A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method

Jansen, Kenneth E.; Whiting, Christian H.; Hulbert, Gregory M.

doi:10.1016/s0045-7825(00)00203-6

Cited by 723 publications

(614 citation statements)

References 18 publications

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“…The methodology applies equally well to laminar and turbulent flows and is thus attractive for applications where the nature of the flow solution is not known a priori. The time-dependent discrete equations are solved using the generalized-α time integrator proposed in Chung and Hulbert (1993) for the equations of structural mechanics, developed in Jansen et al (1999) for fluid dynamics, and further extended in Bazilevs et al (2008) to fluid-structure interaction. A monolithic solution strategy is adopted in Fig.…”

Section: Discretization and Solution Strategiesmentioning

confidence: 99%

Computational vascular fluid–structure interaction: methodology and application to cerebral aneurysms

Bazilevs

Hsu

Zhang

et al. 2010

Biomech Model Mechanobiol

235

132

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A computational vascular fluid-structure interaction framework for the simulation of patient-specific cerebral aneurysm configurations is presented. A new approach for the computation of the blood vessel tissue prestress is also described. Simulations of four patient-specific models are carried out, and quantities of hemodynamic interest such as wall shear stress and wall tension are studied to examine the relevance of fluid-structure interaction modeling when compared to the rigid arterial wall assumption. We demonstrate that flexible wall modeling plays an important role in accurate prediction of patient-specific hemodynamics. Discussion of the clinical relevance of our methods and results is provided.

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Section: Discretization and Solution Strategiesmentioning

confidence: 99%

Computational vascular fluid–structure interaction: methodology and application to cerebral aneurysms

Bazilevs

Hsu

Zhang

et al. 2010

Biomech Model Mechanobiol

235

132

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“…The key idea for first-order schemes has been convex-splitting, however, this idea is not sufficient for second-order schemes, and one has to resort to particular double-well potentials, modified energy statements and/or stabilization. There are also other popular methods that can be used, such as the generalized-α algorithm (Jansen et al, 2000), for which little is known about their stability properties in case of phase-field models.…”

Section: Discussionmentioning

confidence: 99%

“…Such terms are also referred to as artificial viscosity, and are useful in many applications; see e.g., (Labovsky et al, 2009;Jansen et al, 2000). See also (Gomez and Hughes, 2011) for a stabilization of the extended Crank-Nicolson method.…”

Section: Second-order Convex Splittingmentioning

confidence: 99%

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Computational Phase‐Field Modeling

Gómez

Zee

2017

Encyclopedia of Computational Mechanics Second Edition

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Phase-field modeling is emerging as a promising tool for the treatment of problems with interfaces. The classical description of interface problems requires the numerical solution of partial differential equations on moving domains in which the domain motions are also unknowns. The computational treatment of these problems requires moving meshes and is very difficult when the moving domains undergo topological changes. Phase-field modeling may be understood as a methodology to reformulate interface problems as equations posed on fixed domains. In some cases, the phase-field model may be shown to converge to the moving-boundary problem as a regularization parameter tends to zero, which shows the mathematical soundness of the approach. However, this is only part of the story because phase-field models do not need to have a moving-boundary problem associated and can be rigorously derived from classical thermomechanics. In this context, the distinguishing feature is that constitutive models depend on the variational derivative of the free energy. In all, phase-field models open the opportunity for the efficient treatment of outstanding problems in computational mechanics, such as, the interaction of a large number of cracks in three dimensions, cavitation, film and nucleate boiling, tumor growth or fully three-dimensional air-water flows with surface tension. In addition, phase-field models bring a new set of challenges for numerical discretization that will excite the computational mechanics community.

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“…A residual-based variational multi-scale method [18] was implemented to solve the system of equations, using a Newton -Raphson procedure with a multi-stage predictorcorrector algorithm applied at each time step. The generalized2 a method [46,47], an implicit second-order time-accurate method that is also unconditionally stable, was used for time advancement. Readers are referred to the numerical procedures described in [17,25,45,48,49] for further details.…”

Section: Solution Approachmentioning

confidence: 99%

Magnetic resonance imaging-based computational modelling of blood flow and nanomedicine deposition in patients with peripheral arterial disease

Hossain

Zhang

et al. 2015

J. R. Soc. Interface.

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Peripheral arterial disease (PAD) is generally attributed to the progressive vascular accumulation of lipoproteins and circulating monocytes in the vessel walls leading to the formation of atherosclerotic plaques. This is known to be regulated by the local vascular geometry, haemodynamics and biophysical conditions. Here, an isogeometric analysis framework is proposed to analyse the blood flow and vascular deposition of circulating nanoparticles (NPs) into the superficial femoral artery (SFA) of a PAD patient. The local geometry of the blood vessel and the haemodynamic conditions are derived from magnetic resonance imaging (MRI), performed at baseline and at 24 months post intervention. A dramatic improvement in blood flow dynamics is observed post intervention. A 500% increase in peak flow rate is measured in vivo as a consequence of luminal enlargement. Furthermore, blood flow simulations reveal a 32% drop in the mean oscillatory shear index, indicating reduced disturbed flow post intervention. The same patient information (vascular geometry and blood flow) is used to predict in silico in a simulation of the vascular deposition of systemically injected nanomedicines. NPs, targeted to inflammatory vascular molecules including VCAM-1, E-selectin and ICAM-1, are predicted to preferentially accumulate near the stenosis in the baseline configuration, with VCAM-1 providing the highest accumulation (approx. 1.33 and 1.50 times higher concentration than that of ICAM-1 and E-selectin, respectively). Such selective deposition of NPs within the stenosis could be effectively used for the detection and treatment of plaques forming in the SFA. The presented MRI-based computational protocol can be used to analyse data from clinical trials to explore possible correlations between haemodynamics and disease progression in PAD patients, and potentially predict disease occurrence as well as the outcome of an intervention.

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A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method

Cited by 723 publications

References 18 publications

Computational vascular fluid–structure interaction: methodology and application to cerebral aneurysms

Computational vascular fluid–structure interaction: methodology and application to cerebral aneurysms

Computational Phase‐Field Modeling

Magnetic resonance imaging-based computational modelling of blood flow and nanomedicine deposition in patients with peripheral arterial disease

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