Fluid-Structure Interaction with Incompressible Fluids

Čanić, Sunčica

doi:10.1007/978-3-030-54899-5_2

Cited by 2 publications

(2 citation statements)

References 66 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The existence of such a maximal domain Ω M f , namely the existence of M (x), follows by arguments similar to [91,Lemma 2.5] and [90,Lemma 4.5], established in the context of incompressible FSI. Once the maximal fluid domain is defined, we can extend the fluid velocities u n N from Ω n f ,N to this common maximal domain Ω M f , using extensions by zero in Ω M f ∩ (Ω n f ,N ) c .…”

Section: Compactness For the Regularized Problemmentioning

confidence: 88%

“…Therefore, for each fixed N , we can consider the semidiscrete formulation with the test function v N , which we emphasize is discontinuous in time, due to the jumps in ω N at each n∆t . To pass to the limit as N → ∞ we can use the same approach as in [3, Lemma 7.1] and [91,Lemma 2.8], to obtain the following strong convergence results of the velocity test functions v N and their gradients, which will allow us to pass to the limit in the semidiscrete weak formulations:…”

Section: Passing To the Limitmentioning

confidence: 99%

See 1 more Smart Citation

Existence of a weak solution to a regularized moving boundary fluid-structure interaction problem with poroelastic media

Kuan¹,

Čanić²,

Muha³

2024

Comptes Rendus. Mécanique

Self Cite

View full text Add to dashboard Cite

We study the existence of a weak solution to a regularized, moving boundary, fluid-structure interaction problem with multi-layered poroelastic media consisting of a reticular plate located at the interface between the free flow of an incompressible, viscous fluid modeled by the 2D Navier-Stokes equations, and a poroelastic medium modeled by the 2D Biot equations. The existence result holds for both the elastic and viscoelastic Biot model. The free fluid flow and the poroelastic medium are coupled via the moving interface (the reticular plate) through the kinematic and dynamic coupling conditions. The reticular plate is "transparent" to fluid flow. The nonlinear coupling over the moving interface presents a major difficulty since both the fluid domain and the poroelastic medium domain are functions of time, and the finite energy spaces do not provide sufficient regularity for the corresponding weak formulation to be well-defined. This is why in this manuscript we consider a regularized problem by employing convolution with a smooth kernel only where needed. The resulting problem is still very challenging due to the nonlinear coupling and the motion of the fluid and Biot domains. We provide a constructive existence proof for this regularized fluid-poroelastic structure interaction problem. This regularized problem is consistent with the original, nonregularized problem in the sense that the weak solutions constructed here, converge, as the regularization parameter tends to zero, to a classical solution of the original, nonregularized problem when such a classical solution exists, assuming viscoelasticity in the Biot poroelastic matrix [1]. Furthermore, the existence result presented in this manuscript, is a crucial stepping stone for the singular limit problem in which the thickness of the reticular plate tends to zero. Namely, in [1] we will show that, in the case of a Biot poroviscoelastic matrix, the moving boundary problem obtained in the singular limit as the thickness of the plate tends to zero, has a weak solution.

show abstract

Section: Compactness For the Regularized Problemmentioning

confidence: 88%

Section: Passing To the Limitmentioning

confidence: 99%

Existence of a weak solution to a regularized moving boundary fluid-structure interaction problem with poroelastic media

Kuan¹,

Čanić²,

Muha³

2024

Comptes Rendus. Mécanique

Self Cite

View full text Add to dashboard Cite

show abstract

Computational analysis of the impact of aortic bifurcation geometry to AAA haemodynamics

Tikhvinskii

Merzhoeva

Чупахин

et al. 2022

Russian Journal of Numerical Analysis and Mathematical Modelling

View full text Add to dashboard Cite

Abdominal aortic aneurysm is a widespread disease of cardiovascular system. Predicting a moment of its rupture is an important task for modern vascular surgery. At the same time, little attention is paid to the comorbidities, which are often the causes of severe postoperative complications or even death. This work is devoted to a numerical study of the haemodynamics of the model geometry for possible localizations of abdominal aortic aneurysm: on the aortic trunk or on its bifurcation. Both rigid and FSI numerical simulations are considered and compared with the model aortic configuration without aneurysm. It is shown that in the case of localization of the aneurysm on the bifurcation, the pressure in aorta increases upstream. Moreover, only in the case of a special geometry,when the radii of the iliac arteries are equal (r 1 = r 2), and the angle between them is 60 degrees, there is a linear relationship between the pressure in the aorta above the aneurysm and the size of the aneurysm itself: the slope of the straight line is in the interval a ∈ (0.003; 0.857), and the coefficient of determination is R 2 ⩾ 0.75. The area bounded by the curve of the ‘pressure–velocity’ diagram for the values of velocity and pressure upstream in the presence of an aneurysm decreases compared to a healthy case (a vessel without an aneurysm). The simulation results in the rigid and FSI formulations agree qualitatively with each other. The obtained results provide a better understanding of the relationship between the geometrical parameters of the aneurysm and the changing of haemodynamics in the aortic bifurcation and its effect on the cardiovascular system upstream of the aneurysm.

show abstract

Fluid-Structure Interaction with Incompressible Fluids

Cited by 2 publications

References 66 publications

Existence of a weak solution to a regularized moving boundary fluid-structure interaction problem with poroelastic media

Existence of a weak solution to a regularized moving boundary fluid-structure interaction problem with poroelastic media

Computational analysis of the impact of aortic bifurcation geometry to AAA haemodynamics

Contact Info

Product

Resources

About