Ocean Systems Engineering

  • 제12권1호
  • /
  • Pages.63-86
  • /
  • 2022
  • /
  • 2093-6702(pISSN)
  • /
  • 2093-677X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

An enhanced incompressible SPH method for simulation of fluid flow interactions with saturated/unsaturated porous media of variable porosity

  • Shimizu, Yuma (Department of Civil and Earth Resources Engineering, Kyoto University) ;
  • Khayyer, Abbas (Department of Civil and Earth Resources Engineering, Kyoto University) ;
  • Gotoh, Hitoshi (Department of Civil and Earth Resources Engineering, Kyoto University)
  • 투고 : 2021.11.08
  • 심사 : 2022.02.17
  • 발행 : 2022.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

A refined projection-based purely Lagrangian meshfree method is presented towards reliable numerical analysis of fluid flow interactions with saturated/unsaturated porous media of uniform/spatially-varying porosities. The governing equations are reformulated on the basis of two-phase mixture theory with incorporation of volume fraction. These principal equations of mixture are discretized in the context of Incompressible SPH (Smoothed Particle Hydrodynamics) method. Associated with the consideration of governing equations of mixture, a new term arises in the source term of PPE (Poisson Pressure Equation), resulting in modified source term. The linear and nonlinear force terms are included in momentum equation to represent the resistance from porous media. Volume increase of fluid particles are taken into consideration on account of the presence of porous media, and hence multi-resolution ISPH framework is also incorporated. The stability and accuracy of the proposed method are thoroughly examined by reproducing several numerical examples including the interactions between fluid flow and saturated/unsaturated porous media of uniform/spatially-varying porosities. The method shows continuous pressure field, smooth variations of particle volumes and regular distributions of particles at the interface between fluid and porous media.

키워드

과제정보

The research described in this paper was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI Grants Number JP21K14250, JP21H01433, JP18K04368 and JP18H03796.

참고문헌

  1. Akbari, H. and Namin, M. (2013), "Moving particle method for modeling wave interaction with porous structures", Coast. Eng., 74, 59-73. https://doi.org/10.1016/j.coastaleng.2012.12.002
  2. Akbari, H. (2014), "Modified moving particle method for modeling wave interaction with multi layered porous structures", Coast. Eng., 89, 1-19. https://doi.org/10.1016/j.coastaleng.2014.03.004
  3. Akbari, H. and Taherkhani, A. (2019), "Numerical study of wave interaction with a composite breakwater located on permeable bed", Coast. Eng., 146, 1-13. https://doi.org/10.1016/j.coastaleng.2018.12.006
  4. Akbari, H. and Pooyarad, A. (2020), "Wave force on protected submarine pipelines over porous and impermeable beds using SPH numerical model", Appl. Ocean Res., 98, 102118. https://doi.org/10.1016/j.apor.2020.102118
  5. Bandara, S. and Soga, K. (2015), "Coupling of soil deformation and pore fluid flow using material point method", Comput. Geotech., 63, 199-214. https://doi.org/10.1016/j.compgeo.2014.09.009
  6. Basser, H., Rudman, M. and Daly, E. (2017), "SPH modelling of multi-fluid lock-exchange over and within porous media", Adv. Water Resour., 108, 15-28. https://doi.org/10.1016/j.advwatres.2017.07.011
  7. Bui, H.H. and Nguyen, G.D. (2017), "A coupled fluid-solid SPH approach to modelling flow through deformable porous media", Int. J. Solids Struct., 125, 244-264. https://doi.org/10.1016/j.ijsolstr.2017.06.022
  8. Chorin, A.J. (1968), "Numerical solution of the Navier-Stokes equations", Math. Comp., 22, 745-762. https://doi.org/10.1090/S0025-5718-1968-0242392-2
  9. Chorin, A.J. and Marsden, J.E. (1993), A Mathematical Introduction to Fluid Mechanics, Springer, ISBN: 978-0387979182, 172pp.
  10. Darcy, H. (1856), Les fontaines publiques de la ville de dijon. Victor Dalmont, pp. 647.
  11. Drew, D.A. (1983), "Mathematical modeling of two-phase flows", Annu. Rev. Fluid. Mech., 15, 261-291. https://doi.org/10.1146/annurev.fl.15.010183.001401
  12. Drumheller, D.S. (2000), "On theories for reacting immiscible mixtures", Int. J. Eng. Sci., 8, 347-382. https://doi.org/10.1016/S0020-7225(99)00047-6
  13. Farrokhnejad, M. (2013), Numerical Modeling of Solidification Process and Prediction of Mechanical Properties in Magnesium Alloys, Ph.D. Dissertation, The University of Western Ontario, Electronic Thesis and Dissertation Repository. 1459.
  14. Forchheimer, P. (1901), Wasserbewegung durch Boden. Zeitschrift des Vereins Deutscher Ingenieure 45, 1782-1788.
  15. Fu, L. and Jin, Y. (2018), "Macroscopic particle method for channel flow over porous bed", Eng. Appl. Comput. Fluid Mech., 12(1), 13-27. https://doi.org/10.1080/19942060.2017.1331866
  16. Gingold, R.A. and Monaghan, J.J. (1977), "Smoothed particle hydrodynamics: theory and application to non-spherical stars", Mon. Not. R. Astron. Soc., 181, 375-389. https://doi.org/10.1093/mnras/181.3.375
  17. Gotoh, H., Shibahara, T. and Sakai, T. (2001), "Sub-Particle-Scale turbulence model for the MPS method-Lagrangian flow model for hydraulic engineering", Comput. Fluid Dyn. J., 9(4), 339-347.
  18. Gotoh, H. and Khayyer, A. (2018), "On the state-of-the-art of particle methods for coastal and ocean engineering", Coast. Eng., 60(1), 79-103. https://doi.org/10.1080/21664250.2018.1436243
  19. Gotoh, H. (2018), Ryushiho, Morikita Shuppan, ISBN-10: 4627922310. (in Japanese)
  20. Gotoh, H., Khayyer, A. and Shimizu, Y. (2021), "Entirely Lagrangian meshfree computational methods for hydroelastic fluid-structure interactions in ocean engineering-Reliability, adaptivity and generality", Appl. Ocean Res., 115, 102822. https://doi.org/10.1016/j.apor.2021.102822
  21. Gotoh, H. (2022), Nagare no houteishiki, Morikita Shuppan, ISBN-10: 4627676719. (in Japanese)
  22. Gui, Q., Dong, P., Shao, S. and Chen, Y. (2015), "Incompressible SPH simulation of wave interaction with porous structure", Ocean Eng., 110, 126-139. https://doi.org/10.1016/j.oceaneng.2015.10.013
  23. Harada, E, Ikari, H, Khayyer, A. and Gotoh, H. (2019), "Numerical simulation for swash morphodynamics by DEM-MPS coupling model", Coast. Eng., 61(1), 2-14. https://doi.org/10.1080/21664250.2018.1554203
  24. Harada, E., Ikari, H, Tazaki, T. and Gotoh, H. (2021), "Numerical simulation for coastal morphodynamics using DEM-MPS method", Appl. Ocean Res., 117, 102905. https://doi.org/10.1016/j.apor.2021.102905
  25. Ikari, H., Yamano, T. and Gotoh, H. (2020), "Multiphase particle method using an elastoplastic solid phase model for the diffusion of dumped sand from a split hopper", Comp. Fluid., 208, 104639. https://doi.org/10.1016/j.compfluid.2020.104639
  26. Kazemi, E., Tait, S. and Shao, S. (2019), "SPH-based numerical treatment of the interfacial interaction of flow with porous media", Int. J. Numer. Meth. Fl., 92, 219-245. https://doi.org/10.1002/fld.4781
  27. Kazemi, E., Koll, K., Tait, S. and Shao, S. (2020), "SPH modelling of turbulent open channel flow over and within natural gravel beds with rough interfacial boundaries", Adv. Water Res., 140, 103557. https://doi.org/10.1016/j.advwatres.2020.103557
  28. Khayyer, A. and Gotoh, H. (2009), "Modified moving particle semi-implicit methods for the prediction of 2D wave impact pressure", Coast. Eng., 56, 419-440. https://doi.org/10.1016/j.coastaleng.2008.10.004
  29. Khayyer, A. and Gotoh, H. (2010), "A Higher order Laplacian model for enhancement and stabilization of pressure calculation by the MPS method", Appl. Ocean Res., 32(1), 124-131. https://doi.org/10.1016/j.apor.2010.01.001
  30. Khayyer, A. and Gotoh, H. (2011), "Enhancement of stability and accuracy of the moving particle semi-implicit method", J. Comput. Phys., 230, 3093-3118. https://doi.org/10.1016/j.jcp.2011.01.009
  31. Khayyer, A., Gotoh, H., Falahaty, H, Shimizu, Y. and Nishijima, K. (2017a), "Towards development of a reliable fully-Lagrangian MPS-based FSI solver for simulation of 2D hydroelastic slamming", Ocean Syst. Eng., 7(3), 299-318. https://doi.org/10.12989/ose.2017.7.3.299
  32. Khayyer, A., Gotoh, H., Shimizu, Y., Gotoh, K. and Shao, S. (2017b), "An enhanced particle method for simulation of fluid flow interactions with saturated porous media", J. Japan Soc. Civil Engineers, Ser. B2 (coastal Engineering). 73, I_841-I_846. https://doi.org/10.2208/kaigan.73.I_841
  33. Khayyer, A., Gotoh, H. and Shimizu, Y. (2017c), "Comparative study on accuracy and conservation properties of two particle regularization schemes and proposal of an optimized particle shifting scheme in ISPH context", J. Comput. Phys., 332, 236-256. https://doi.org/10.1016/j.jcp.2016.12.005
  34. Khayyer, A., Gotoh, H., Shimizu, Y., Gotoh, K., Falahaty, H. and Shao, S. (2018a), "Development of a projection-based SPH method for numerical wave flume with porous media of variable porosity", Coast. Eng., 140, 1-22. https://doi.org/10.1016/j.coastaleng.2018.05.003
  35. Khayyer, A., Gotoh, H., Falahaty, H. and Shimizu, Y. (2018b), "An enhanced ISPH-SPH coupled method for simulation of incompressible fluid-elastic structure interactions", Comput. Phys. Commun., 232, 139-164. https://doi.org/10.1016/j.cpc.2018.05.012
  36. Khayyer, A., Tsuruta, N., Shimizu, Y. and Gotoh, H. (2019a), "Multi-resolution MPS for incompressible fluid-elastic structure interactions in ocean engineering", Appl. Ocean Res., 82, 397-414. https://doi.org/10.1016/j.apor.2018.10.020
  37. Khayyer, A., Gotoh, H. and Shimizu, Y. (2019b), "A projection-based particle method with optimized particle shifting for multiphase flows with large density ratios and discontinuous density fields", Comp. Fluid., 179, 356-371. https://doi.org/10.1016/j.compfluid.2018.10.018
  38. Khayyer, A., Shimizu, Y., Gotoh, H. and Hattori, S. (2021a), "Multi-resolution ISPH-SPH for accurate and efficient simulation of hydroelastic fluid-structure interactions in ocean engineering", Ocean Eng., 226, 108652. https://doi.org/10.1016/j.oceaneng.2021.108652
  39. Khayyer, A., Gotoh, H., Shimizu, Y. and Nishijima, Y. (2021b), "A 3D Lagrangian meshfree projection-based solver for hydroelastic Fluid-Structure Interactions", J. Fluid. Struct., 105, 103342. https://doi.org/10.1016/j.jfluidstructs.2021.103342
  40. Khayyer, A., Shimizu, Y., Gotoh, H. and Nagashima, K. (2021c), "A coupled incompressible SPH-Hamiltonian SPH solver for hydroelastic FSI corresponding to composite structures", Appl. Math. Model., 94, 242-271. https://doi.org/10.1016/j.apm.2021.01.011
  41. Kim, K.S. and Kim, M.H. (2018), "Simulation of viscous and inviscid rayleigh-taylor instability with surface tension by using MPS", Ocean Syst. Eng., 8(2), 167-182. https://doi.org/10.12989/OSE.2018.8.2.167
  42. Koshizuka, S. and Oka, Y. (1996), "Moving particle semi-implicit method for fragmentation of incompressible fluid", Nucl. Sci. Eng., 123, 421-434. https://doi.org/10.13182/nse96-a24205
  43. Larese, A., Rossi, R. and Onate, E. (2012), "A coupled PFEM-Eulerian approach for the solution of porous FSI problems", Comput. Mech., 50, 805-819. https://doi.org/10.1007/s00466-012-0768-9
  44. Larese, A., Rossi, R. and Onate, E. (2015), "Finite element modeling of free surface ow in variable porosity media", Arch. Comput. Method. Eng., 22(4), 637-653. https://doi.org/10.1007/s11831-014-9140-x
  45. Luo, M., Khayyer, A. and Lin, P. (2021), "Particle methods in ocean and coastal engineering", Appl. Ocean Res., 114, 102734. https://doi.org/10.1016/j.apor.2021.102734
  46. Liu, P.L.F., Lin, P., Chang, K.A. and Sakakiyama, T. (1999), "Numerical modeling of wave interaction with porous structures", J. Waterw. Port Coast. Ocean Eng., 125(6), 322-330. https://doi.org/10.1061/(ASCE)0733-950X(1999)125:6(322)
  47. Losada, I.J., Lara, J.L. and Jesus, M.D. (2016), "Modeling the interaction of water waves with porous coastal structures", J. Waterw. Port, Coastal, Ocean Eng., 142(6), 03116003. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000361
  48. Lucy, L.B. (1977), "A numerical approach to the testing of fission hypothesis", Astron. J., 82, 1013-1024. https://doi.org/10.1086/112164
  49. Matsunaga, T. and Koshizuka, S. (2022), "Stabilized LSMPS method for complex free-surface flow simulation", Comp. Meth. Appl. Mech. Eng., 389(1), 114416. https://doi.org/10.1016/j.cma.2021.114416
  50. Monaghan, J.J. (1992), "Smoothed particle hydrodynamics", Ann. Rev. Astron. Astrophys., 30, 543-574. https://doi.org/10.1146/annurev.aa.30.090192.002551
  51. Moran, R. (2013), Mejora de la seguridad de las presas de escollera frente a percolacion accidental mediante protecciones tipo rapie. PhD Thesis: Universidad Politecnica de Madrid, Madrid, Spain.
  52. Nguyen, H.X., Dinh, V.N. and Basu, B. (2021), "A comparison of smoothed particle hydrodynamics simulation with exact results from a nonlinear water wave model", Ocean Syst. Eng., 11(2), 185-201.
  53. Ni, J. and Beckermann, C. (1991), "A volume-averaged two-phase model for transport phenomena during solidification", Metall. Trans. B 22B, 349-361.
  54. Pahar, G. and Dhar, A. (2016), "Modeling free-surface flow in porous media with modified incompressible SPH", Eng. Anal. Bound. Elem., 68, 75-85. https://doi.org/10.1016/j.enganabound.2016.04.001
  55. Pahar, G. and Dhar, A. (2017), "On modification of pressure gradient operator in integrated ISPH for multifluid and porous media flow with free-surface", Eng. Anal. Bound. Elem., 80, 38-48. https://doi.org/10.1016/j.enganabound.2017.02.015
  56. Peng, C., Xu, G., Wu, W., Yu, H.S. and Wang, C. (2017), "Multiphase SPH modeling of free surface flow in porous media with variable porosity", Comput. Geotech., 81, 239-248. https://doi.org/10.1016/j.compgeo.2016.08.022
  57. Pitman, B. and Le, L. (2005), "A two-fluid model for avalanche and debris flows", Philos. T. R. Soc. A, 363, 1573-1601. https://doi.org/10.1098/rsta.2005.1596
  58. Ren, B., Wen, H., Dong, P. and Wang, Y. (2014), "Numerical simulation of wave interaction with porous structures using an improved smoothed particle hydrodynamic method", Coast. Eng., 88, 88-100. https://doi.org/10.1016/j.coastaleng.2014.02.006
  59. Ren, B., Wen, H., Dong, P. and Wang, Y. (2016), "Improved SPH simulation of wave motions and turbulent flows through porous media", Coast. Eng., 107, 14-27. https://doi.org/10.1016/j.coastaleng.2015.10.004
  60. Shao, S. and Lo, E.Y.M. (2003), "Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface", Adv. Water Resour., 26, 787-800. https://doi.org/10.1016/S0309-1708(03)00030-7
  61. Shao, S. (2010), "Incompressible SPH flow model for wave interactions with porous media", Coast. Eng., 57(3), 304-316. https://doi.org/10.1016/j.coastaleng.2009.10.012
  62. Shimizu, Y. and Gotoh, H. (2016), "Toward enhancement of MPS method for ocean engineering: Effect of time-integration schemes", Int. J. Offshore Polar Eng., 26(4), 378-384. https://doi.org/10.17736/ijope.2016.mk46
  63. Shimizu, Y., Gotoh, H. and Khayyer, A. (2018), "An MPS-based particle method for simulation of multiphase flows characterized by high density ratios by incorporation of space potential particle concept", Comp. Math. Appl., 76, 1108-1129. https://doi.org/10.1016/j.camwa.2018.06.002
  64. Shimizu, Y., Khayyer, A., Gotoh, H. and Nagashima, K. (2020), "An enhanced multiphase ISPH-based method for accurate modeling of oil spill", Coast. Eng. J., 62(4), 625-646. https://doi.org/10.1080/21664250.2020.1815362
  65. Shimizu, Y., Khayyer, A. and Gotoh, H. (2021), "An SPH-based fully-Lagrangian meshfree implicit FSI solver with high-order discretization terms", Eng. Anal. Bound. Elem. (accepted)
  66. Sun, P.N., Colagrossi, A., Marrone, S., Antuono, M. and Zhang, A.M. (2019), "A consistent approach to particle shifting in the δ-Plus-SPH model", Comp. Meth. Appl. Mech. Eng., 348, 912-934. https://doi.org/10.1016/j.cma.2019.01.045
  67. Tazaki, T., Harada, E. and Gotoh, H. (2021), "Vertical sorting process in oscillating water tank using DEM-MPS coupling model", Coast. Eng., 165, 103765. https://doi.org/10.1016/j.coastaleng.2020.103765
  68. Tsurudome, C., Liang, D., Shimizu, Y., Khayyer, A. and Gotoh, H. (2020), "Incompressible SPH simulation of solitary wave propagation on permeable beaches", J. Hydrodyn., 32, 664-671. https://doi.org/10.1007/s42241-020-0042-0
  69. Tsurudome, C., Liang, D., Shimizu, Y., Khayyer, A. and Gotoh, H. (2021), "Study of beach permeability's influence on solitary wave runup with ISPH method", Appl. Ocean Res., 117.
  70. Tsuruta, N., Khayyer, A. and Gotoh, H. (2013), "A short note on dynamic stabilization of moving particle semi-implicit method", Comp. Fluid., 82, 158-164. https://doi.org/10.1016/j.compfluid.2013.05.001
  71. Tsuruta, N., Gotoh, H., Suzuki, K., Ikari, H. and Shimosako, K. (2019), "Development of PARISPHERE as the particle-based numerical wave flume for coastal engineering problems", Coast. Eng., 61(1), 41-62. https://doi.org/10.1080/21664250.2018.1560683
  72. Vacondio, R., Altomare, C., De Leffe, M., Hu, X.Y., Le Touze, D., Lind, S., Maronglu, J.C., Marrone, S., Rogers, B.D. and Souto-Iglesias, A. (2021), "Grand challenges for Smoothed Particle Hydrodynamics numerical schemes", Comp. Part. Mech., 8, 575-588. https://doi.org/10.1007/s40571-020-00354-1
  73. Wendland, H. (1995), "Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree", Adv. Comp. Math., 4, 389-396. https://doi.org/10.1007/BF02123482
  74. Wen, H., Ren, B. and Wang, G. (2018), "3D SPH porous flow model for wave interaction with permeable structures", Appl. Ocean Res., 75, 223-233. https://doi.org/10.1016/j.apor.2018.04.003
  75. Wen, H., Ren, B., Dong, P. and Zhu, G. (2020a), "Numerical analysis of wave-induced current within the inhomogeneous coral reef using a refined SPH model", Coast. Eng., 156, 103616. https://doi.org/10.1016/j.coastaleng.2019.103616
  76. Wen, H., Ren, B., Zhu, G. and Wang, G. (2020b), "SPH evaluation of the hydrodynamic consequences induced by reef degradation", Wave Motion, 96, 102579. https://doi.org/10.1016/j.wavemoti.2020.102579