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Adaptive mesh refinement immersed boundary method for simulations of laminar flows past a moving thin elastic structure

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Abstract

One of the critical issues in numerical simulation of fluid-structure interaction problems is inaccuracy of the solutions, especially for flows past a stationary thin elastic structure where large deformations occur. High resolution is required to capture the flow characteristics near the fluid-structure interface to enhance accuracy of the solutions within proximity of the thin deformable body. Hence, in this work, an algorithm is developed to simulate fluid-structure interactions of moving deformable structures with very thin thicknesses. In this algorithm, adaptive mesh refinement (AMR) is integrated with immersed boundary finite element method (IBFEM) with two-stage pressure-velocity corrections. Despite successive interpolation of the flow field by IBM, the governing equations were solved using a fixed structured mesh, which significantly reduces the computational time associated with mesh reconstruction. The cut-cell IBM is used to predict the body forces while FEM is used to predict deformation of the thin elastic structure in order to integrate the motions of the fluid and solid at the interface. AMR is used to discretize the governing equations and obtain solutions that efficiently capture the thin boundary layer at the fluid-solid interface. The AMR-IBFEM algorithm is first verified by comparing the drag coefficient, lift coefficient, and Strouhal number for a benchmark case (laminar flow past a circular cylinder at Re = 100) and the results showed good agreement with those of other researchers. The algorithm is then used to simulate 2-D laminar flows past stationary and moving thin structures positioned perpendicular to the freestream direction. The results also showed good agreement with those obtained from the arbitrary Lagrangian-Eulerian (ALE) algorithm for elastic thin boundaries. It is concluded that the AMR-IBFEM algorithm is capable of predicting the characteristics of laminar flow past an elastic structure with acceptable accuracy (error of ∼0.02%) with only ∼1% of the computational time for simulations with full mesh refinement.

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References

  1. Diniz dos Santos N., Gerbeau J. F., Bourgat J. F. A partitioned fluid-structure algorithm for elastic thin valves with contact [J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(19–20): 1750–1761.

    Article  MathSciNet  MATH  Google Scholar 

  2. Zhou K., Liu J. K., Chen W. S. Numerical and experimental studies of hydrodynamics of flapping foils [J]. Journal of Hydrodynamics, 2018, 30(2): 258–266.

    Article  Google Scholar 

  3. Peskin C. S. Numerical analysis of blood flow in the heart. [J]. Journal of Computational Physics, 1977, 25(3): 220–252.

    Article  MathSciNet  MATH  Google Scholar 

  4. 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 

  5. McQueen D. M., Peskin C. S. A three-dimensional computational method for blood flow in the heart. II. contractile fibers [J]. Journal of Computational Physics, 1989, 82(2): 289–297.

    Article  MATH  Google Scholar 

  6. Lee J., Lee S. Fluid-structure interaction analysis on a flexible plate normal to a free stream at low Reynolds numbers [J]. Journal of Fluids and Structures, 2012, 29: 18–34.

    Article  Google Scholar 

  7. Mittal R., Iaccarino G. Immersed boundary methods [J]. Annual Review of Fluid Mechanics, 2005, 37: 239–261.

    Article  MathSciNet  MATH  Google Scholar 

  8. Mori Y., Peskin C. S. Implicit second-order immersed boundary methods with boundary mass [J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(25–28): 2049–2067.

    Article  MathSciNet  MATH  Google Scholar 

  9. 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 

  10. Su S. W., Lai M. C., Lin C. A. An immersed boundary technique for simulating complex flows with rigid boundary [J]. Computers and Fluids, 2007, 36(2): 313–324.

    Article  MATH  Google Scholar 

  11. Angot P., Bruneau C. H., Fabrie P. A penalization method to take into account obstacles in incompressible viscous flows [J]. Numerische Mathematik, 1999, 81(4): 497–520.

    Article  MathSciNet  MATH  Google Scholar 

  12. Kevlahan N. K. R., Ghidaglia J. M. Computation of turbulent flow past an array of cylinders using a spectral method with Brinkman penalization [J]. European Journal of Mechanics-B/Fluids, 2001, 20(3): 333–350.

    Article  MATH  Google Scholar 

  13. Miao S., Hendrickson K., Liu Y. Computation of three-dimensional multiphase flow dynamics by fully-coupled immersed flow (FCIF) solver [J]. Journal of Computational Physics, 2017, 350: 97–116.

    Article  MathSciNet  MATH  Google Scholar 

  14. 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 

  15. Ye T., Mittal R., Udaykumar H. S. et al. An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries [J]. Journal of Computational Physics, 1999 156(2): 209–240.

    Article  MathSciNet  MATH  Google Scholar 

  16. Kirkpatrick M. P., Armfield S. W., Kent J. H. A representation of curved boundaries for the solution of the Navier-Stokes equations on a staggered three-dimensional Cartesian grid [J]. Journal of Computational Physics, 2003, 184(1): 1–36.

    Article  MATH  Google Scholar 

  17. Kajishima T., Takiguchi S., Hamasaki H. et al. Turbulence structure of particle-laden flow in a vertical plane channel due to vortex shedding [J]. International Journal Series B Fluids and Thermal Engineering, 2001, 44(4): 526–535.

    Article  Google Scholar 

  18. Breugem W. P. A second-order accurate immersed boundary method for fully resolved simulations of particle-laden flows [J]. Journal of Computational Physics, 2012, 231(13): 4469–4498.

    Article  MathSciNet  MATH  Google Scholar 

  19. Di S., Ge W. Simulation of dynamic fluid-solid interactions with an improved direct-forcing immersed boundary method [J]. Particuology, 2015, 18: 22–34.

    Article  Google Scholar 

  20. Kempe T., Frohlich J. An improved immersed boundary method with direct forcing for the simulation of particle laden flows [J]. Journal of Computational Physics, 2012, 231(9): 3663–3684.

    Article  MathSciNet  MATH  Google Scholar 

  21. Yang J. Sharp interface direct forcing immersed boundary methods: A summary of some algorithms and applications [J]. Journal of Hydrodynamics, 2016, 28(5): 713–730.

    Article  Google Scholar 

  22. Kajishima T., Takeuchi S. Simulation of fluid-structure interaction based on an immersed-solid method [J]. Journal of Mechanical Engineering and Sciences, 2013, 5: 555–561.

    Article  Google Scholar 

  23. Cheny Y., Botella O. The LS-STAG method: A new immersed boundary/level-set method for the computation of incompressible viscous flows in complex moving geometries with good conservation properties [J]. Journal of Computational Physics, 2010, 229(4): 1043–1076.

    Article  MathSciNet  MATH  Google Scholar 

  24. Meyer M., Devesa A., Hickel S. et al. A conservative immersed interface method for large-eddy simulation of incompressible flows [J]. Journal of Computational Physics, 2010, 229(18): 6300–6317.

    Article  MathSciNet  MATH  Google Scholar 

  25. Udaykumar H. S., Shyy W., Rao M. M. Elafint: A mixed Eulerian-Lagrangian method for fluid flows with complex and moving boundaries [J]. International Journal for Numerical Methods in Fluids, 1996, 22(8): 691–712.

    Article  MathSciNet  MATH  Google Scholar 

  26. Udaykumar H. S., Mittal R., Shyy W. Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids [J]. Journal of Computational Physics, 1999, 153(2): 535–574.

    Article  MATH  Google Scholar 

  27. Hu X. Y., Khoo B. C., Adams N. A. et al. A conservative interface method for compressible flows [J]. Journal of Computational Physics, 2006, 219(2): 553–578.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  30. Hartmann D., Meinke M., Schröder W. An adaptive multilevel multigrid formulation for Cartesian hierarchical grid methods [J]. Computers and Fluids, 2008, 37(9): 1103–1125.

    Article  MathSciNet  MATH  Google Scholar 

  31. Griffith B. E. Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions [J]. International Journal for Numerical Methods in Biomedical Engineering, 2012, 28(3): 317–345.

    Article  MathSciNet  MATH  Google Scholar 

  32. 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 

  33. Yang F. C., Chen X. P. Numerical simulation of two-dimensional viscous flows using combined finite element-immersed boundary method [J]. Journal of Hydrodynamics, 2015, 27(5): 658–667.

    Article  Google Scholar 

  34. Michael T., Yang J., Stern F. A sharp interface approach for cavitation modeling using volume-of-fluid and ghost-fluid methods [J]. Journal of Hydrodynamics, 2017, 29(6): 917–925.

    Article  Google Scholar 

  35. Posa A., Vanella M., Balaras E. An adaptive reconstruction for Lagrangian, direct-forcing, immersed-boundary methods [J]. Journal of Computational Physics, 2017, 351: 422–436.

    Article  MathSciNet  MATH  Google Scholar 

  36. Miyauchi S., Ito A., Takeuchi S. et al. Fixed-mesh approach for different dimensional solids in fluid flows: Application to biological mechanics [J]. Journal of Mechanical Engineering and Sciences, 2014, 6: 818–844.

    Article  Google Scholar 

  37. Miyauchi S., Takeuchi S., Kajishima T. A numerical method for interaction problems between fluid and membranes with arbitrary permeability for fluid [J]. Journal of Computational Physics, 2017, 345: 33–57.

    Article  MathSciNet  MATH  Google Scholar 

  38. Yuki Y., Takeuchi S., Kajishima T. Efficient immersed boundary method for strong interaction problem of arbitrary shape object with the self-induced flow [J]. Journal of Fluid Science and Technology, 2007, 2(1): 1–11.

    Article  Google Scholar 

  39. Ya T. M. Y. S. T., Takeuchi S., Kajishima T. Immersed boundary and finite element methods approach for interaction of an elastic body and fluid by two-stage correction of velocity and pressure [C]. ASME/JSME 2007 5th Joint Fluids Engineering Conference, San Diego, California, USA, 2007, 75–81.

  40. Miyauchi S., Omori T., Takeuchi S. et al. Numerical simulation of unsteady flow through a two-dimensional channel with a vocal cord model [C]. ASME-JSME-KSME 2011 Joint Fluids Engineering Conference, Hamamatsu, Japan, 2011, 3683–3688.

  41. Schäfer M., Turek S., Durst F. et al. Benchmark computations of laminar flow around a cylinder (Flow simulation with high-performance computers) [M]. Wiesbaden, Germany: Springer, 1996, 547–566.

    MATH  Google Scholar 

  42. Verkaik A. C., Hulsen M. A., Bogaerds A. C. B. et al. An overlapping domain technique coupling spectral and finite elements for fluid flow [J]. Computers and Fluids, 2014, 100: 336–346.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Centre for Integrated Design for Advanced Mechanical Systems, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia, 43600, Bangi, Selangor, Malaysia

    Mohammed Suleman Aldlemy, Mohammad Rasidi Rasani & A. K. Ariffin

  2. Department of Mechanical Engineering, College of Mechanical Engineering Technology, Benghazi, Libya

    Mohammed Suleman Aldlemy

  3. Department of Mechanical Engineering, Faculty of Engineering, Universiti Teknologi Petronas, 31750, Tronoh, Perak, Malaysia

    T. M. Y. S. Tuan Ya

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  1. Mohammed Suleman Aldlemy
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  2. Mohammad Rasidi Rasani
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  3. A. K. Ariffin
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  4. T. M. Y. S. Tuan Ya
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Correspondence to Mohammed Suleman Aldlemy.

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Biography: Mohammed Suleman Aldlemy (1975-), Male, Ph. D., Associate Professor

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Aldlemy, M.S., Rasani, M.R., Ariffin, A.K. et al. Adaptive mesh refinement immersed boundary method for simulations of laminar flows past a moving thin elastic structure. J Hydrodyn 32, 148–160 (2020). https://doi.org/10.1007/s42241-020-0008-2

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  • DOI: https://doi.org/10.1007/s42241-020-0008-2

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