Application of a locally conservative Galerkin (LCG) method for modelling blood flow through a patient‐specific carotid bifurcation

Bevan, Rhodri L. T.; Nithiarasu, Perumal; Loon, Raoul van; Sazonov, Igor; Luckraz, Heyman; Garnham, Andrew

doi:10.1002/fld.2313

Cited by 19 publications

(20 citation statements)

References 65 publications

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“…We note that Equation (28) has been derived by assuming that the viscous-flux jump terms across inter-element borders are negligible. We also note that the last term of that equation, in its original form in [52], was written as a global integral Q n rather than a series of element-level integrals.…”

Section: Remark 13mentioning

confidence: 99%

Space–time fluid–structure interaction modeling of patient‐specific cerebral aneurysms

Tezduyar

Takizawa

Brummer

et al. 2011

Numer Methods Biomed Eng

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SUMMARYWe provide an extensive overview of the core and special techniques developed earlier by the Team for Advanced Flow Simulation and Modeling (T AFSM) for space-time fluid-structure interaction (FSI) modeling of patient-specific cerebral aneurysms. The core FSI techniques are the Deforming-SpatialDomain/Stabilized Space-Time (DSD/SST) formulation and the stabilized space-time FSI (SSTFSI) technique. The special techniques include techniques for calculating an estimated zero-pressure (EZP) arterial geometry, a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape, techniques for using variable arterial wall thickness, mesh generation techniques for building layers of refined fluid mechanics mesh near the arterial walls, a recipe for pre-FSI computations that improve the convergence of the FSI computations, the Sequentially-Coupled Arterial FSI (SCAFSI) technique and its multiscale versions, techniques for the projection of fluid-structure interface stresses, calculation of the wall shear stress (WSS) and calculation of the oscillatory shear index (OSI) and arterial-surface extraction and boundary condition techniques. We show how these techniques work with results from earlier computations. We also describe the arterial FSI techniques developed and implemented recently by the T AFSM and present a sample from a wide set of patient-specific cerebral-aneurysm models we computed recently.

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Section: Remark 13mentioning

confidence: 99%

Space–time fluid–structure interaction modeling of patient‐specific cerebral aneurysms

Tezduyar

Takizawa

Brummer

et al. 2011

Numer Methods Biomed Eng

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“…A mesh is deemed valid for blood flow simulations if it allows recovery of outputs of physical interest. In arteries, the mesh should be fine enough to capture wall shear stress (WSS) (Celik et al 2008) and, to this end, the construction of a boundary layer mesh is essential, even at low Reynolds numbers (Bevan et al 2010). Here WSS expresses the magnitude of tangential viscous forces exerted by the fluid on the lumen boundary Σ t , defined by…”

Section: Building the Computational Meshmentioning

confidence: 99%

The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications

Quarteroni

Manzoni

Vergara³

2017

Acta Numerica

182

125

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Mathematical and numerical modelling of the cardiovascular system is a research topic that has attracted remarkable interest from the mathematical community because of its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. In this review article we will address the two principal components of the cardiovascular system: arterial circulation and heart function. We will systematically describe all aspects of the problem, ranging from data imaging acquisition, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, proposing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiocirculatory system, the multiscale nature of the physiological processes involved, and the need to devise computational methods that are stable, reliable and efficient. Critical issues involve filtering the data, identifying the parameters of mathematical models, devising optimal treatments and accounting for uncertainties. For this reason, we will devote the last part of the paper to control and inverse problems, including parameter estimation, uncertainty quantification and the development of reduced-order models that are of paramount importance when solving problems with high complexity, which would otherwise be out of reach.

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“…The genesis of such aneurysms is still the subject of intensive discussions, but it is generally accepted that mechanical factors play a fundamental role beside genetics and other risk factors . Over the last years, the influence of mechanical factors on both the growth and rupture risk of aneurysms have been investigated intensively by computational methods (see, e.g., ). The complexity of such numerical simulations increase dramatically, if blood flow through the vessel is included into the modeling process to evaluate, for example, the influence of shear stress on the wall of the artery or to compute exact time‐depending hydro‐static pressure levels.…”

Section: Numerical Examplesmentioning

confidence: 99%

A dual mortar approach for mesh tying within a variational multiscale method for incompressible flow

Ehrl

Popp

Gravemeier

et al. 2014

Numerical Methods in Fluids

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SUMMARY In the present work, the coupling of computational subdomains with non‐conforming discretizations is addressed in the context of residual‐based variational multiscale finite element methods for incompressible fluid flow. A mortar method using dual Lagrange multipliers is introduced for handling the coupling conditions at arbitrary fluid–fluid interfaces. Recently, mortar methods have been successfully applied in the field of nonlinear solid mechanics, for example, to weakly impose interface constraints for finite deformation contact. The focus of this study is on both the integration of the dual mortar approach into an existing variational multiscale finite element framework and the investigation of the resulting interplay between variational multiscale and coupling terms. We analyze the effects of either constraining only velocity or both velocity and pressure degrees of freedom at the internal interfaces using dual Lagrange multipliers. In analogy to other problem classes, we exploit the fact that the dual mortar approach allows for an efficient condensation of the additional Lagrange multiplier degrees of freedom from the global system of equations. As a result, the typical but often undesirable saddle‐point structure of this system is completely removed. The proposed method is validated numerically for various three‐dimensional examples, including a complex patient‐specific aneurysm, and its accuracy and efficiency in comparison with standard conforming discretizations is demonstrated. Copyright © 2014 John Wiley & Sons, Ltd.

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Application of a locally conservative Galerkin (LCG) method for modelling blood flow through a patient‐specific carotid bifurcation

Cited by 19 publications

References 65 publications

Space–time fluid–structure interaction modeling of patient‐specific cerebral aneurysms

Space–time fluid–structure interaction modeling of patient‐specific cerebral aneurysms

The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications

A dual mortar approach for mesh tying within a variational multiscale method for incompressible flow

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