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A novel non-reflecting boundary condition for fluid dynamics solved by smoothed particle hydrodynamics

Published online by Cambridge University Press:  03 December 2018

Pingping Wang ,
A-Man Zhang Open the ORCID record for A-Man Zhang [Opens in a new window] ,
Furen Ming ,
Pengnan Sun  and
Han Cheng
Pingping Wang
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
A-Man Zhang*
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
Furen Ming
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
Pengnan Sun
Affiliation:
Ecole Centrale Nantes, LHEEA res. dept. (ECN and CNRS), 44300 Nantes, France
Han Cheng
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
*
†Email address for correspondence: zhangaman@hrbeu.edu.cn
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Abstract

Non-reflecting boundary conditions (NRBCs) play an important role in computational fluid dynamics (CFD). A novel NRBC based on the method of characteristics using timeline interpolations is proposed for fluid dynamics solved by smoothed particle hydrodynamics (SPH). It is performed by four layers of particles whose pressures and velocities are obtained through the Lagrange interpolation in the time domain which is derived from the propagation of characteristic waves between particles. The proposed NRBC can allow outward travelling pressure and velocity messages to pass through the boundary without obvious reflection. That is, with the implementation of the NRBC, the solution in a finite computational domain of interest is close to that in an infinite domain. Several numerical tests show that this NRBC is robust and applicable for a broad variety of hydrodynamics ranging from low to high speed.

JFM classification

Mathematical Foundations: Computational methods Mathematical Foundations: Mathematical Foundations
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 860 , 10 February 2019 , pp. 81 - 114
Copyright
© 2018 Cambridge University Press 

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References

Adami, S., Hu, X. Y. & Adams, N. A. 2010 A conservative SPH method for surfactant dynamics. J. Comput. Phys. 229 (5), 1909–1926.Google Scholar
Adami, S., Hu, X. Y. & Adams, N. A. 2012 A generalized wall boundary condition for smoothed particle hydrodynamics. J. Comput. Phys. 231 (21), 7057–7075.Google Scholar
Alpert, B., Greengard, L. & Hagstrom, T. 2000 Rapid evaluation of nonreflecting boundary kernels for time-domain wave propagation. SIAM J. Numer. Anal. 37 (4), 1138–1164.Google Scholar
Altomare, C., Domínguez, J. M., Crespo, A. J. C., González-Cao, J., Suzuki, T., Gómez-Gesteira, M. & Troch, P. 2017 Long-crested wave generation and absorption for SPH-based dualsphysics model. Coast. Engng 127, 37–54.Google Scholar
Alvarado-Rodríguez, C. E., Klapp, J., Sigalotti, L. D. G., Domínguez, J. M. & Sánchez, E. D. L. C. 2017 Nonreflecting outlet boundary conditions for incompressible flows using SPH. Comput. Fluids 159, 177–188.Google Scholar
Antuono, M., Colagrossi, A., Marrone, S. & Molteni, D. 2010 Free surface flows solved by means of SPH schemes with numerical diffusive terms. Comput. Phys. Commun. 181 (3), 532–549.Google Scholar
Bai, K. J. 1977 The added mass of two-dimensional cylinders heaving in water of finite depth. J. Fluid Mech. 81 (1), 85–105.Google Scholar
Baum, M., Poinsot, T. & Venin, D. 1995 Accurate boundary conditions for multicomponent reactive flows. J. Comput. Phys. 116 (2), 247–261.Google Scholar
Bayliss, A. & Turkel, E. 1980 Radiation boundary condition for wave-like equations. Commun. Pure Appl. Maths 33 (6), 707–725.Google Scholar
Benz, W. 1990 Smooth Particle Hydrodynamics: A Review. Springer.Google Scholar
Berenger, J. P. 1994 A perfectly matched layer for the absorption of electromagnetic waves. Phys. Plasmas 114 (2), 185–200.Google Scholar
Bermúdez, A., Hervella-Nieto, L., Prieto, A. & Rodríguez, R. 2010 Perfectly matched layers for time-harmonic second order elliptic problems. Arch. Comput. Meth. Engng 17 (1), 77–107.Google Scholar
Cao, X. Y., Ming, F. R. & Zhang, A. M. 2014 Sloshing in a rectangular tank based on SPH simulation. Appl. Ocean Res. 47 (2), 241–254.Google Scholar
Cheng, H., Zhang, A. M. & Ming, F. R. 2017 Study on coupled dynamics of ship and flooding water based on experimental and SPH methods. Phys. Fluids 29 (10), 107101.Google Scholar
Colagrossi, A., Bouscasse, B., Antuono, M. & Marrone, S. 2012 Particle packing algorithm for SPH schemes. Comput. Phys. Commun. 183 (8), 1641–1653.Google Scholar
Cui, P., Zhang, A. M. & Wang, S. P. 2016 Small-charge underwater explosion bubble experiments under various boundary conditions. Phys. Fluids 28 (11), 117103.Google Scholar
Dobratz, B.1981 LLNL explosive handbook: properties of chemical explosives and explosives simulants. Report UCRL-52997. Lawrence Livermore National Laboratory, Livermore, CA, USA.Google Scholar
Engquist, B. & Majda, A. 1977 Absorbing boundary conditions for the numerical simulation of waves. Proc. Natl Acad. Sci. USA 74 (5), 1765.Google Scholar
Ferrari, A., Fraccarollo, L., Dumbser, M., Toro, E. F. & Armanini, A. 2010 Three-dimensional flow evolution after a dam break. J. Fluid Mech. 663, 456–477.Google Scholar
Gingold, R. A & Monaghan, J. J. 1977 Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181 (3), 375–389.Google Scholar
Givoli, D. 1992 Numerical Methods For Problems in Infinite Domains. Elsevier.Google Scholar
Givoli, D. 1999 Recent advances in the DtN FE method. Arch. Comput. Meth. Engng 6 (2), 71–116.Google Scholar
Gong, K., Liu, H. & Wang, B. L. 2009 Water entry of a wedge based on SPH model with an improved boundary treatment. J. Hydrodyn. 21 (6), 750–757.Google Scholar
Grenier, N., Antuono, M., Colagrossi, A., Le, T. & Alessandrini, B. 2009 An Hamiltonian interface SPH formulation for multi-fluid and free surface flows. J. Comput. Phys. 228 (22), 8380–8393.Google Scholar
Grinstein, F. F. 1994 Open boundary conditions in the simulation of subsonic turbulent shear flows. J. Comput. Phys. 115 (1), 43–55.Google Scholar
Hagstrom, T. 1999 Radiation boundary conditions for the numerical simulation of waves. Acta Numerica 8, 47–106.Google Scholar
Hirschler, M., Kunz, P., Huber, M., Hahn, F. & Nieken, U. 2016 Open boundary conditions for ISPH and their application to micro-flow. J. Comput. Phys. 307, 614–633.Google Scholar
Hou, Q., Kruisbrink, A. C. H., Pearce, F. R., Tijsseling, A. S. & Yue, T. 2014 Smoothed particle hydrodynamics simulations of flow separation at bends. Comput. Fluids 90 (4), 138–146.Google Scholar
Huang, C., Zhang, D. H., Shi, Y. X., Si, Y. L. & Huang, B. 2018 Coupled finite particle method with a modified particle shifting technology. Intl J. Numer. Meth. Engng 113 (2), 179–207.Google Scholar
Kim, J. H. & Shin, H. C. 2008 Application of the ALE technique for underwater explosion analysis of a submarine liquefied oxygen tank. Ocean Engng 35 (8C9), 812–822.Google Scholar
Klaseboer, E., Hung, K. C., Wang, C., Wang, C. W., Khoo, B. C., Boyce, P., Debono, S. & Charlier, H. 2005 Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure. J. Fluid Mech. 537, 387–413.Google Scholar
Kreiss, H. O. 1970 Initial boundary value problems for hyperbolic systems. Commun. Pure Appl. Maths 23 (3), 277–298.Google Scholar
Landrini, M., Colagrossi, A., Greco, M. & Tulin, M. P. 2007 Gridless simulations of splashing processes and near-shore bore propagation. J. Fluid Mech. 591, 183–213.Google Scholar
Lastiwka, M., Basa, M. & Quinlan, N. J. 2010 Permeable and non-reflecting boundary conditions in SPH. Intl J. Numer. Meth. Fluids 61 (7), 709–724.Google Scholar
Lind, S. J., Xu, R., Stansby, P. K. & Rogers, B. D. 2012 Incompressible smoothed particle hydrodynamics for free-surface flows: a generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves. J. Comput. Phys. 231 (4), 1499–1523.Google Scholar
Liu, G. R. & Liu, M. B. 2003 Smoothed Particle Hydrodynamics: A Meshfree Particle Method. World Scientific.Google Scholar
Liu, M. B. & Liu, G. R. 2006 Restoring particle consistency in smoothed particle hydrodynamics. Appl. Numer. Maths 56 (1), 19–36.Google Scholar
Liu, M. B., Liu, G. R., Lam, K. Y. & Zong, Z. 2003 Smoothed particle hydrodynamics for numerical simulation of underwater explosion. Comput. Mech. 30 (2), 106–118.Google Scholar
Liu, W. T., Ming, F. R., Zhang, A. M., Miao, X. H. & Liu, Y. L. 2018 Continuous simulation of the whole process of underwater explosion based on eulerian finite element approach. Appl. Ocean Res. 80, 125–135.Google Scholar
Lubich, C. 2002 Fast Convolution for Nonreflecting Boundary Conditions. Society for Industrial and Applied Mathematics.Google Scholar
Lucy, L. B. 1977 A numerical approach to the testing of the fission hypothesis. Astron. J. 82 (82), 1013–1024.Google Scholar
Marrone, S.2012 Enhanced SPH modeling of free-surface flows with large deformations. PhD thesis, University of Rome.Google Scholar
Marrone, S., Antuono, M., Colagrossi, A., Colicchio, G., Touzé, D. L. & Graziani, G. 2011 𝛿-SPH model for simulating violent impact flows. Comput. Meth. Appl. Mech. Engng 200 (13C16), 1526–1542.Google Scholar
Marrone, S., Colagrossi, A., Antuono, M., Colicchio, G. & Graziani, G. 2013 An accurate SPH modeling of viscous flows around bodies at low and moderate Reynolds numbers. J. Comput. Phys. 245 (1), 456–475.Google Scholar
Ming, F. R., Sun, P. N. & Zhang, A. M. 2017 Numerical investigation of rising bubbles bursting at a free surface through a multiphase SPH model. Meccanica 52, 2665–2684.Google Scholar
Ming, F. R., Zhang, A. M., Cheng, H. & Sun, P. N. 2018 Numerical simulation of a damaged ship cabin flooding in transversal waves with smoothed particle hydrodynamics method. Ocean Engng 165, 336–352.Google Scholar
Ming, F. R., Zhang, A. M., Xue, Y. Z. & Wang, S. P. 2016 Damage characteristics of ship structures subjected to shockwaves of underwater contact explosions. Ocean Engng 117, 359–382.Google Scholar
Molteni, D. & Colagrossi, A. 2009 A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH. Comput. Phys. Commun. 180 (6), 861–872.Google Scholar
Monaghan, J. J. 1988 An introduction to SPH. Comput. Phys. Commun. 48 (1), 89–96.Google Scholar
Monaghan, J. J. 1989 On the problem of penetration in particle methods. J. Comput. Phys. 82 (1), 1–15.Google Scholar
Monaghan, J. J. 1994 Simulating free surface flows with SPH. J. Comput. Phys. 110 (2), 399–406.Google Scholar
Monaghan, J. J. & Gingold, R. A. 1983 Shock simulation by the particle method SPH. J. Comput. Phys. 52 (2), 374–389.Google Scholar
Morris, J. P. 2000 Simulating surface tension with smoothed particle hydrodynamics. Intl J. Numer. Meth. Fluids 33 (3), 333–353.Google Scholar
Morris, J. P., Fox, P. J. & Zhu, Y. 1997 Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys. 136 (1), 214–226.Google Scholar
Okong’O, N. & Bellan, J. 2002 Consistent Boundary Conditions for Multicomponent Real Gas Mixtures Based on Characteristic Waves. Academic Press.Google Scholar
Poinsot, T. J. & Lelef, S. K. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101 (1), 104–129.Google Scholar
Randles, P. W. & Libersky, L. D. 1996 Smoothed particle hydrodynamics: some recent improvements and applications. Comput. Meth. Appl. Mech. Engng 139 (1C4), 375–408.Google Scholar
Steinberg, D. J. 1987 Spherical Explosions and the Equation of State of Water. Military Technology Weaponry and National Defense.Google Scholar
Sun, P. N., Ming, F. R. & Zhang, A. M. 2015 Numerical simulation of interactions between free surface and rigid body using a robust SPH method. Ocean Engng 98, 32–49.Google Scholar
Tafuni, A., Domínguez, J. M., Vacondio, R. & Crespo, A. J. C. 2017 Accurate and efficient SPH open boundary conditions for real 3-D engineering problems. Proc. SPHERIC, 12th Intl Workshop, Munich, Germany, June, pp. 346–354.Google Scholar
Tafuni, A., Domínguez, J. M., Vacondio, R. & Crespo, A. J. C. 2018 A versatile algorithm for the treatment of open boundary conditions in smoothed particle hydrodynamics GPU models. Comput. Meth. Appl. Mech. Engng 342, 604–624.Google Scholar
Tafuni, A., Domínguez, J. M., Vacondio, R., Sahin, I. & Crespo, A. J. C. 2016 Open boundary conditions for large-scale SPH simulations. Proc. SPHERIC, 11th Intl Workshop, Ourense, Spain, June, pp. 204–210.Google Scholar
Tartakovsky, A. M., Meakin, P., Scheibe, T. D. & West, R. M. E. 2007 Simulations of reactive transport and precipitation with smoothed particle hydrodynamics. J. Comput. Phys. 222 (2), 654–672.Google Scholar
Thompson, K. W. 1990 Time dependent boundary conditions for hyperbolic systems. J. Comput. Phys. 89 (2), 439–461.Google Scholar
Ulrich, C., Leonardi, M. & Rung, T. 2013 Multi-physics SPH simulation of complex marine-engineering hydrodynamic problems. Ocean Engng 64 (6), 109–121.Google Scholar
Wang, G. H., Zhang, S. R., Yu, M., Li, H. B. & Kong, Y. 2014 Investigation of the shock wave propagation characteristics and cavitation effects of underwater explosion near boundaries. Appl. Ocean Res. 46 (2), 40–53.Google Scholar
Xie, W. F., Liu, T. G. & Khoo, B. C. 2006 Application of a one-fluid model for large scale homogeneous unsteady cavitation: the modified Schmidt model. Comput. Fluids 35 (10), 1177–1192.Google Scholar
Zamyshlyaev, B. V. & Yakovlev, Y. S. 1973 Dynamic Loads in Underwater Explosion. Naval Intelligence Support Center.Google Scholar
Zhang, A. M., Wu, W. B., Liu, Y. L. & Wang, Q. X. 2017 Nonlinear interaction between underwater explosion bubble and structure based on fully coupled model. Phys. Fluids 29 (8), 082111.Google Scholar
Zhang, A. M., Yang, W. S. & Yao, X. L. 2012 Numerical simulation of underwater contact explosion. Appl. Ocean Res. 34 (1), 10–20.Google Scholar
Zhao, R. & Faltinsen, O. 1993 Water entry of two-dimensional bodies. J. Fluid Mech. 246, 593–612.Google Scholar