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A sharp-interface immersed smoothed point interpolation method with improved mass conservation for fluid-structure interaction problems

  • Special Column on the 3rd Symposium on Computational Marine Hydrodynamics (Guest Editor De-Cheng Wan)
  • Published:
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Abstract

To solve the problem of inaccurate boundary identification and to eliminate the spurious pressure oscillation in the previously developed immersed smoothed point interpolation method (IS-PIM), a new sharp-interface IS-PIM combining mass conservation algorithm, called Sharp-ISPIM-Mass, is proposed in this work. Based on the so called sharp-interface method, the technique of quadratic local velocity reconstruction has been developed by combining with the mass conservation algorithm, which enables the present method improve the accuracy of the velocity field and satisfy the mass conservation condition near the boundary field. So the proposed method would not encounter the problem of spurious mass flux. In addition, a new form of FSI force evaluation considering pressure and viscous force to perform a whole function from the fluid domain to fictitious fluid domain is introduced, which makes the present method obtain more accurate results of FSI force than the original one. Through the numerical studies of a number of benchmark examples, the performance of the Sharp-ISPIM-Mass has been examined and illustrated.

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References

  1. Wang S., Zhang G., Zhang Z. et al. An immersed smoothed point interpolation method (IS-PIM) for fluid-structure interaction problems [J]. International Journal for Numerical Methods in Fluids, 2017, 85(4): 213–234.

    Article  MathSciNet  Google Scholar 

  2. Sun P., Ming F., Zhang A. et al. Numerical simulation of interactions between free surface and rigid body using a robust SPH method [J]. Ocean Engineering, 2015, 98: 32–49.

    Article  Google Scholar 

  3. Zhang A. M., Ren S. F., Li Q. et al. 3D numerical simulation on fluid-structure interaction of structure subjected to underwater explosion with cavitation [J]. Applied Mathematics and Mechanics (Engilsh Edition), 2012, 33(9): 1191–1206.

    Article  MathSciNet  Google Scholar 

  4. Yeganeh A., Gotoh H., Sakai T. Applicability of Euler-Lagrange coupling multiphase-flow model to bed-load transport under high bottom shear [J]. Journal of Hydraulic Research, 2000, 38(5): 389–398.

    Article  Google Scholar 

  5. Erzincanli B., Sahin M. An arbitrary Lagrangian-Eulerian formulation for solving moving boundary problems with large displacements and rotations [J]. Journal of Computational Physics, 2013, 255(24): 660–679.

    Article  MathSciNet  MATH  Google Scholar 

  6. Yao J., Liu G. N., Narmoneva D. A. et al. Immersed smoothed finite element method for fluid-structure interaction simulation of aortic valves [J]. Computational Mechanics, 2012, 50(6): 789–804.

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhang A. M., Sun P. N., Ming F. R. et al. Smoothed particle hydrodynamics and its applications in fluid-structure interactions [J]. Jounal of Hydrodynamics, 2017, 29(2): 187–216.

    Article  Google Scholar 

  8. Liu M. B., Zhang Z. L. Smoothed particle hydrodynamics (SPH) for modeling fluid-structure interactions [J]. Science China Physics, Mechanics and Astronomy, 2019, 62(8): 5–42.

    Article  MathSciNet  Google Scholar 

  9. Liu M., Shao S., Chang J. On the treatment of solid boundary in smoothed particle hydrodynamics [J]. Science China Technological Sciences, 2012, 55(1): 244–254.

    Article  MATH  Google Scholar 

  10. Zhang A., Ming F., Cao X. Total Lagrangian particle method for the large-deformation analyses of solids and curved shells [J]. Acta Mechanica, 2014, 225(1): 253–275.

    Article  MathSciNet  MATH  Google Scholar 

  11. Peskin C. S. Flow patterns around heart valves: A numerical method [J]. Journal of Computational Physics, 1972, 10(2): 252–271.

    Article  MathSciNet  MATH  Google Scholar 

  12. Uhlmann M. An immersed boundary method with direct forcing for the simulation of particulate flows [J]. Journal of Computational Physics, 2005, 209(2): 448–476.

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhang Z. Q., Liu G. R., Khoo B. C. Immersed smoothed finite element method for two dimensional fluid-structure interaction problems [J]. International Journal for Numerical Methods in Engineering, 2012, 90(10): 1292–1320.

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang L., Gerstenberger A., Wang X. et al. Immersed finite element method [J]. Computer Methods in Applied Mechanics and Engineering, 2016, 193(21–22): 2051–2067.

    MathSciNet  MATH  Google Scholar 

  15. Zhang G., Wang S., Lu H. et al. Coupling immersed method with node-based partly smoothed point interpolation method (NPS-PIM) for large-displacement fluid-structure interaction problems [J]. Ocean Engineering, 2018, 157: 180–201.

    Article  Google Scholar 

  16. Liu G. R., Zhang G. Y. Smoothed point interpolation methods: G space theory and weakened weak forms [M]. Singapore: World Scientific, 2013.

    Book  MATH  Google Scholar 

  17. Liu G. R., Zhang G. Y. A novel scheme of strain-constructed point interpolation method for static and dynamic mechanics problems [J]. International Journal of Applied Mechanics, 2009, 1(1): 233–258.

    Article  Google Scholar 

  18. Tang Q., Zhang G. Y., Liu G. R. A three-dimensional adaptive analysis using the meshfree node-based smoothed point interpolation method (NS-PIM) [J]. Engineering Analysis with Boundary Elements, 2011, 35(10): 1123–1135.

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhang G., Lu H., Yu D. et al. A node-based partly smoothed point interpolation method (NPS-PIM) for dynamic analysis of solids [J]. Engineering analysis with boundary elements, 2018, 87: 165–172.

    Article  MathSciNet  MATH  Google Scholar 

  20. Zhang G. Y., Li Y., Gao X. X. et al. Smoothed point interpolation method for elastoplastic analysis [J]. International Journal of Computational Methods, 2015, 12(4): 1540013-.

    Article  MathSciNet  MATH  Google Scholar 

  21. Massarotti N., Nithiarasu P., Zienkiewicz O. C. Characteristic-based-split (CBS) algorithm for incompressible flow problems with heat transfer [J]. International Journal of Numerical Methods for Heat and Fluid Flow, 1998, 8(8): 969–990.

    Article  MATH  Google Scholar 

  22. Hashemi M. Y., Zamzamian K. A multidimensional characteristic-based method for making incompressible flow calculations on unstructured grids [J]. Journal of Computational and Applied Mathematics, 2014, 259: 752–759.

    Article  MathSciNet  MATH  Google Scholar 

  23. Xiao H. Z., Jie O., Lin Z. The characteristic-based split (CBS) meshfree method for free surface flow problems in ALE formulation [J]. International Journal for Numerical Methods in Fluids, 2011, 65(7): 798–811.

    Article  MathSciNet  MATH  Google Scholar 

  24. Jiang C., Yao J. B., Zhang Z. Q. et al. A sharp-interface immersed smoothed finite element method for interactions between incompressible flows and large deformation solids [J]. Computer Methods in Applied Mechanics and Engineering, 2018, 340: 24–53.

    Article  MathSciNet  MATH  Google Scholar 

  25. Roma A. M., Peskin C. S., Berger M. J. An adaptive version of the immersed boundary method [J]. Journal of Computational Physics, 1999, 153(2): 509–534.

    Article  MathSciNet  MATH  Google Scholar 

  26. Gilmanov A., Sotiropoulos F. A hybrid Cartesian/immersed boundary method for simulating flows with 3D geometrically complex moving bodies [J]. Journal of Computational Physics, 2005, 207(2): 457–492.

    Article  MATH  Google Scholar 

  27. Tseng Y. H., Ferziger J. H. A ghost-cell immersed boundary method for flow in complex geometry [J]. Journal of Computational Physics, 2003, 192(2): 593–623.

    Article  MathSciNet  MATH  Google Scholar 

  28. Luo H. Immersed boundary method [J]. Annual Review of Fluid Mechanics, 2010, 14(37): 239–261.

    Google Scholar 

  29. Sotiropoulos F., Yang X. Immersed boundary methods for simulating fluid-structure interaction [J]. Progress in Aerospace Sciences, 2014, 65(5): 1–21.

    Article  Google Scholar 

  30. Kamakoti R., Wei S. Evaluation of geometric conservation law using pressure-based fluid solver and moving grid technique [J]. International Journal of Numerical Methods for Heat and Fluid Flow, 2004, 14(7): 851–865.

    Article  MATH  Google Scholar 

  31. Seo J. H., Mittal R. A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations [J]. Journal of Computational Physics, 2011, 230(19): 7347–7363.

    Article  MathSciNet  MATH  Google Scholar 

  32. Udaykumar H. S., Mittal R., Rampunggoon P. et al. A sharp interface cartesian grid method for simulating flows with complex moving boundaries [J]. Journal of Computational Physics, 2001, 174(1): 345–380.

    Article  MATH  Google Scholar 

  33. Wang S., Cai Y., Zhang G. et al., A coupled immersed boundary-lattice Boltzmann method with smoothed point interpolation method for fluid-structure interaction problems [J]. International Journal for Numerical Methods in Fluids, 2018, 88(8): 363–384.

    Article  MathSciNet  Google Scholar 

  34. Wendt J., Bourzutschky M., Mallinckrodt A. J. et. al. Computational fluid dynamics: An introduction [J]. Computers in Physics, 1992, 7(5): 542–542.

    Article  Google Scholar 

  35. Balaras E. Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddy simulations [J]. Computers and Fluids, 2004, 33(3): 375–404.

    Article  MATH  Google Scholar 

  36. Mittal R., Dong H., Bozkurttas M. et al. A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries [J]. Journal of Computational Physics, 2008, 227(10): 4825–4852.

    Article  MathSciNet  MATH  Google Scholar 

  37. Riahi H., Meldi M., Favier J. et al. A pressure-corrected immersed boundary method for the numerical simulation of compressible flows [J]. Journal of Computational Physics, 2018, 374: 361–383.

    Article  MathSciNet  MATH  Google Scholar 

  38. Kumar M., Roy S. A sharp interface immersed boundary method for moving geometries with mass conservation and smooth pressure variation [J]. Computers and Fluids, 2016, 137: 15–35

    Article  MathSciNet  MATH  Google Scholar 

  39. Kim J., Kim D., Choi H. An immersed-boundary finite-volume method for simulations of flow in complex geometries [J]. Journal of Computational Physics, 2001, 171(1): 132–150.

    Article  MathSciNet  MATH  Google Scholar 

  40. Zhang Z. Q., Liu G. R., Khoo B. C. A three dimensional immersed smoothed finite element method (3D IS-FEM) for fluid-structure interaction problems [J]. Computational Mechanics, 2012, 51(2): 129–150.

    Article  MathSciNet  MATH  Google Scholar 

  41. Dunne T. An Eulerian approach to fluid-structure interaction and goal-oriented mesh adaptation [J]. International Journal for Numerical Methods in Fluids, 2010, 51(9–10): 1017–1039.

    MathSciNet  MATH  Google Scholar 

  42. Zhao H., Freund J. B., Moser R. D. A fixed-mesh method for incompressible flow-structure systems with finite solid deformations [J]. Journal of Computational Physics, 2008, 227(6): 3114–3140.

    Article  MathSciNet  MATH  Google Scholar 

  43. Russell D., Wang Z. J. A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow [J]. Journal of Computational Physics, 2003, 191(1): 177–205.

    Article  MathSciNet  MATH  Google Scholar 

  44. Calhoun D. A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions [J]. Journal of Computational Physics, 2002, 176(2): 231–275.

    Article  MathSciNet  MATH  Google Scholar 

  45. Tucker P. G., Pan Z. A Cartesian cut cell method for incompressible viscous flow [J]. Applied Mathematical Modelling, 2000, 24(8): 591–606.

    Article  MATH  Google Scholar 

  46. Dennis S. C. R., Chang G. Z. Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100 [J]. Journal of Fluid Mechanics, 1970, 42: 471–489.

    Article  MATH  Google Scholar 

  47. Fornberg B. A numerical study of steady viscous flow past a circular [J]. Journal of Fluid Mechanics, 1980, 98: 819–855.

    Article  MATH  Google Scholar 

  48. Coutanceau M., Bouard R. Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation: 1. Steady flow. [J]. Journal of Fluid Mechanics, 1977, 79: 231–256.

    Article  Google Scholar 

  49. Glowinski R., Pan T. W., Hesla T. I. et al. A distributed Lagrange multiplier/fictitious domain method for flows around moving rigid bodies: Application to particulate flow [J]. International Journal for Numerical Methods in Fluids, 1999, 30(8): 1043–1066.

    Article  MATH  Google Scholar 

  50. Leal L. G. Bubbles, drops and particles [J]. International Journal of Multiphase Flow, 1979, 5(3): 229–230.

    Article  Google Scholar 

  51. Turek S., Hron J. Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow [R]. Lecture Notes in Computational Science and Engineering, Fluid-Structure Interaction: Modelling, Simulation, Optimisation, 2006, 371–385.

  52. Heil M., Hazel A. L., Boyle J. Solvers for large-displacement fluid-structure interaction problems: Segregated versus monolithic approaches [J]. Computational Mechanics, 2008, 43(1): 91–101.

    Article  MATH  Google Scholar 

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Acknowledgements

This work was supported by the High-technology ship research project of Ministry of Industry and Information Technology of China (Grant No. 2017-614), the Joint Found for Equipment Pre Research and China Shipbuilding Industry Corporation (Grant No. 614B042802-28), the Fundamental Research Funds for the Central Universities (Grant No. DUT2017TB05), the China Postdoctoral Science Foundation (Grant No. 2018M641693), the Liaoning Revitalization Talents Program (Grant No. XLYC1908027), the Science Foundation of Hunan Province (Grant No. 2019JJ50790) and the computation support of the Supercomputing Center of Dalian University of Technology.

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, School of Naval Architecture, Dalian University of Technology, Dalian, 116023, China

    Bo-qian Yan, Gui-yong Zhang, Qi-hang Xiao & Zhe Sun

  2. Department of Fisheries and Oceans, Bedford Institute of Oceanography, Dartmouth, Canada

    Shuangqiang Wang

  3. Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai, 200240, China

    Gui-yong Zhang

  4. Key Laboratory of Traffic Safety on Track of Ministry of Education, School of Traffic and Transportation Engineering, Central South University, Changsha, 410076, China

    Chen Jiang

  5. Joint International Research Laboratory of Key Technology for Rail Traffic Safety, Central South University, Changsha, 410076, China

    Chen Jiang

  6. National and Local Joint Engineering Research Center of Safety Technology for Rail Vehicle, Central South University, Changsha, 410076, China

    Chen Jiang

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  1. Bo-qian Yan
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  2. Shuangqiang Wang
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  3. Gui-yong Zhang
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  4. Chen Jiang
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  5. Qi-hang Xiao
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  6. Zhe Sun
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Correspondence to Gui-yong Zhang.

Additional information

Project supported by the National Natural Science Foundation of China (Grant Nos. 51639003, 51809035).

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Yan, Bq., Wang, S., Zhang, Gy. et al. A sharp-interface immersed smoothed point interpolation method with improved mass conservation for fluid-structure interaction problems. J Hydrodyn 32, 267–285 (2020). https://doi.org/10.1007/s42241-020-0025-1

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  • DOI: https://doi.org/10.1007/s42241-020-0025-1

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