Explicit Coupling Schemes for a Fluid-Fluid Interaction Problem Arising in Hemodynamics

Fernández, Miguel Ángel; Gerbeau, Jean-Frédéric; Smaldone, Saverio

doi:10.1137/130948653

Cited by 15 publications

(8 citation statements)

References 31 publications

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“…Inspired by recent work on explicit coupling schemes [44], we employed a generalized Robin-like boundary condition to weakly prescribe velocity and traction fields at the interface Γ I . Among the advantages of such an approach is its independence from the solution strategy adopted in the full-scale simulation, thus making coupling possible, even between solvers using different finite element spaces (i.e.…”

Section: Methodsmentioning

confidence: 99%

Hemodynamics‐driven deposition of intraluminal thrombus in abdominal aortic aneurysms

Achille

Tellides

Humphrey

2016

Numer Methods Biomed Eng

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Accumulating evidence suggests that intraluminal thrombus plays many roles in the natural history of abdominal aortic aneurysms. There is, therefore, a pressing need for computational models that can describe and predict the initiation and progression of thrombus in aneurysms. In this paper, we introduce a phenomenological metric for thrombus deposition potential and use hemodynamic simulations based on medical images from six patients to identify best-fit values of the two key model parameters. We then introduce a shape optimization method to predict the associated radial growth of the thrombus into the lumen based on the expectation that thrombus initiation will create a thrombogenic surface, which in turn will promote growth until increasing hemodynamically induced frictional forces prevent any further cell or protein deposition. Comparisons between predicted and actual intraluminal thrombus in the six patient-specific aneurysms suggest that this phenomenological description provides a good first estimate of thrombus deposition. We submit further that, because the biologically active region of the thrombus appears to be confined to a thin luminal layer, predictions of morphology alone may be sufficient to inform fluid-solid-growth models of aneurysmal growth and remodeling.

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Section: Methodsmentioning

confidence: 99%

Hemodynamics‐driven deposition of intraluminal thrombus in abdominal aortic aneurysms

Achille

Tellides

Humphrey

2016

Numer Methods Biomed Eng

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“…Remark The coupling strategies between two subproblems may cause numerical instability due to the artificial energy transfer across the interface . Moreover, the weak formulation contains an interface term

\frac{1}{ρ} \int_{double-struckI} φ_{f} false({\overset{v}{true}}_{s} - {\overset{v}{true}}_{f} false) \cdot {\overset{n}{true}}_{d} d l

, which is difficult to control.…”

Section: Preliminaries Weak Formulation and Finite Element Spacesmentioning

confidence: 99%

“…Moreover, the weak formulation contains an interface term

\frac{1}{ρ} \int_{double-struckI} φ_{f} false({\overset{v}{true}}_{s} - {\overset{v}{true}}_{f} false) \cdot {\overset{n}{true}}_{d} d l

, which is difficult to control. To overcome this difficulty, we introduce a mesh dependent stabilization term

\frac{γ}{ρ h} \int_{double-struckI} false({\overset{u}{true}}_{s} - {\overset{u}{true}}_{f} false) \cdot {\overset{n}{true}}_{d} false({\overset{v}{true}}_{s} - {\overset{v}{true}}_{f} false) \cdot {\overset{n}{true}}_{d} d l

and a penalty parameter γ in the variational formulation . The stabilization term ensures the well‐posedness of the finite element algorithms.…”

Section: Preliminaries Weak Formulation and Finite Element Spacesmentioning

confidence: 99%

“…Then, we obtain a noniterative splitting of the originally coupled problem into three decoupled subproblems. On the other hand, the coupling feature of the model may cause numerical instability due to the artificial energy transfer across the interface . To overcome this difficulty, a stabilization term with a penalty parameter, which is essentially known as Nitsche's stabilization for interface problem, is added to ensure the existence and uniqueness of the finite element discretization of the dual‐porosity‐Stokes model .…”

Section: Introductionmentioning

confidence: 99%

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Coupled and decoupled stabilized mixed finite element methods for nonstationary dual‐porosity‐Stokes fluid flow model

Mahbub

Nasu

et al. 2019

Numerical Meth Engineering

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In this paper, we propose and analyze two stabilized mixed finite element methods for the dual-porosity-Stokes model, which couples the free flow region and microfracture-matrix system through four interface conditions on an interface. The first stabilized mixed finite element method is a coupled method in the traditional format. Based on the idea of partitioned time stepping, the four interface conditions, and the mass exchange terms in the dual-porosity model, the second stabilized mixed finite element method is decoupled in two levels and allows a noniterative splitting of the coupled problem into three subproblems. Due to their superior conservation properties and convenience of the computation of flux, mixed finite element methods have been widely developed for different types of subsurface flow problems in porous media. For the mixed finite element methods developed in this article, no Lagrange multiplier is used, but an interface stabilization term with a penalty parameter is added in the temporal discretization. This stabilization term ensures the numerical stability of both the coupled and decoupled schemes. The stability and the convergence analysis are carried out for both the coupled and decoupled schemes. Three numerical experiments are provided to demonstrate the accuracy, efficiency, and applicability of the proposed methods. KEYWORDS decoupled numerical methods, dual-porosity-Stokes model, horizontal wellbore, mixed finite elements, stabilization Int J Numer Methods Eng. 2019;120:803-833. wileyonlinelibrary.com/journal/nme 804 AL MAHBUB ET AL.model, It is not surprising that a great deal of effort has been devoted to develop appropriate numerical methods to solve the (Navier-)Stokes-Darcy fluid flow system, including coupled finite element methods, 17-21 domain decomposition methods, 22-31 Lagrange multiplier methods, 3,32,33 mortar finite element methods, 34,35 least-square methods, 36-38 partitioned time-stepping methods, 39,40 two-grid and multigrid methods, 41-44 discontinuous Galerkin finite element methods, 45-50 boundary integral methods, 51,52 and many others. [53][54][55][56][57][58] Although the traditional Stokes-Darcy model has been well studied, it has limitation to describe the heterogeneity of the porous medium which contains multiple porosities. It is worth to notice that the realistic naturally fractured reservoir consists of two coexisting and interacting medium, namely, tight matrix and microfractures. Furthermore, it is more important to characterize the intrinsic properties and accurately modeled the flow interactions between each medium. 59,60 The first multiporosity model was proposed by Barenblatt et al 61 for the naturally fractured reservoir in 1960 where the microfracture and matrix systems are formulated by individual but overlapping continua. Warren and Root 62 developed a homogeneous orthotropic dual-porosity model in 1963 based on the model proposed by Barenblatt. There are many applications for the dual-porosity model such as the geothermal system, hydrogeology, pe...

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“…This results in numerical instabilities [25]. To this point, Nitsches interface method is used to control the artificial energy transfers [26,27,28,29,17]. On the other hand, we need to consider how to solve the nonlinear term in Navier-Stokes equation.…”

Section: Introductionmentioning

confidence: 99%

Decoupled Modified Characteristic Finite Element Method with Different Subdomain Time Steps for Nonstationary Dual-Porosity-Navier-Stokes Model

Cao¹,

Li³

2020

Preprint

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In this paper, we develop the numerical theory of decoupled modified characteristic finite element method with different subdomain time steps for the mixed stabilized formulation of nonstationary dual-porosity-Navier-Stokes model. Based on partitioned time-stepping methods, the system is decoupled, which means that the Navier-Stokes equations and two different Darcy equations are solved independently at each time step of subdomain. In particular, the Navier-Stokes equations are solved by the modified characteristic finite element method, which overcome the computational difficulties caused by the nonlinear term. In order to increase the efficiency, different time steps are used to different subdomains. The stability of this method is proved. In addition, we verify the optimal L 2 -norm error convergence order of the solutions by mathematical induction, whose proof implies the uniform L ∞ -boundedness of the fully discrete velocity solution. Finally, some numerical tests are presented to show efficiency of the proposed method.

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Explicit Coupling Schemes for a Fluid-Fluid Interaction Problem Arising in Hemodynamics

Cited by 15 publications

References 31 publications

Hemodynamics‐driven deposition of intraluminal thrombus in abdominal aortic aneurysms

Hemodynamics‐driven deposition of intraluminal thrombus in abdominal aortic aneurysms

Coupled and decoupled stabilized mixed finite element methods for nonstationary dual‐porosity‐Stokes fluid flow model

Decoupled Modified Characteristic Finite Element Method with Different Subdomain Time Steps for Nonstationary Dual-Porosity-Navier-Stokes Model

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