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Computational multi-phase convective conjugate heat transfer on overlapping meshes: a quasi-direct coupling approach via Schwarz alternating method

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Abstract

We present a new computational framework to simulate the multi-phase convective conjugate heat transfer (CHT) problems emanating from realistic manufacturing processes. The paper aims to address the challenges of boundary-fitted and immersed boundary approaches, which cannot simultaneously achieve fluid-solid interface accuracy and geometry-flexibility in simulating this class of multi-physics systems. The method development is built on a stabilized Arbitrary Lagrangian-Eulerian (ALE)-based finite element thermal multi-phase formulation, which is discretized by overlapping one boundary-fitted mesh and non-boundary-fitted mesh with a quasi-direct coupling approach via Schwarz alternating method. The framework utilizes a volume-of-fluid (VoF)-based multi-phase flow model coupled with a thermodynamics model with phase transitions to capture the conjugate heat transfer between the solid and multi-phase flows and the multi-stage boiling and condensation phenomena. The quasi-direct coupling approach allows the exact and automatic enforcement of temperature and heat-flux compatibility at the fluid-solid interface with large property discontinuities. From the perspective of method development, the proposed framework fully exploits boundary-fitted approach’s strength in resolving fluid-solid interface and boundary layers and immersed boundary approach’s geometry flexibility in handling moving objects while circumventing each individual’s limitations. From the perspective of industry applications, such as water quenching processes, the resulting model can enable accurate temperature prediction directly from process parameters without invoking the conventional empirical heat transfer coefficient (HTC)-based approach that requires intensive calibration. We present the mathematical formulation and numerical implementation in detail and demonstrate the claimed features of the proposed framework through a set of benchmark problems and real-world water quenching processes. The accuracy of the proposed framework is carefully assessed by comparing the prediction with other computational results and experimental measurements.

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References

  1. Luikov A, Perelman T, Levitin R, Gdalevich L (1970) Heat transfer from a plate in a compressible gas flow. Int J Heat Mass Transf 13(8):1261–1270

    Article  MATH  Google Scholar 

  2. Xiao B, Wang Q, Jadhav P, Li K (2010) An experimental study of heat transfer in aluminum castings during water quenching. J Mater Process Technol 210(14):2023–2028

    Article  Google Scholar 

  3. Lua J, Yan J, Li P, Zhao Z, Karuppiah A, Stuebner M (2021) Novel multi-physics-based modeling of a quenching process with thermal-metallurgical-mechanical interactions in aluminum components, in: 77th Annual Vertical Flight Society Forum and Technology Display: The Future of Vertical Flight, FORUM 2021, Vertical Flight Society

  4. Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329–349

    Article  MATH  Google Scholar 

  5. Takizawa K, Bazilevs Y, Tezduyar T (2012) Space-time and ALE-VMS techniques for patient-specific cardiovascular fluid-structure interaction modeling. Archives of Computational Methods in Engineering 19(2):171–225

    Article  MATH  Google Scholar 

  6. Bazilevs Y, Hsu M, Takizawa K, Tezduyar T (2012) ALE-VMS and ST-VMS methods for computer modeling of wind-turbine rotor aerodynamics and fluid-structure interaction. Math Models Methods Appl Sci 22(supp02):1230002

    Article  MATH  Google Scholar 

  7. Calderer R, Zhu L, Gibson R, Masud A (2015) Residual-based turbulence models and arbitrary lagrangian-eulerian framework for free surface flows. Math Models Methods Appl Sci 25(12):2287–2317

    Article  MATH  Google Scholar 

  8. Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Interface projection techniques for fluid-structure interaction modeling with moving-mesh methods. Comput Mech 43:39–49. https://doi.org/10.1007/s00466-008-0261-7

    Article  MATH  Google Scholar 

  9. Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119:73–94. https://doi.org/10.1016/0045-7825(94)00077-8

    Article  MATH  Google Scholar 

  10. Hsu M-C, Bazilevs Y (2012) Fluid-structure interaction modeling of wind turbines: simulating the full machine. Comput Mech. https://doi.org/10.1007/s00466-012-0772-0

    Article  MATH  Google Scholar 

  11. Peskin CS (1972) Flow patterns around heart valves: a numerical method. J Comput Phys 10(2):252–271

    Article  MATH  Google Scholar 

  12. Parvizian J, Düster A, Rank E (2007) Finite cell method: h- and p- extension for embedded domain methods in solid mechanics. Comput Mech 41:122–133

    Article  MATH  Google Scholar 

  13. Düster A, Parvizian J, Yang Z, Rank E (2008) The finite cell method for three-dimensional problems of solid mechanics. Comput Methods Appl Mech Eng 197(45–48):3768–3782

    Article  MATH  Google Scholar 

  14. Xu F, Schillinger D, Kamensky D, Varduhn V, Wang C, Hsu M (2016) The tetrahedral finite cell method for fluids: Immersogeometric analysis of turbulent flow around complex geometries. Computers & Fluids 141:135–154

    Article  MATH  Google Scholar 

  15. Main A, Scovazzi G (2018) The shifted boundary method for embedded domain computations. part i: Poisson and stokes problems,. J Comput Phys 372:972–995

    Article  MATH  Google Scholar 

  16. Main A, Scovazzi G (2018) The shifted boundary method for embedded domain computations. part ii: Linear advection–diffusion and incompressible navier–stokes equations,. J Comput Phys 372:996–1026

    Article  MATH  Google Scholar 

  17. Song T, Main A, Scovazzi G, Ricchiuto M (2018) The shifted boundary method for hyperbolic systems: Embedded domain computations of linear waves and shallow water flows. J Comput Phys 369:45–79

    Article  MATH  Google Scholar 

  18. Li K, Atallah N, Main A, Scovazzi G (2020) The shifted interface method: A flexible approach to embedded interface computations. Int J Numer Meth Eng 121(3):492–518

    Article  Google Scholar 

  19. Colomés O, Main A, Nouveau L, Scovazzi G (2021) A weighted shifted boundary method for free surface flow problems. J Comput Phys 424:109837

    Article  MATH  Google Scholar 

  20. Hansbo A, Hansbo P (2002) An unfitted finite element method, based on nitsche’s method, for elliptic interface problems. Comput Methods Appl Mech Eng 191(47–48):5537–5552

    Article  MATH  Google Scholar 

  21. Bazilevs Y, Kamran K, Moutsanidis G, Benson DJ, Oñate E (2017) A new formulation for air-blast fluid-structure interaction using an immersed approach. Part I: basic methodology and FEM-based simulations, Computational Mechanics 60(1):83–100

    MATH  Google Scholar 

  22. Bazilevs Y, Moutsanidis G, Bueno J, Kamran K, Kamensky D, Hillman MC, Gomez H, Chen JS (2017) A new formulation for air-blast fluid-structure interaction using an immersed approach: Part II–coupling of IGA and meshfree discretizations. Comput Mech 60(1):101–116

    Article  MATH  Google Scholar 

  23. Behzadinasab M, Moutsanidis G, Trask N, Foster J, Bazilevs Y (2021) Coupling of iga and peridynamics for air-blast fluid-structure interaction using an immersed approach. Forces in Mechanics 4:100045

    Article  Google Scholar 

  24. Moutsanidis G, Koester J, Tupek M, Chen J, Bazilevs Y (2020) Treatment of near-incompressibility in meshfree and immersed-particle methods. Computational particle mechanics 7(2):309–327

    Article  Google Scholar 

  25. Moutsanidis G, Kamensky D, Chen J, Bazilevs Y (2018) Hyperbolic phase field modeling of brittle fracture: Part ii-immersed iga-rkpm coupling for air-blast-structure interaction. J Mech Phys Solids 121:114–132

    Article  Google Scholar 

  26. Liu WK, Liu Y, Farrell D, Zhang L, Wang XS, Fukui Y, Patankar N, Zhang Y, Bajaj C, Lee J et al (2006) Immersed finite element method and its applications to biological systems. Comput Methods Appl Mech Eng 195(13–16):1722–1749

    Article  MATH  Google Scholar 

  27. Zhang L, Gerstenberger A, Wang X, Liu W (2004) Immersed finite element method. Comput Methods Appl Mech Eng 193(21–22):2051–2067

    Article  MATH  Google Scholar 

  28. Zhang LT, j. v. n. p. y. p. Gay M Immersed finite element method for fluid-structure interactions

  29. Wang X, Zhang L (2010) Interpolation functions in the immersed boundary and finite element methods. Comput Mech 45(4):321–334

    Article  MATH  Google Scholar 

  30. Wang X, Zhang L, Liu W (2009) On computational issues of immersed finite element methods. J Comput Phys 228(7):2535–2551

    Article  MATH  Google Scholar 

  31. Wang X, Zhang L (2013) Modified immersed finite element method for fully-coupled fluid-structure interactions. Comput Methods Appl Mech Eng 267:150–169

    Article  MATH  Google Scholar 

  32. Schillinger D, Dede L, Scott MA, Evans J, Borden M, Rank E, Hughes T (2012) An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of nurbs, immersed boundary methods, and t-spline cad surfaces. Comput Methods Appl Mech Eng 249:116–150

    Article  MATH  Google Scholar 

  33. Hsu M-C, Kamensky D, Xu F, Kiendl J, Wang C, Wu MCH, Mineroff J, Reali A, Bazilevs Y, Sacks MS (2015) Dynamic and fluid-structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models. Comput Mech 55:1211–1225

    Article  MATH  Google Scholar 

  34. Kamensky D, Hsu M-C, Schillinger D, Evans JA, Aggarwal A, Bazilevs Y, Sacks MS, Hughes TJR (2015) An immersogeometric variational framework for fluid-structure interaction: Application to bioprosthetic heart valves. Comput Methods Appl Mech Eng 284:1005–1053

    Article  MATH  Google Scholar 

  35. Zhu Q, Xu F, Xu S, Hsu M, Yan J (2020) An immersogeometric formulation for free-surface flows with application to marine engineering problems. Comput Methods Appl Mech Eng 361:112748

    Article  MATH  Google Scholar 

  36. Volkov E (1968) The method of composite meshes for finite and infinite regions with piecewise smooth boundary. Trudy Matematicheskogo Instituta imeni VA Steklova 96:117–148

    Google Scholar 

  37. Henshaw W (1994) A fourth-order accurate method for the incompressible navier-stokes equations on overlapping grids. J Comput Phys 113(1):13–25

    Article  MATH  Google Scholar 

  38. Henshaw W, Chand K (2009) A composite grid solver for conjugate heat transfer in fluid-structure systems. J Comput Phys 228(10):3708–3741

    Article  MATH  Google Scholar 

  39. Appelö D, Banks J, Henshaw W, Schwendeman D (2012) Numerical methods for solid mechanics on overlapping grids: Linear elasticity. J Comput Phys 231(18):6012–6050

    Article  MATH  Google Scholar 

  40. Koblitz A, Lovett S, Nikiforakis N, Henshaw W (2017) Direct numerical simulation of particulate flows with an overset grid method. J Comput Phys 343:414–431

    Article  MATH  Google Scholar 

  41. Meng F, Banks J, Henshaw W, Schwendeman D (2020) Fourth-order accurate fractional-step imex schemes for the incompressible navier-stokes equations on moving overlapping grids. Comput Methods Appl Mech Eng 366:113040

    Article  MATH  Google Scholar 

  42. MEAKIN R (1993) Moving body overset grid methods for complete aircraft tiltrotor simulations, in: 11th Computational Fluid Dynamics Conference, p. 3350

  43. Chan W (2009) Overset grid technology development at nasa ames research center. Computers & Fluids 38(3):496–503

    Article  Google Scholar 

  44. Chandar D, Damodaran M (2010) Numerical study of the free flight characteristics of a flapping wing in low reynolds numbers. AIAA J. Aircraft 47(1):141–150

    Article  Google Scholar 

  45. Lani A, Sjögreen B, Yee H, Henshaw W (2013) Variable high-order multiblock overlapping grid methods for mixed steady and unsteady multiscale viscous flows, part ii: hypersonic nonequilibrium flows. Communications in Computational Physics 13(2):583–602

    Article  MATH  Google Scholar 

  46. Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid-structure interaction: methods and applications. Wiley, Hoboken

    Book  MATH  Google Scholar 

  47. De Schepper S, Heynderickx G, Marin G (2009) Modeling the evaporation of a hydrocarbon feedstock in the convection section of a steam cracker. Computers & Chemical Engineering 33(1):122–132

    Article  Google Scholar 

  48. De Schepper S, Heynderickx G, Marin G (2008) Cfd modeling of all gas-liquid and vapor-liquid flow regimes predicted by the baker chart. Chem Eng J 138(1–3):349–357

    Article  Google Scholar 

  49. Hughes T, Mallet M (1986) A new finite element formulation for computational fluid dynamics: Iv. a discontinuity-capturing operator for multidimensional advective-diffusive systems. Comput Methods Appl Mech Eng 58(3):329–336

    Article  MATH  Google Scholar 

  50. Tezduyar TE, Senga M (2006) Stabilization and shock-capturing parameters in supg formulation of compressible flows. Comput Methods Appl Mech Eng 195(13–16):1621–1632

    Article  MATH  Google Scholar 

  51. Bazilevs Y, Hughes TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Computers & Fluids 36:12–26

    Article  MATH  Google Scholar 

  52. Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 32:199–259

    Article  MATH  Google Scholar 

  53. Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28:1–44

    MATH  Google Scholar 

  54. Hughes T, Franca L, Hulbert G (1989) A new finite element formulation for computational fluid dynamics : Viii. the galerkin/least-squares method for advective-diffusive equations,. Comput Methods Appl Mech Eng 73(2):173–189

    Article  MATH  Google Scholar 

  55. Harari I, Hughes T (1992) What are c and h?: Inequalities for the analysis and design of finite element methods. Comput Methods Appl Mech Eng 97(2):157–192

    Article  MATH  Google Scholar 

  56. Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37

    Article  MATH  Google Scholar 

  57. Takizawa K, Bazilevs Y, Tezduyar TE (2012) Space-time and ALE-VMS techniques for patient-specific cardiovascular fluid-structure interaction modeling. Archives of Computational Methods in Engineering 19:171–225. https://doi.org/10.1007/s11831-012-9071-3

    Article  MATH  Google Scholar 

  58. Bazilevs Y, Hsu M-C, Takizawa K, Tezduyar TE (2012) ALE-VMS and ST-VMS methods for computer modeling of wind-turbine rotor aerodynamics and fluid-structure interaction. Math Models Methods Appl Sci 22(supp02):1230002. https://doi.org/10.1142/S0218202512300025

    Article  MATH  Google Scholar 

  59. Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational Fluid-Structure Interaction: Methods and Applications. Wiley. https://doi.org/10.1002/9781118483565

    Article  MATH  Google Scholar 

  60. Bazilevs Y, Takizawa K, Tezduyar TE (2013) Challenges and directions in computational fluid-structure interaction. Math Models Methods Appl Sci 23:215–221. https://doi.org/10.1142/S0218202513400010

    Article  MATH  Google Scholar 

  61. Bazilevs Y, Takizawa K, Tezduyar TE (2015) New directions and challenging computations in fluid dynamics modeling with stabilized and multiscale methods. Math Models Methods Appl Sci 25:2217–2226. https://doi.org/10.1142/S0218202515020029

    Article  MATH  Google Scholar 

  62. Bazilevs Y, Takizawa K, Tezduyar TE (2019) Computational analysis methods for complex unsteady flow problems. Math Models Methods Appl Sci 29:825–838. https://doi.org/10.1142/S0218202519020020

    Article  MATH  Google Scholar 

  63. Takizawa K, Tezduyar TE (2012) Computational methods for parachute fluid-structure interactions. Archives of Computational Methods in Engineering 19:125–169. https://doi.org/10.1007/s11831-012-9070-4

    Article  MATH  Google Scholar 

  64. Takizawa K, Fritze M, Montes D, Spielman T, Tezduyar TE (2012) Fluid-structure interaction modeling of ringsail parachutes with disreefing and modified geometric porosity. Comput Mech 50:835–854. https://doi.org/10.1007/s00466-012-0761-3

    Article  Google Scholar 

  65. Takizawa K, Tezduyar TE, Boben J, Kostov N, Boswell C, Buscher A (2013) Fluid-structure interaction modeling of clusters of spacecraft parachutes with modified geometric porosity. Comput Mech 52:1351–1364. https://doi.org/10.1007/s00466-013-0880-5

    Article  MATH  Google Scholar 

  66. Takizawa K, Tezduyar TE, Boswell C, Tsutsui Y, Montel K (2015) Special methods for aerodynamic-moment calculations from parachute FSI modeling. Comput Mech 55:1059–1069. https://doi.org/10.1007/s00466-014-1074-5

    Article  Google Scholar 

  67. Kalro V, Tezduyar TE (2000) A parallel 3D computational method for fluid-structure interactions in parachute systems. Comput Methods Appl Mech Eng 190:321–332. https://doi.org/10.1016/S0045-7825(00)00204-8

    Article  MATH  Google Scholar 

  68. Zhu Q, Yan J, Tejada-Martínez A, Bazilevs Y (2020) Variational multiscale modeling of langmuir turbulent boundary layers in shallow water using isogeometric analysis. Mech Res Commun 108:103570. https://doi.org/10.1016/j.mechrescom.2020.103570

    Article  Google Scholar 

  69. Ravensbergen M, Helgedagsrud TA, Bazilevs Y, Korobenko A (2020) A variational multiscale framework for atmospheric turbulent flows over complex environmental terrains. Comput Methods Appl Mech Eng 368:113182. https://doi.org/10.1016/j.cma.2020.113182

    Article  MATH  Google Scholar 

  70. Yan J, Korobenko A, Tejada-Martinez AE, Golshan R, Bazilevs Y (2017) A new variational multiscale formulation for stratified incompressible turbulent flows. Computers & Fluids 158:150–156. https://doi.org/10.1016/j.compfluid.2016.12.004

    Article  MATH  Google Scholar 

  71. Cen H, Zhou Q, Korobenko A (2022) Wall-function-based weak imposition of dirichlet boundary condition for stratified turbulent flows. Computers & Fluids 234:105257

    Article  MATH  Google Scholar 

  72. Bazilevs Y, Hsu M-C, Akkerman I, Wright S, Takizawa K, Henicke B, Spielman T, Tezduyar TE (2011) 3D simulation of wind turbine rotors at full scale. Part I: Geometry modeling and aerodynamics, International Journal for Numerical Methods in Fluids 65:207–235. https://doi.org/10.1002/fld.2400

    Article  MATH  Google Scholar 

  73. Takizawa K, Henicke B, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48:333–344. https://doi.org/10.1007/s00466-011-0589-2

    Article  MATH  Google Scholar 

  74. Takizawa K, Henicke B, Montes D, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Numerical-performance studies for the stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48:647–657. https://doi.org/10.1007/s00466-011-0614-5

    Article  MATH  Google Scholar 

  75. Takizawa K, Tezduyar TE, McIntyre S, Kostov N, Kolesar R, Habluetzel C (2014) Space-time VMS computation of wind-turbine rotor and tower aerodynamics. Comput Mech 53:1–15. https://doi.org/10.1007/s00466-013-0888-x

    Article  MATH  Google Scholar 

  76. Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C, Øiseth O, Mathisen KM, Kostov N, McIntyre S (2014) Engineering analysis and design with ALE-VMS and space-time methods. Archives of Computational Methods in Engineering 21:481–508. https://doi.org/10.1007/s11831-014-9113-0

    Article  MATH  Google Scholar 

  77. Takizawa K (2014) Computational engineering analysis with the new-generation space-time methods. Comput Mech 54:193–211. https://doi.org/10.1007/s00466-014-0999-z

    Article  Google Scholar 

  78. Bazilevs Y, Takizawa K, Tezduyar TE, Hsu M-C, Kostov N, McIntyre S (2014) Aerodynamic and FSI analysis of wind turbines with the ALE-VMS and ST-VMS methods. Archives of Computational Methods in Engineering 21:359–398. https://doi.org/10.1007/s11831-014-9119-7

    Article  MATH  Google Scholar 

  79. Takizawa K, Tezduyar TE, Mochizuki H, Hattori H, Mei S, Pan L, Montel K (2015) Space-time VMS method for flow computations with slip interfaces (ST-SI). Math Models Methods Appl Sci 25:2377–2406. https://doi.org/10.1142/S0218202515400126

    Article  MATH  Google Scholar 

  80. Otoguro Y, Mochizuki H, Takizawa K, Tezduyar TE (2020) Space-time variational multiscale isogeometric analysis of a tsunami-shelter vertical-axis wind turbine. Comput Mech 66:1443–1460. https://doi.org/10.1007/s00466-020-01910-5

    Article  MATH  Google Scholar 

  81. Ravensbergen M, Bayram AM, Korobenko A (2020) The actuator line method for wind turbine modelling applied in a variational multiscale framework. Comput Fluids 201:104465. https://doi.org/10.1016/j.compfluid.2020.104465

    Article  MATH  Google Scholar 

  82. Korobenko A, Hsu M-C, Akkerman I, Bazilevs Y (2013) Aerodynamic simulation of vertical-axis wind turbines. J Appl Mech 81:021011. https://doi.org/10.1115/1.4024415

    Article  Google Scholar 

  83. Bazilevs Y, Korobenko A, Deng X, Yan J, Kinzel M, Dabiri JO (2014) FSI modeling of vertical-axis wind turbines. J Appl Mech 81:081006. https://doi.org/10.1115/1.4027466

    Article  Google Scholar 

  84. Korobenko A, Bazilevs Y, Takizawa K, Tezduyar TE (2018) Recent advances in ALE-VMS and ST-VMS computational aerodynamic and FSI analysis of wind turbines. In: Tezduyar TE (ed) Frontiers in Computational Fluid–Structure Interaction and Flow Simulation: Research from Lead Investigators under Forty – 2018, Modeling and Simulation in Science, Engineering and Technology. Springer, Berlin, pp 253–336. https://doi.org/10.1007/978-3-319-96469-0_7

    Chapter  Google Scholar 

  85. Korobenko A, Bazilevs Y, Takizawa K, Tezduyar TE (2019) Computer modeling of wind turbines: 1. ALE-VMS and ST-VMS aerodynamic and FSI analysis, Archives of Computational Methods in Engineering 26:1059–1099. https://doi.org/10.1007/s11831-018-9292-1

    Article  Google Scholar 

  86. Bayram AM, Bear C, Bear M, Korobenko A (2020) Performance analysis of two vertical-axis hydrokinetic turbines using variational multiscale method. Comput Fluids 200:104432. https://doi.org/10.1016/j.compfluid.2020.104432

    Article  MATH  Google Scholar 

  87. Yan J, Korobenko A, Deng X, Bazilevs Y (2016) Computational free-surface fluid-structure interaction with application to floating offshore wind turbines. Comput Fluids 141:155–174. https://doi.org/10.1016/j.compfluid.2016.03.008

    Article  MATH  Google Scholar 

  88. Yan J, Deng X, Xu F, Xu S, Zhu Q (2020) Numerical simulations of two back-to-back horizontal axis tidal stream turbines in free-surface flows. Journal of Applied Mechanics 87(6). https://doi.org/10.1115/1.4046317

  89. Kuraishi T, Zhang F, Takizawa K, Tezduyar TE (2021) Wind turbine wake computation with the st-vms method, isogeometric discretization and multidomain method: I. computational framework. Comput Mech 68(1):113–130

    Article  MATH  Google Scholar 

  90. Kuraishi T, Zhang F, Takizawa K, Tezduyar TE (2021) Wind turbine wake computation with the st-vms method, isogeometric discretization and multidomain method: Ii. spatial and temporal resolution,. Comput Mech 68(1):175–184

    Article  MATH  Google Scholar 

  91. Ravensbergen M, Mohamed A, Korobenko A (2020) The actuator line method for wind turbine modelling applied in a variational multiscale framework. Computers & Fluids 201:104465

    Article  MATH  Google Scholar 

  92. Mohamed A, Bear C, Bear M, Korobenko A (2020) Performance analysis of two vertical-axis hydrokinetic turbines using variational multiscale method. Computers & Fluids 200:104432

    Article  MATH  Google Scholar 

  93. Bayram A, Korobenko A (2020) Variational multiscale framework for cavitating flows, Computational Mechanics 1–19

  94. Yan J, Deng X, Korobenko A, Bazilevs Y (2017) Free-surface flow modeling and simulation of horizontal-axis tidal-stream turbines. Comput Fluids 158:157–166. https://doi.org/10.1016/j.compfluid.2016.06.016

    Article  MATH  Google Scholar 

  95. Zhu Q, Yan J (2021) A moving-domain CFD solver in FEniCS with applications to tidal turbine simulations in turbulent flows. Computers & Mathematics with Applications 81:532–546

    Article  MATH  Google Scholar 

  96. Bayram AM, Korobenko A (2020) Variational multiscale framework for cavitating flows. Comput Mech 66:49–67. https://doi.org/10.1007/s00466-020-01840-2

    Article  MATH  Google Scholar 

  97. Cen H, Zhou Q, Korobenko A (2021) Variational multiscale framework for cavitating flows. Computers & Fluids 214:104765. https://doi.org/10.1016/j.compfluid.2020.104765

    Article  MATH  Google Scholar 

  98. Codoni D, Moutsanidis G, Hsu M-C, Bazilevs Y, Johansen C, Korobenko A (2021) Stabilized methods for high-speed compressible flows: toward hypersonic simulations. Comput Mech 67:785–809. https://doi.org/10.1007/s00466-020-01963-6

    Article  MATH  Google Scholar 

  99. Terahara T, Takizawa K, Tezduyar TE, Bazilevs Y, Hsu M-C (2020) Heart valve isogeometric sequentially-coupled FSI analysis with the space-time topology change method. Comput Mech 65:1167–1187. https://doi.org/10.1007/s00466-019-01813-0

    Article  MATH  Google Scholar 

  100. Hsu M-C, Kamensky D, Bazilevs Y, Sacks MS, Hughes TJR (2014) Fluid-structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation. Comput Mech 54:1055–1071. https://doi.org/10.1007/s00466-014-1059-4

    Article  MATH  Google Scholar 

  101. Johnson EL, Wu MCH, Xu F, Wiese NM, Rajanna MR, Herrema AJ, Ganapathysubramanian B, Hughes TJR, Sacks MS, Hsu M-C (2020) Thinner biological tissues induce leaflet flutter in aortic heart valve replacements. Proc Natl Acad Sci 117:19007–19016

    Article  Google Scholar 

  102. Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C (2019) Computational cardiovascular flow analysis with the variational multiscale methods. Journal of Advanced Engineering and Computation 3:366–405. https://doi.org/10.25073/jaec.201932.245

    Article  Google Scholar 

  103. Kuraishi T, Terahara T, Takizawa K, Tezduyar T (2022) Computational flow analysis with boundary layer and contact representation: I. tire aerodynamics with road contact. J Mech 38:77–87

    Article  Google Scholar 

  104. Terahara T, Kuraishi T, Takizawa K, Tezduyar T (2022) Computational flow analysis with boundary layer and contact representation: Ii. heart valve flow with leaflet contact,. J Mech 38:185–194

    Article  Google Scholar 

  105. Otoguro Y, Takizawa K, Tezduyar TE, Nagaoka K, Avsar R, Zhang Y (2019) Space-time VMS flow analysis of a turbocharger turbine with isogeometric discretization: Computations with time-dependent and steady-inflow representations of the intake/exhaust cycle. Comput Mech 64:1403–1419. https://doi.org/10.1007/s00466-019-01722-2

    Article  MATH  Google Scholar 

  106. Otoguro Y, Takizawa K, Tezduyar TE, Nagaoka K, Mei S (2019) Turbocharger turbine and exhaust manifold flow computation with the Space-Time Variational Multiscale Method and Isogeometric Analysis. Computers & Fluids 179:764–776. https://doi.org/10.1016/j.compfluid.2018.05.019

  107. Xu F, Moutsanidis G, Kamensky D, Hsu M-C, Murugan M, Ghoshal A, Bazilevs Y (2017) Compressible flows on moving domains: Stabilized methods, weakly enforced essential boundary conditions, sliding interfaces, and application to gas-turbine modeling. Computers & Fluids 158:201–220. https://doi.org/10.1016/j.compfluid.2017.02.006

    Article  MATH  Google Scholar 

  108. Takizawa K, Tezduyar TE, Kuraishi T (2015) Multiscale ST methods for thermo-fluid analysis of a ground vehicle and its tires. Math Models Methods Appl Sci 25:2227–2255. https://doi.org/10.1142/S0218202515400072

    Article  MATH  Google Scholar 

  109. Kuraishi T, Takizawa K, Tabata S, Asada S, Tezduyar TE (2014) Multiscale thermo-fluid analysis of a tire. In: Proceedings of the 19th Japan Society of Computational Engineering and Science Conference, Hiroshima, Japan

  110. Takizawa K, Tezduyar TE, Kuraishi T (2016) Flow analysis around a tire with actual geometry, road contact and deformation, in preparation

  111. Kuraishi T, Takizawa K, Tezduyar TE (2018) Space–time computational analysis of tire aerodynamics with actual geometry, road contact and tire deformation. In: Tezduyar TE (ed) Frontiers in Computational Fluid–Structure Interaction and Flow Simulation: Research from Lead Investigators under Forty – 2018, Modeling and Simulation in Science, Engineering and Technology. Springer, Berlin, pp 337–376. https://doi.org/10.1007/978-3-319-96469-0_8

    Chapter  Google Scholar 

  112. Kuraishi T, Takizawa K, Tezduyar TE (2019) Tire aerodynamics with actual tire geometry, road contact and tire deformation. Comput Mech 63:1165–1185. https://doi.org/10.1007/s00466-018-1642-1

    Article  MATH  Google Scholar 

  113. Kuraishi T, Takizawa K, Tezduyar TE (2019) Space-time computational analysis of tire aerodynamics with actual geometry, road contact, tire deformation, road roughness and fluid film. Comput Mech 64:1699–1718. https://doi.org/10.1007/s00466-019-01746-8

    Article  MATH  Google Scholar 

  114. Yan J, Korobenko A, Deng X, Bazilevs Y (2016) Computational free-surface fluid-structure interaction with application to floating offshore wind turbines. Computers & Fluids 141:155–174

    Article  MATH  Google Scholar 

  115. Hsu M, Akkerman I, Bazilevs Y (2012) Wind turbine aerodynamics using ALE-VMS: Validation and the role of weakly enforced boundary conditions. Comput Mech 50(4):499–511

    Article  Google Scholar 

  116. Zhu Q, Yan J (2021) A mixed interface-capturing/interface-tracking formulation for thermal multi-phase flows with emphasis on metal additive manufacturing processes. Comput Methods Appl Mech Eng 383:113910

    Article  MATH  Google Scholar 

  117. Liu J, Lan I, Tikenogullari O, Marsden A (2021) A note on the accuracy of the generalized-\(\alpha \) scheme for the incompressible navier-stokes equations. Int J Numer Meth Eng 122(2):638–651

    Article  Google Scholar 

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Acknowledgements

This work is funded by the U.S. Navy through the contract of N68335-21-C-0057. J. Yan also wants to acknowledge the support of computational facilities from Texas Advanced Computing Center through the allocation of CTS20014.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Champaign, IL, USA

    Ze Zhao, Qiming Zhu & Jinhui Yan

  2. Global Engineering and Materials, Inc, Princeton, USA

    Anand Karuppiah, Michael Stuebner & Jim Lua

  3. Naval Air Systems Command, Maryland, USA

    Nam Phan

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  1. Ze Zhao
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  7. Jinhui Yan
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Correspondence to Jinhui Yan.

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Zhao, Z., Zhu, Q., Karuppiah, A. et al. Computational multi-phase convective conjugate heat transfer on overlapping meshes: a quasi-direct coupling approach via Schwarz alternating method. Comput Mech 71, 71–88 (2023). https://doi.org/10.1007/s00466-022-02217-3

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