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Published in: Computational Mechanics 6/2015

01-06-2015 | Original Paper

Interaction of complex fluids and solids: theory, algorithms and application to phase-change-driven implosion

Authors: Jesus Bueno, Carles Bona-Casas, Yuri Bazilevs, Hector Gomez

Published in: Computational Mechanics | Issue 6/2015

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Abstract

There is a large body of literature dealing with the interaction of solids and classical fluids, but the mechanical coupling of solids and complex fluids remains practically unexplored, at least from the computational point of view. Yet, complex fluids produce much richer physics than classical fluids when they interact with solids, especially at small scales. Here, we couple a nonlinear hyperelastic solid with a single-component two-phase flow, where the fluid can condensate and evaporate naturally due to temperature and/or pressure changes. We propose a fully-coupled fluid–structure interaction algorithm to solve the problem. We illustrate the viability of the theoretical framework and the effectiveness of our algorithms by solving several problems of phase-change-driven implosion, a physical process in which a thin structure collapses due to the condensation of a fluid.

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Literature
1.
go back to reference Bazilevs Y, Beiro Da Veiga L, Cottrell JA, Hughes TJR, Sangalli G (2006a) Isogeometric Analysis: approximation, stability and error estimates for h-refined meshes. Math Models Methods Appl Sci 16(07):1031–1090MATHMathSciNetCrossRef Bazilevs Y, Beiro Da Veiga L, Cottrell JA, Hughes TJR, Sangalli G (2006a) Isogeometric Analysis: approximation, stability and error estimates for h-refined meshes. Math Models Methods Appl Sci 16(07):1031–1090MATHMathSciNetCrossRef
2.
go back to reference Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006b) Isogeometric Fluid–Structure Interaction analysis with applications to arterial blood flow. Comput Mech 38(4–5):310–322MATHMathSciNetCrossRef Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006b) Isogeometric Fluid–Structure Interaction analysis with applications to arterial blood flow. Comput Mech 38(4–5):310–322MATHMathSciNetCrossRef
3.
go back to reference Bazilevs Y, Calo VM, Cottrell JA, Hughes TJR, Reali A, Scovazzi G (2007) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197(14):173–201MATHMathSciNetCrossRef Bazilevs Y, Calo VM, Cottrell JA, Hughes TJR, Reali A, Scovazzi G (2007) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197(14):173–201MATHMathSciNetCrossRef
4.
go back to reference Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric Fluid–Structure Interaction: theory, algorithms, and computations. Comput Mech 43(1):3–37MATHMathSciNetCrossRef Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric Fluid–Structure Interaction: theory, algorithms, and computations. Comput Mech 43(1):3–37MATHMathSciNetCrossRef
5.
go back to reference Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2009) Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the jarvik 2000 left ventricular assist device. Comput. Methods Appl Mech Eng 198(45):3534–3550MATHMathSciNetCrossRef Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2009) Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the jarvik 2000 left ventricular assist device. Comput. Methods Appl Mech Eng 198(45):3534–3550MATHMathSciNetCrossRef
6.
go back to reference Bazilevs Y, Calo VM, Cottrell JA, Evans JA, Hughes TJR, Lipton S, Scott MA, Sederberg TW (2010) Isogeometric Analysis using T-splines. Comput. Methods Appl Mech Eng 199(58):229–263MATHMathSciNetCrossRef Bazilevs Y, Calo VM, Cottrell JA, Evans JA, Hughes TJR, Lipton S, Scott MA, Sederberg TW (2010) Isogeometric Analysis using T-splines. Comput. Methods Appl Mech Eng 199(58):229–263MATHMathSciNetCrossRef
7.
go back to reference Bazilevs Y, Hsu M-C, Kiendl J, Wüchner R, Bletzinger K-U (2011) 3D simulation of wind turbine rotors at full scale. Part II: fluid–structure interaction modeling with composite blades. Int J Numer Methods Fluids 65(1–3):236–253MATHCrossRef Bazilevs Y, Hsu M-C, Kiendl J, Wüchner R, Bletzinger K-U (2011) 3D simulation of wind turbine rotors at full scale. Part II: fluid–structure interaction modeling with composite blades. Int J Numer Methods Fluids 65(1–3):236–253MATHCrossRef
8.
go back to reference Bazilevs Y, Takizawa K, Tezduyar TE (2013a) Challenges and directions in computational fluid–structure interaction. Math Models Methods Appl Sci 23:215–221MATHMathSciNetCrossRef Bazilevs Y, Takizawa K, Tezduyar TE (2013a) Challenges and directions in computational fluid–structure interaction. Math Models Methods Appl Sci 23:215–221MATHMathSciNetCrossRef
9.
go back to reference Bazilevs Y, Takizawa K, Tezduyar TE (2013b) Computational fluid–structure interaction. Methods and applications. Wiley, ChichesterMATHCrossRef Bazilevs Y, Takizawa K, Tezduyar TE (2013b) Computational fluid–structure interaction. Methods and applications. Wiley, ChichesterMATHCrossRef
10.
go back to reference 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. Arch Comput Methods Eng, published online. doi:10.1007/s11831-014-9119-7 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. Arch Comput Methods Eng, published online. doi:10.​1007/​s11831-014-9119-7
11.
go back to reference Benson DJ, Bazilevs Y, Hsu MC, Hughes TJR (2010) Isogeometric shell analysis: the Reissner–Mindlin shell. Comput Methods Appl Mech Eng 199(5):276–289MATHMathSciNetCrossRef Benson DJ, Bazilevs Y, Hsu MC, Hughes TJR (2010) Isogeometric shell analysis: the Reissner–Mindlin shell. Comput Methods Appl Mech Eng 199(5):276–289MATHMathSciNetCrossRef
12.
go back to reference Borden MJ, Verhoosel CV, Scott MA, Hughes TJR, Landis CM (2012) A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng 217–220:77–95 Borden MJ, Verhoosel CV, Scott MA, Hughes TJR, Landis CM (2012) A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng 217–220:77–95
14.
go back to reference Chen L-Q (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32(1):113–140CrossRef Chen L-Q (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32(1):113–140CrossRef
15.
go back to reference Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-\(\alpha \) method. J Appl Mech 60:371–375MATHMathSciNetCrossRef Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-\(\alpha \) method. J Appl Mech 60:371–375MATHMathSciNetCrossRef
16.
go back to reference Cottrell JA, Reali A, Bazilevs Y, Hughes TJR (2006) Isogeometric Analysis of structural vibrations. Comput Methods Appl Mech Eng 195(4143):5257–5296MATHMathSciNetCrossRef Cottrell JA, Reali A, Bazilevs Y, Hughes TJR (2006) Isogeometric Analysis of structural vibrations. Comput Methods Appl Mech Eng 195(4143):5257–5296MATHMathSciNetCrossRef
17.
go back to reference Cottrell JA, Hughes TJR, Reali A (2007) Studies of refinement and continuity in Isogeometric structural analysis. Comput Methods Appl Mech Eng 196(4144):4160–4183MATHMathSciNetCrossRef Cottrell JA, Hughes TJR, Reali A (2007) Studies of refinement and continuity in Isogeometric structural analysis. Comput Methods Appl Mech Eng 196(4144):4160–4183MATHMathSciNetCrossRef
18.
go back to reference Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, ChichesterCrossRef Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, ChichesterCrossRef
19.
go back to reference Cueto-Felgueroso L, Juanes R (2008) Nonlocal interface dynamics and pattern formation in gravity-driven unsaturated flow through porous media. Phys Rev Lett 101:244504CrossRef Cueto-Felgueroso L, Juanes R (2008) Nonlocal interface dynamics and pattern formation in gravity-driven unsaturated flow through porous media. Phys Rev Lett 101:244504CrossRef
20.
go back to reference Dettmer WG, Peric D (2008) On the coupling between fluid flow and mesh motion in the modelling of fluid–structure interaction. Comput Mech 43:81–90MATHCrossRef Dettmer WG, Peric D (2008) On the coupling between fluid flow and mesh motion in the modelling of fluid–structure interaction. Comput Mech 43:81–90MATHCrossRef
21.
go back to reference Diehl D (2007) Higher order schemes for simulation of compressible liquid–vapor flows with phase change. PhD Thesis, Albert-Ludwigs-Universitat Diehl D (2007) Higher order schemes for simulation of compressible liquid–vapor flows with phase change. PhD Thesis, Albert-Ludwigs-Universitat
22.
go back to reference Donea J, Huerta A (2003) Finite element methods for flow problems. Wiley, ChichesterCrossRef Donea J, Huerta A (2003) Finite element methods for flow problems. Wiley, ChichesterCrossRef
23.
go back to reference Donea J, Huerta A, Ponthot J-Ph, Rodrguez-Ferran A (2004) Encyclopedia of computational mechanics. Arbitrary Lagrangian–Eulerian methods, vol 1, Chapter 14. Wiley, New York Donea J, Huerta A, Ponthot J-Ph, Rodrguez-Ferran A (2004) Encyclopedia of computational mechanics. Arbitrary Lagrangian–Eulerian methods, vol 1, Chapter 14. Wiley, New York
25.
go back to reference Elguedj T, Bazilevs Y, Calo VM, Hughes TJR (2008) \(\bar{B}\) and \(\bar{F}\) projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements. Comput Methods Appl Mech Eng 197(3340):2732–2762MATHCrossRef Elguedj T, Bazilevs Y, Calo VM, Hughes TJR (2008) \(\bar{B}\) and \(\bar{F}\) projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements. Comput Methods Appl Mech Eng 197(3340):2732–2762MATHCrossRef
26.
go back to reference Farhat C, Rallu A, Shankaran S (2008) A higher-order generalized Ghost Fluid Method for the Poor for the three-dimensional two-phase flow computation of underwater implosions. J Comput Phys 227(16):7674–7700MATHCrossRef Farhat C, Rallu A, Shankaran S (2008) A higher-order generalized Ghost Fluid Method for the Poor for the three-dimensional two-phase flow computation of underwater implosions. J Comput Phys 227(16):7674–7700MATHCrossRef
27.
go back to reference Farhat C, Rallu A, Wang K, Belytschko T (2010) Robust and provably second-order explicit–explicit and implicit–explicit staggered time-integrators for highly non-linear compressible Fluid–Structure Interaction problems. Int J Numer Methods Eng 84(1):73–107MATHMathSciNetCrossRef Farhat C, Rallu A, Wang K, Belytschko T (2010) Robust and provably second-order explicit–explicit and implicit–explicit staggered time-integrators for highly non-linear compressible Fluid–Structure Interaction problems. Int J Numer Methods Eng 84(1):73–107MATHMathSciNetCrossRef
28.
go back to reference Galenko PK, Gomez H, Kropotin NV, Elder KR (2013) Unconditionally stable method and numerical solution of the hyperbolic phase-field crystal equation. Phys Rev E 88(1):013310CrossRef Galenko PK, Gomez H, Kropotin NV, Elder KR (2013) Unconditionally stable method and numerical solution of the hyperbolic phase-field crystal equation. Phys Rev E 88(1):013310CrossRef
29.
go back to reference Gelbart WM, Ben-Shaul A (1996) The new science of complex fluids. J Phys Chem 100(31):13169–13189CrossRef Gelbart WM, Ben-Shaul A (1996) The new science of complex fluids. J Phys Chem 100(31):13169–13189CrossRef
30.
go back to reference Gibbs JW (1876) On the equilibrium of heterogeneous substances. Trans Conn Acad 3:108–248 Gibbs JW (1876) On the equilibrium of heterogeneous substances. Trans Conn Acad 3:108–248
31.
go back to reference Gomez H, Hughes TJR (2011) Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models. J Comput Phys 230(13):5310–5327MATHMathSciNetCrossRef Gomez H, Hughes TJR (2011) Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models. J Comput Phys 230(13):5310–5327MATHMathSciNetCrossRef
32.
go back to reference Gomez H, Calo VM, Bazilevs Y, Hughes TJR (2008) Isogeometric Analysis of the Cahn–Hilliard phase-field model. Comput Methods Appl Mech Eng 197:4333–4352MATHMathSciNetCrossRef Gomez H, Calo VM, Bazilevs Y, Hughes TJR (2008) Isogeometric Analysis of the Cahn–Hilliard phase-field model. Comput Methods Appl Mech Eng 197:4333–4352MATHMathSciNetCrossRef
33.
go back to reference Gomez H, Hughes TJR, Nogueira X, Calo VM (2010) Isogeometric Analysis of the isothermal Navier–Stokes–Korteweg equations. Comput Methods Appl Mech Eng 199(25–28):1828–1840MATHMathSciNetCrossRef Gomez H, Hughes TJR, Nogueira X, Calo VM (2010) Isogeometric Analysis of the isothermal Navier–Stokes–Korteweg equations. Comput Methods Appl Mech Eng 199(25–28):1828–1840MATHMathSciNetCrossRef
34.
go back to reference Gomez H, Cueto-Felgueroso L, Juanes R (2013) Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium. J Comput Phys 238:217–239MathSciNetCrossRef Gomez H, Cueto-Felgueroso L, Juanes R (2013) Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium. J Comput Phys 238:217–239MathSciNetCrossRef
35.
go back to reference Gomez H, Reali A, Sangalli G (2014) Accurate, efficient, and (iso) geometrically flexible collocation methods for phase-field models. J Comput Phys 262:153–171MathSciNetCrossRef Gomez H, Reali A, Sangalli G (2014) Accurate, efficient, and (iso) geometrically flexible collocation methods for phase-field models. J Comput Phys 262:153–171MathSciNetCrossRef
36.
go back to reference Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian–Eulerian Finite Element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29(3):329–349MATHMathSciNetCrossRef Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian–Eulerian Finite Element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29(3):329–349MATHMathSciNetCrossRef
37.
go back to reference Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric Analysis: CAD, Finite Elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl Mech Eng 194(3941):4135–4195MATHMathSciNetCrossRef Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric Analysis: CAD, Finite Elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl Mech Eng 194(3941):4135–4195MATHMathSciNetCrossRef
38.
go back to reference Ikeda CM (2012) Fluid–Structure Interactions. Implosions of shell structures and wave impact on a flat plate. PhD Thesis, University of Maryland Ikeda CM (2012) Fluid–Structure Interactions. Implosions of shell structures and wave impact on a flat plate. PhD Thesis, University of Maryland
39.
go back to reference Jansen KE, Whiting CH, Hulbert GM (2000) A generalized-\(\alpha \) method for integrating the filtered Navier–Stokes equations with a stabilized Finite Element Method. Comput Methods Appl Mech Eng 190(34):305–319MATHMathSciNetCrossRef Jansen KE, Whiting CH, Hulbert GM (2000) A generalized-\(\alpha \) method for integrating the filtered Navier–Stokes equations with a stabilized Finite Element Method. Comput Methods Appl Mech Eng 190(34):305–319MATHMathSciNetCrossRef
40.
go back to reference 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 119:73–94MATHCrossRef 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 119:73–94MATHCrossRef
41.
go back to reference Kamran K, Rossi R, Oñate E, Idelshon SR (2013a) A compressible Lagrangian framework for modeling the fluid–structure interaction in the underwater implosion of an aluminum cylinder. Math Models Methods Appl Sci 23(02):339–367MATHMathSciNetCrossRef Kamran K, Rossi R, Oñate E, Idelshon SR (2013a) A compressible Lagrangian framework for modeling the fluid–structure interaction in the underwater implosion of an aluminum cylinder. Math Models Methods Appl Sci 23(02):339–367MATHMathSciNetCrossRef
42.
go back to reference Kamran K, Rossi R, Oñate E, Idelsohn SR (2013b) A compressible Lagrangian framework for the simulation of the underwater implosion of large air bubbles. Comput Methods Appl Mech Eng 255:210–225MATHCrossRef Kamran K, Rossi R, Oñate E, Idelsohn SR (2013b) A compressible Lagrangian framework for the simulation of the underwater implosion of large air bubbles. Comput Methods Appl Mech Eng 255:210–225MATHCrossRef
43.
go back to reference Lipton S, Evans JA, Bazilevs Y, Elguedj T, Hughes TJR (2010) Robustness of isogeometric structural discretizations under severe mesh distortion. Comput Methods Appl Mech Eng 199(5):357–373MATHCrossRef Lipton S, Evans JA, Bazilevs Y, Elguedj T, Hughes TJR (2010) Robustness of isogeometric structural discretizations under severe mesh distortion. Comput Methods Appl Mech Eng 199(5):357–373MATHCrossRef
44.
go back to reference Liu J (2014) Thermodynamically consistent modeling and simulation of multiphase flows. PhD Thesis, The University of Texas at Austin Liu J (2014) Thermodynamically consistent modeling and simulation of multiphase flows. PhD Thesis, The University of Texas at Austin
45.
go back to reference Liu J, Gomez H, Evans JA, Hughes TJR, Landis CM (2013) Functional entropy variables: a new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier–Stokes–Korteweg equations. J Comput Phys 248:47–86MathSciNetCrossRef Liu J, Gomez H, Evans JA, Hughes TJR, Landis CM (2013) Functional entropy variables: a new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier–Stokes–Korteweg equations. J Comput Phys 248:47–86MathSciNetCrossRef
46.
go back to reference Long CC, Marsden AL, Bazilevs Y (2013) Fluid–structure interaction simulation of pulsatile ventricular assist devices. Comput Mech 52:971–981MATHCrossRef Long CC, Marsden AL, Bazilevs Y (2013) Fluid–structure interaction simulation of pulsatile ventricular assist devices. Comput Mech 52:971–981MATHCrossRef
47.
go back to reference Long CC, Esmaily-Moghadam M, Marsden AL, Bazilevs Y (2014a) Computation of residence time in the simulation of pulsatile ventricular assist devices. Comput Mech 54:911–919MATHMathSciNetCrossRef Long CC, Esmaily-Moghadam M, Marsden AL, Bazilevs Y (2014a) Computation of residence time in the simulation of pulsatile ventricular assist devices. Comput Mech 54:911–919MATHMathSciNetCrossRef
48.
go back to reference Long CC, Marsden AL, Bazilevs Y (2014b) Shape optimization of pulsatile ventricular assist devices using FSI to minimize thrombotic risk. Comput Mech 54:921–932MATHMathSciNetCrossRef Long CC, Marsden AL, Bazilevs Y (2014b) Shape optimization of pulsatile ventricular assist devices using FSI to minimize thrombotic risk. Comput Mech 54:921–932MATHMathSciNetCrossRef
49.
go back to reference Penrose O, Fife PC (1990) Thermodynamically consistent models of phase-field type for the kinetic of phase transitions. Physica D 43(1):44–62MATHMathSciNetCrossRef Penrose O, Fife PC (1990) Thermodynamically consistent models of phase-field type for the kinetic of phase transitions. Physica D 43(1):44–62MATHMathSciNetCrossRef
50.
go back to reference Rallu ASD (2009) A multiphase fluid–structure computational framework for underwater implosion problems. PhD Thesis, Stanford University Rallu ASD (2009) A multiphase fluid–structure computational framework for underwater implosion problems. PhD Thesis, Stanford University
51.
go back to reference Sedzinski J, Biro M, Oswald A, Tinevez J-Y, Salbreux G, Paluch E (2011) Polar actomyosin contractility destabilizes the position of the cytokinetic furrow. Nature 476(7361):462–466CrossRef Sedzinski J, Biro M, Oswald A, Tinevez J-Y, Salbreux G, Paluch E (2011) Polar actomyosin contractility destabilizes the position of the cytokinetic furrow. Nature 476(7361):462–466CrossRef
52.
go back to reference Shao D, Levine H, Rappel W-J (2012) Coupling actin flow, adhesion, and morphology in a computational cell motility model. Proc Natl Acad Sci USA 109(18):6851–6856CrossRef Shao D, Levine H, Rappel W-J (2012) Coupling actin flow, adhesion, and morphology in a computational cell motility model. Proc Natl Acad Sci USA 109(18):6851–6856CrossRef
53.
go back to reference Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New YorkMATH Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New YorkMATH
54.
go back to reference Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid–structure interactions with large displacements. J Appl Mech 70:58–63MATHCrossRef Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid–structure interactions with large displacements. J Appl Mech 70:58–63MATHCrossRef
56.
go back to reference Suito H, Takizawa K, Huynh VQH, Sze D, Ueda T (2014) FSI analysis of the blood flow and geometrical characteristics in the thoracic aorta. Comput Mech 54:1035–1045MATHCrossRef Suito H, Takizawa K, Huynh VQH, Sze D, Ueda T (2014) FSI analysis of the blood flow and geometrical characteristics in the thoracic aorta. Comput Mech 54:1035–1045MATHCrossRef
57.
58.
go back to reference Takizawa K, Tezduyar TE (2014) Space–time computation techniques with continuous representation in time (ST-C). Comput Mech 53(1):91–99MATHMathSciNetCrossRef Takizawa K, Tezduyar TE (2014) Space–time computation techniques with continuous representation in time (ST-C). Comput Mech 53(1):91–99MATHMathSciNetCrossRef
59.
go back to reference Takizawa K, Bazilevs Y, Tezduyar TE (2012) Space–Time and ALE-VMS techniques for patient-specific cardiovascular Fluid–Structure Interaction modeling. Arch Comput Methods Eng 19(2):171–225MathSciNetCrossRef Takizawa K, Bazilevs Y, Tezduyar TE (2012) Space–Time and ALE-VMS techniques for patient-specific cardiovascular Fluid–Structure Interaction modeling. Arch Comput Methods Eng 19(2):171–225MathSciNetCrossRef
60.
go back to reference Takizawa K, Montes D, Fritze M, McIntyre S, Boben J, Tezduyar TE (2013a) Methods for FSI modeling of spacecraft parachute dynamics and cover separation. Math Models Methods Appl Sci 23:307–338MATHMathSciNetCrossRef Takizawa K, Montes D, Fritze M, McIntyre S, Boben J, Tezduyar TE (2013a) Methods for FSI modeling of spacecraft parachute dynamics and cover separation. Math Models Methods Appl Sci 23:307–338MATHMathSciNetCrossRef
61.
go back to reference Takizawa K, Montes D, McIntyre S, Tezduyar TE (2013b) Space–time VMS methods for modeling of incompressible flows at high Reynolds numbers. Math Models Methods Appl Sci 23:223–248 Takizawa K, Montes D, McIntyre S, Tezduyar TE (2013b) Space–time VMS methods for modeling of incompressible flows at high Reynolds numbers. Math Models Methods Appl Sci 23:223–248
62.
go back to reference Takizawa K, Tezduyar TE, Boben J, Kostov N, Boswell C, Buscher A (2013c) Fluid–structure interaction modeling of clusters of spacecraft parachutes with modified geometric porosity. Comput Mech 52(6):1351–1364MATHCrossRef Takizawa K, Tezduyar TE, Boben J, Kostov N, Boswell C, Buscher A (2013c) Fluid–structure interaction modeling of clusters of spacecraft parachutes with modified geometric porosity. Comput Mech 52(6):1351–1364MATHCrossRef
63.
go back to reference Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2013d) Patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms. Comput Mech 51:1061–1073MATHMathSciNetCrossRef Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2013d) Patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms. Comput Mech 51:1061–1073MATHMathSciNetCrossRef
64.
go back to reference Takizawa K, Takagi H, Tezduyar TE, Torii R (2014a) Estimation of element-based zero-stress state for arterial FSI computations. Comput Mech 54:895–910MATHMathSciNetCrossRef Takizawa K, Takagi H, Tezduyar TE, Torii R (2014a) Estimation of element-based zero-stress state for arterial FSI computations. Comput Mech 54:895–910MATHMathSciNetCrossRef
65.
go back to reference Takizawa K, Bazilevs Y, Tezduyar TE, Long CC, Marsden AL, Schjodt K (2014b) ST and ALE-VMS methods for patient-specific cardiovascular fluid mechanics modeling. Math Models Methods Appl Sci 24:2437–2486MATHMathSciNetCrossRef Takizawa K, Bazilevs Y, Tezduyar TE, Long CC, Marsden AL, Schjodt K (2014b) ST and ALE-VMS methods for patient-specific cardiovascular fluid mechanics modeling. Math Models Methods Appl Sci 24:2437–2486MATHMathSciNetCrossRef
66.
go back to reference Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C, Oiseth O, Mathisen KM, Kostov N, McIntyre S (2014c) Engineering analysis and design with ALE-VMS and space–time methods. Arch Comput Methods Eng, published online. doi:10.1007/s11831-014-9113-0 Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C, Oiseth O, Mathisen KM, Kostov N, McIntyre S (2014c) Engineering analysis and design with ALE-VMS and space–time methods. Arch Comput Methods Eng, published online. doi:10.​1007/​s11831-014-9113-0
67.
go back to reference Takizawa K, Tezduyar TE, Kolesar R, Boswell C, Kanai T, Montel K (2014d) Multiscale methods for gore curvature calculations from FSI modeling of spacecraft parachutes. Comput Mech, published online. doi:10.1007/s00466-014-1069-2 Takizawa K, Tezduyar TE, Kolesar R, Boswell C, Kanai T, Montel K (2014d) Multiscale methods for gore curvature calculations from FSI modeling of spacecraft parachutes. Comput Mech, published online. doi:10.​1007/​s00466-014-1069-2
68.
go back to reference Takizawa K, Tezduyar TE, Boswell C, Kolesar R, Montel K (2014e) FSI modeling of the reefed stages and disreefing of the Orion spacecraft parachutes. Comput Mech 54(5):1203–1220MATHMathSciNetCrossRef Takizawa K, Tezduyar TE, Boswell C, Kolesar R, Montel K (2014e) FSI modeling of the reefed stages and disreefing of the Orion spacecraft parachutes. Comput Mech 54(5):1203–1220MATHMathSciNetCrossRef
69.
go back to reference Takizawa K, Tezduyar TE, Buscher A, Asada S (2014f) Space–time fluid mechanics computation of heart valve models. Comput Mech 54:973–986MATHMathSciNetCrossRef Takizawa K, Tezduyar TE, Buscher A, Asada S (2014f) Space–time fluid mechanics computation of heart valve models. Comput Mech 54:973–986MATHMathSciNetCrossRef
70.
go back to reference Takizawa K, Tezduyar TE, Buscher A, Asada S (2014g) Space–time interface-tracking with topology change (ST-TC). Comput Mech 54(4):955–971MATHMathSciNetCrossRef Takizawa K, Tezduyar TE, Buscher A, Asada S (2014g) Space–time interface-tracking with topology change (ST-TC). Comput Mech 54(4):955–971MATHMathSciNetCrossRef
71.
go back to reference Takizawa K, Tezduyar TE, Kostov N (2014h) Sequentially-coupled space–time FSI analysis of bio-inspired flapping-wing aerodynamics of an MAV. Comput Mech 54:213–233MATHMathSciNetCrossRef Takizawa K, Tezduyar TE, Kostov N (2014h) Sequentially-coupled space–time FSI analysis of bio-inspired flapping-wing aerodynamics of an MAV. Comput Mech 54:213–233MATHMathSciNetCrossRef
72.
go back to reference Takizawa K, Tezduyar TE, McIntyre S, Kostov N, Kolesar R, Habluetzel C (2014i) Space–time VMS computation of wind-turbine rotor and tower aerodynamics. Comput Mech 53(1):1–15MATHCrossRef Takizawa K, Tezduyar TE, McIntyre S, Kostov N, Kolesar R, Habluetzel C (2014i) Space–time VMS computation of wind-turbine rotor and tower aerodynamics. Comput Mech 53(1):1–15MATHCrossRef
73.
go back to reference Takizawa K, Torii R, Takagi H, Tezduyar TE, Xu XY (2014j) Coronary arterial dynamics computation with medical-image-based time-dependent anatomical models and element-based zero-stress state estimates. Comput Mech 54:1047–1053MATHCrossRef Takizawa K, Torii R, Takagi H, Tezduyar TE, Xu XY (2014j) Coronary arterial dynamics computation with medical-image-based time-dependent anatomical models and element-based zero-stress state estimates. Comput Mech 54:1047–1053MATHCrossRef
74.
go back to reference Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8:83–130MATHCrossRef Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8:83–130MATHCrossRef
75.
go back to reference Tezduyar TE, Sathe S (2007) Modeling of fluid–structure interactions with the space–time finite elements: solution techniques. Int J Numer Methods Fluids 54:855–900MATHMathSciNetCrossRef Tezduyar TE, Sathe S (2007) Modeling of fluid–structure interactions with the space–time finite elements: solution techniques. Int J Numer Methods Fluids 54:855–900MATHMathSciNetCrossRef
76.
go back to reference Tezduyar TE, Behr M, Mittal S, Johnson AA (1992) Computation of unsteady incompressible flows with the finite element methods-space–time formulations, iterative strategies and massively parallel implementations. In: New methods in transient analysis, PVP-Vol. 246/AMD-Vol. 143. ASME, New York, pp 7–24 Tezduyar TE, Behr M, Mittal S, Johnson AA (1992) Computation of unsteady incompressible flows with the finite element methods-space–time formulations, iterative strategies and massively parallel implementations. In: New methods in transient analysis, PVP-Vol. 246/AMD-Vol. 143. ASME, New York, pp 7–24
77.
go back to reference Tezduyar TE, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26(10):27–36 Tezduyar TE, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26(10):27–36
78.
go back to reference Tezduyar TE, Sathe S, Keedy R, Stein K (2006a) Space–time finite element techniques for computation of fluid–structure interactions. Comput Methods Appl Mech Eng 195(17–18):2002–2027MATHMathSciNetCrossRef Tezduyar TE, Sathe S, Keedy R, Stein K (2006a) Space–time finite element techniques for computation of fluid–structure interactions. Comput Methods Appl Mech Eng 195(17–18):2002–2027MATHMathSciNetCrossRef
79.
go back to reference Tezduyar TE, Sathe S, Stein K (2006b) Solution techniques for the fully-discretized equations in computation of fluid–structure interactions with the space–time formulations. Comput Methods Appl Mech Eng 195:5743–5753MATHMathSciNetCrossRef Tezduyar TE, Sathe S, Stein K (2006b) Solution techniques for the fully-discretized equations in computation of fluid–structure interactions with the space–time formulations. Comput Methods Appl Mech Eng 195:5743–5753MATHMathSciNetCrossRef
80.
go back to reference Thiele U, Archer AJ, Robbins MJ, Gomez H, Knobloch E (2013) Localized states in the conserved Swift–Hohenberg equation with cubic nonlinearity. Phys Rev E 87(4):042915CrossRef Thiele U, Archer AJ, Robbins MJ, Gomez H, Knobloch E (2013) Localized states in the conserved Swift–Hohenberg equation with cubic nonlinearity. Phys Rev E 87(4):042915CrossRef
81.
go back to reference Turner SE (2007) Underwater implosion of glass spheres. J Acoust Soc Am 121(2):844–852CrossRef Turner SE (2007) Underwater implosion of glass spheres. J Acoust Soc Am 121(2):844–852CrossRef
82.
go back to reference van der Waals JD (1979) The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density. J Stat Phys 20(2):200–244CrossRef van der Waals JD (1979) The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density. J Stat Phys 20(2):200–244CrossRef
83.
go back to reference Vilanova G, Colominas I, Gomez H (2013) Capillary networks in tumor angiogenesis: from discrete endothelial cells to phase-field averaged descriptions via isogeometric analysis. Int J Numer Methods Biomed Eng 29(10):1015–1037MathSciNetCrossRef Vilanova G, Colominas I, Gomez H (2013) Capillary networks in tumor angiogenesis: from discrete endothelial cells to phase-field averaged descriptions via isogeometric analysis. Int J Numer Methods Biomed Eng 29(10):1015–1037MathSciNetCrossRef
84.
go back to reference Zhang Y, Bazilevs Y, Goswami S, Bajaj CL, Hughes TJR (2007) Patient-specific vascular NURBS modeling for Isogeometric Analysis of blood flow. Comput Methods Appl Mech Eng 196(2930):2943–2959MATHMathSciNetCrossRef Zhang Y, Bazilevs Y, Goswami S, Bajaj CL, Hughes TJR (2007) Patient-specific vascular NURBS modeling for Isogeometric Analysis of blood flow. Comput Methods Appl Mech Eng 196(2930):2943–2959MATHMathSciNetCrossRef
Metadata
Title
Interaction of complex fluids and solids: theory, algorithms and application to phase-change-driven implosion
Authors
Jesus Bueno
Carles Bona-Casas
Yuri Bazilevs
Hector Gomez
Publication date
01-06-2015
Publisher
Springer Berlin Heidelberg
Published in
Computational Mechanics / Issue 6/2015
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-014-1098-x

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