phys, 12, 620-631, (1998)
[42] Patankar, S. V.; Spalding, D. B., A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, Int J Heat Mass Transf, 15, 1787-1806, (1972) · Zbl 0246.76080
[43] Issa, R. I., Solution of the implicitly discretised fluid flow equations by operator-splitting, J Comput Phys, 62, 40-65, (1986) · Zbl 0619.76024
[44] Batchelor, F. R., An introduction to fluid dynamics, (1967), Cambridge University Press · Zbl 0152.44402
[45] Dopazo, C., On conditional averages for intermittent turbulent flows, J Fluid Mech, 81, 433-438, (1977) · Zbl 0362.76103
[46] Ashgriz, N., Handbook of atomization and sprays: theory and applications, (2011), Springer Science & Business Media
[47] Wilcox, D. C., Turbulence modeling for CFD, (1993), DCW Industries
[48] Ito, K.; Li, Z., Interface conditions for Stokes equations with a discontinuous viscosity and surface sources, Appl Math Lett, 19, 229-234, (2006) · Zbl 1096.76014
[49] Versteeg, H. K.; Malalasekera, W., An introduction to computational fluid dynamics: the finite volume method, (1995), Pearson Education Limited
[50] Ferziger, J. H.; Peric, M., Computational methods for fluid dynamics, (1996), Springer · Zbl 0869.76003
[51] Demirdžić, I., On the discretization of the diffusion term in finite-volume continuum mechanics, Numer Heat Transf B, 68, 1-10, (2015)
[52] Rhie, C. M.; Chow, W. L., A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation, AIAA J, 21, 1525-1532, (1983) · Zbl 0528.76044
[53] Vukčević, V.; Östman, A.; Jasak, H., Rapid simulations of pure sway motion using FVM in openfoam, Proceedings of workshop on verification and validation of ship manoeuvring simulation methods (SIMMAN 2014), (2014)
[54] Jasak, H.; Weller, H. G., Application of the finite volume method and unstructured meshes to linear elasticity, Int J Numer Methods Eng, 48, 267-287, (2000) · Zbl 0990.74077
[55] Specialist committee on CFD in marine hydrodynamics. Final report and recommendations to the 27th ITTC. Proceedings of the 27th International Towing Tank Conference Aug.-Sep. 2014 [available online; accessed 20.08.15].
[56] Pereira, F. S.; Vaz, G.; Eca, L., On the numerical requirements of RANS and hybrid turbulence models, Proceedings of the MARINE 2015 conference, 886-902, (2015)
[57] Li, D.; Hallander, J.; Johansson, T.; Karlsson, R., Cavitation dynamics and underwater radiated noise signature of a ship with a cavitating propeller, Proceedings of the MARINE 2015 conference, 401-412, (2015)
[58] Menter, F. R., Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J, 32, 8, 1598-1605, (1994)
[59] Jasak, H.; Vukčević, V.; Christ, D., Rapid free surface simulation for steady-state hull resistance with FVM using openfoam, Proceedings of the 30th symposium on naval hydrodynamics, 548-554, (2014)
[60] Yang, C.; Löhner, R., Calculation of ship sinkage and trim using a finite element method and unstructured grids, Int J CFD, 16, 3, 217-227, (2002) · Zbl 1076.76546
[61] Coutsias, E. A.; Romero, L., The quaternions with an application to rigid body dynamics, Department of Mathematics and Statistics, (1999)
[62] Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P., Numerical recipes in C++: the art of scientific computing, (2002), Cambridge University Press · Zbl 1078.65500
[63] Demiridžić, I.; Perić, M., Space conservation law in finite volume calculations of fluid flow, Int J Numer Methods Fluids, 8, 1037-1050, (1988) · Zbl 0647.76018
[64] Simonsen, C. D.; Otzen, J. F.; Joncquey, S.; Stern, F., EFD and CFD for KCS heaving and pitching in regular head waves, J Mar Sci Technol, 18, 435-459, (2013)
[65] Muzaferija, S.; Perić, M., Computation of free-surface flows using the finite-volume method and moving grids, Numer Heat Transf B, 32, 369-384, (1997)
[66] Tokyo workshop, Tokyo 2015: a workshop on CFD in ship hydrodynamics. http://www.t2015.nmri.go.jp/; 2015 [online; accessed 20.08.15].
[67] Larsson L, Stern F, Visonneau M, Hirata N, Hino T, Kim J, editors. Tokyo 2015: a workshop on CFD in ship hydrodynamics; vol. 2. Tokyo, Japan: NMRI (National Maritime Research Institute); 2015.
[68] Larsson L, Stern F, Visonneau M, Hirata N, Hino T, Kim J, editors. Tokyo 2015: a workshop on CFD in ship hydrodynamics; vol. 3. Tokyo, Japan: NMRI (National Maritime Research Institute); 2015.
[69] Hirsch, C., Numerical computation of internal and external flows, Computational methods for inviscid and viscous flows, vol. 2, (1984), John Wiley & Sons
[70] van Leer, B., Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection, J Comput Phys, 23, 276-299, (1977) · Zbl 0339.76056
[71] Saad, Y., Iterative methods for sparse linear systems, (2003), Society for Industrial and Applied Mathematics, SIAM Philadelphia · Zbl 1002.65042
[72] Hestens, M.; Steifel, E., Method of conjugate gradients for solving linear systems, J Res, 29, 409-436, (1952)
[73] van der Vorst, H., BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems, SIAM J Sci Comput, 13, 631-644, (1992) · Zbl 0761.65023
[74] Roache, P., Quantification of uncertainty in computational fluid dynamics, Ann Rev Fluid Mech, 29, 123-160, (1997)
[75] Stern, F.; Wilson, R. V.; Coleman, H. W.; Paterson, E. G., Comprehensive approach to verification and validation of CFD simulations - part 1: methodology and procedures, J Fluids Eng, 123, 4, 793-802, (2001)
[76] Tuković, Z., Finite volume method on domains of varying shape (in Croatian), (2005), Faculty of Mechanical Engineering and Naval Architecture Zagreb, [Ph.D. thesis]
[77] NPARC alliance CFD verification and validation web site. Examining spatial (grid) convergence. http://www.grc.nasa.gov/WWW/wind/valid/tutorial/spatconv.html; 2016 [online; accessed 01.04.16].
[78] Raven, C. H.; van der Ploeg, A.; Starke, B., Computation of free-surface viscous flows at model and full scale by a steady iterative approach, Proceedings of the 25th symposium on naval hydrodynamics, (2004)
[79] Van, S. H.; Kim, W. J.; Yim, G. T.; Kim, D. H.; Lee, C. J., Experimental investigation of the flow characteristics around practical hull forms, Proceedings of the 3rd Osaka colloguium on advanced CFD applications to ship flow and hull form design, (1998)
[80] Kim, W. J.; Van, S. H.; Kim, D., Measurment of flows around modern commercial ship models, Exp Fluids, 31, 567-578, (2001)
[81] Simonsen, C. D.; Otzen, J. F.; Stern, F., EFD and CFD for KCS heaving and pitching in regular head waves, Proceedings of the 27th symposium on naval hydrodynamics, (2008)
[82] Jasak, H.; Vukčević, V.; Gatin, I., Numerical simulation of wave loads on static offshore structures, CFD for wind and tidal offshore turbines, 95-105, (Springer, 2015)
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