DISCOVERY l REPORT ISSN 2278–5469 EISSN 2278–5450 l OPEN ACCESS Page225 Modeling blood flow with unilateral stenosis based on interpenetration model Umurdin Dalabaev ABSTRACT The paper deals with the numerical simulation of the flow of Newtonian fluid by the control volume method, which simulates the flow of blood in a blood vessel with stenosis. An interpenetrating model of two-phase media is used to describe the process. Based on this model, under appropriate simplifying assumptions, we obtain the Navier-Stokes equations in the free (outside the stenosis region) zone, and in the stenotic region, we obtain a system of equations generalizing the filtration equation. Stenosis is viewed as a porous medium. The influence of the Reynolds number and the degree of stenosis on the nature of the flow on the behavior of blood is investigated. Keywords: Blood flow; stenosis; Navier-Stokes equation INTRODUCTION Arterial stenosis occurs due to the deposition of cholesterol on its walls. Stenoses restrict blood flow. This change in blood flow caused by stenosis can lead to the development of arterial disease and arterial deformity. With stenosis of the artery, the nature of the blood flow in the lower part of the artery changes significantly. These changes are highly dependent on the degree of stenosis. Due to the presence of moderate or severe stenosis in the lower course, the course is severely disrupted and, therefore, the course becomes unevenly complex. Many studies have been investigated to understand the nature of blood flow disturbances in stenosis. Both experimental and numerical methods have been used by various researchers to determine the development of stenosis and its magnitude [1-4]. It is assumed here that the movement in the vessels is laminar. To simulate the flow of blood in vessels with stenosis, we use an interpenetrating model. We consider stenosis as the second phase in an interpenetrating model for describing heterogeneous media with a fixed zero velocity. The area free from stenosis, the blood flow is described by the Navier-Stokes equations. We represent stenosis as a porous medium. Flow description model Consider an interpenetrating model describing the flows of two-phase media in a Cartesian coordinate system (two-dimensional problem) [6-7]: DISCOVERY 57(303), March, 2021 To Cite: Umurdin Dalabaev. Modeling blood flow with unilateral stenosis based on interpenetration model. Discovery, 2021, 57(303), 225-229 Author Affiliation: University of World Economy and Diplomacy, Uzbekistan E-mail: udalabaev@mail.ru Peer-Review History Received: 19 December 2020 Reviewed & Revised: 20/December/2020 to 30/January/2021 Accepted: 31 January 2021 Published: March 2021 Peer-review External peer-review was done through double-blind method. Publication License © The Author(s) 2021. Open Access. This article is licensed under a Creative Commons Attribution License 4.0 (CC BY 4.0)., which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. DISCOVERY SCIENTIFIC SOCIETY