Comparison of inviscid and viscid one-dimensional models of blood flow in arteries

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Comparison of inviscid and viscid one-dimensional models of blood flow in arteries. / Krivovichev, Gerasim V. .

In: Applied Mathematics and Computation, Vol. 418, 126856, 01.04.2022.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{100591105a93424c87e1ff21878f84f9,

title = "Comparison of inviscid and viscid one-dimensional models of blood flow in arteries",

abstract = "The paper is devoted to the comparison of one-dimensional blood flow models in application to the solution of model problems. In the viscid case, the non-Newtonian properties of blood are considered. Original one-dimensional models, based on the Carreau, Carreau–Yasuda, Cross, and Powell–Eyring rheological models, are constructed by the averaging of the Navier–Stokes equations. The approach to the analytical solution of problems in the inviscid case is proposed. The originality of the method is based on the small perturbation of the initial rest state, corresponding to zero velocity. It leads to the solution of the linear wave equations. The solutions of three problems — for the infinite, semi-infinite, and finite intervals are obtained. The examples are presented for the small parameter value ∼10−2. Analytical solutions are used for the comparison of different one-dimensional models of blood flow, where the viscosity (Newtonian and non-Newtonian) is considered. The problems for the viscid models are solved numerically by the third-order WENO scheme. As the results of the comparison of models, the effects of the viscosity and velocity profile are analyzed. From a practical viewpoint, the solutions obtained by the perturbation method can be used for the testing of programs for numerical simulations and for the comparison of different blood flow models.",

keywords = "Blood flow, Hemodynamics, Non-Newtonian fluid, One-dimensional model",

author = "Krivovichev, {Gerasim V.}",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2022",

month = apr,

day = "1",

doi = "10.1016/j.amc.2021.126856",

language = "English",

volume = "418",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Comparison of inviscid and viscid one-dimensional models of blood flow in arteries

AU - Krivovichev, Gerasim V.

PY - 2022/4/1

Y1 - 2022/4/1

N2 - The paper is devoted to the comparison of one-dimensional blood flow models in application to the solution of model problems. In the viscid case, the non-Newtonian properties of blood are considered. Original one-dimensional models, based on the Carreau, Carreau–Yasuda, Cross, and Powell–Eyring rheological models, are constructed by the averaging of the Navier–Stokes equations. The approach to the analytical solution of problems in the inviscid case is proposed. The originality of the method is based on the small perturbation of the initial rest state, corresponding to zero velocity. It leads to the solution of the linear wave equations. The solutions of three problems — for the infinite, semi-infinite, and finite intervals are obtained. The examples are presented for the small parameter value ∼10−2. Analytical solutions are used for the comparison of different one-dimensional models of blood flow, where the viscosity (Newtonian and non-Newtonian) is considered. The problems for the viscid models are solved numerically by the third-order WENO scheme. As the results of the comparison of models, the effects of the viscosity and velocity profile are analyzed. From a practical viewpoint, the solutions obtained by the perturbation method can be used for the testing of programs for numerical simulations and for the comparison of different blood flow models.

AB - The paper is devoted to the comparison of one-dimensional blood flow models in application to the solution of model problems. In the viscid case, the non-Newtonian properties of blood are considered. Original one-dimensional models, based on the Carreau, Carreau–Yasuda, Cross, and Powell–Eyring rheological models, are constructed by the averaging of the Navier–Stokes equations. The approach to the analytical solution of problems in the inviscid case is proposed. The originality of the method is based on the small perturbation of the initial rest state, corresponding to zero velocity. It leads to the solution of the linear wave equations. The solutions of three problems — for the infinite, semi-infinite, and finite intervals are obtained. The examples are presented for the small parameter value ∼10−2. Analytical solutions are used for the comparison of different one-dimensional models of blood flow, where the viscosity (Newtonian and non-Newtonian) is considered. The problems for the viscid models are solved numerically by the third-order WENO scheme. As the results of the comparison of models, the effects of the viscosity and velocity profile are analyzed. From a practical viewpoint, the solutions obtained by the perturbation method can be used for the testing of programs for numerical simulations and for the comparison of different blood flow models.

KW - Blood flow

KW - Hemodynamics

KW - Non-Newtonian fluid

KW - One-dimensional model

UR - http://www.scopus.com/inward/record.url?scp=85121120415&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2021.126856

DO - 10.1016/j.amc.2021.126856

M3 - Article

AN - SCOPUS:85121120415

VL - 418

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

M1 - 126856

ER -

ID: 89961619