Pressure drop matrix for a bifurcation with defects

Kozlov, Vladimir; Назаров, С. А.; Zavorokhin, G. L.

doi:10.32523/2306-6172-2019-7-3-33-55

Cited by 3 publications

(6 citation statements)

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“…In the case of the Dirichlet boundary condition we can prove a resolvent estimate on the imaginary axis (λ = iω, ω is real) with exponential weights independent on ω. In the case of the elastic boundary condition exponential weights depends on ω. Becuase of that we can not put in ( 16) the same exponential weight as in (13).…”

Section: Preliminariesmentioning

confidence: 97%

Modeling of Fluid Flow in a Flexible Vessel with Elastic Walls

Kozlov

Назаров

Zavorokhin

2021

J. Math. Fluid Mech.

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We exploit a two-dimensional model (Ghosh et al. in Q J Mech Appl Math 71(3):349–367, 2018; Kozlov and Nazarov in Dokl Phys 56(11):560–566, 2011, J Math Sci 207(2):249–269, 2015) describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue and the 3D fluid flow into account. We study time periodic flows in an infinite cylinder with such intricate boundary conditions. The main result is that solutions of this problem do not depend on the period and they are nothing else but the time independent Poiseuille flow. Similar solutions of the Stokes equations for the rigid wall (the no-slip boundary condition) depend on the period and their profile depends on time.

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Section: Preliminariesmentioning

confidence: 97%

Modeling of Fluid Flow in a Flexible Vessel with Elastic Walls

Kozlov

Назаров

Zavorokhin

2021

J. Math. Fluid Mech.

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“…Since we have in mind an application to the blood flow in the blood circulatory system, we are interested in periodic in time solutions. One of goals of this paper is to describe all periodic solutions to the problem (3), (4), (9) which are bounded in R × C ∋ (t, x).…”

Section: Preliminariesmentioning

confidence: 99%

Modeling of fluid flow in a flexible vessel with elastic walls

Kozlov,

Nazarov,

Zavorokhin

2021

Preprint

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We exploit a two-dimensional model [7], [6] and [1] describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue and the 3D fluid flow into account. We study time periodic flows in a cylinder with such compound boundary conditions. The main result is that solutions of this problem do not depend on the period and they are nothing else but the time independent Poiseuille flow. Similar solutions of the Stokes equations for the rigid wall (the no-slip boundary condition) depend on the period and their profile depends on time.

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“…Now we prove the existence and uniqueness of weak solutions to the boundary value problem (1.1)-(1.2), cf. [12].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…This is achieved by using classical shape optimization techniques. The pressure drop matrix was introduced in [12,18] as an integral characteristic of a junction of several pipes with absolutely rigid walls. It appears that the elements of this matrix are included in the modified Kirchhoff transmission conditions, which describe more adequately the total pressure loss at the bifurcation point of the flow passed through the corresponding junction of the pipes, see [3,9,10].…”

Section: Introductionmentioning

confidence: 99%

“…In Section 1, we consider the Stokes system in an unbounded domain with cylindrical outlets to infinity (see, e.g., [1,2,4,14,21]) and prove the unique solvability of the problem stated in the class of "energy" solutions, see [12] for details. For obtaining the asymptotic behavior of the solution, we exploit special homogeneous solutions to the Stokes problem with non-zero flux and with a linear growth in the pressure at infinity (see [18]).…”

Section: Introductionmentioning

confidence: 99%

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A Mathematical Model of an Arterial Bifurcation

Zavorokhin

2019

UMJ

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An asymptotic model of an arterial bifurcation is presented. We propose a simple approximate method of calculation of the pressure drop matrix. The entries of this matrix are included in the modified transmission conditions, which were introduced earlier by Kozlov and Nazarov, and which give better approximation of 3D flow by 1D flow near a bifurcation of an artery as compared to the classical Kirchhoff conditions. The present modeling takes into account the heuristic Murrey cubic law.

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Pressure drop matrix for a bifurcation with defects

Cited by 3 publications

References 0 publications

Modeling of Fluid Flow in a Flexible Vessel with Elastic Walls

Modeling of Fluid Flow in a Flexible Vessel with Elastic Walls

Modeling of fluid flow in a flexible vessel with elastic walls

A Mathematical Model of an Arterial Bifurcation

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