共查询到20条相似文献，搜索用时 15 毫秒
1.
Hossein Tamim Abbas Abbassi Nasser Fatouraee 《Mathematical Methods in the Applied Sciences》2020,43(8):5579-5601
Abnormal accumulation of macromolecules such as low-density lipoproteins (LDLs) in the arterial wall causes narrowing and blockage of vessels, which leads to atherosclerosis. Effects of pulsatile nature of blood flows as well as the initial length on transport of the LDL species in the arterial boundary layer region are analyzed numerically in the present work. The set of governing equations consisting of continuity, Navier-Stokes, and species transport is solved using a projection method based on the second-order central difference discretization. The obtained results are in excellent agreement with the pertinent data. The computational results imply that the flow field and concentration distribution are time dependent but the variation of the filtration velocity can be ignored. The LDL concentration boundary layer thickness decreases in the outer part and increases in the inner part for both with or without straight length. Presence of initial straight length generates about 26% growth in the boundary layer thickness, although its effect on the LDL surface concentration (LSC) is negligible. The maximum LSC is related to the regions with minimum wall shear stress in the inner part of the curved artery, which have more potential for formation of atherosclerosis. A new numerical correlation between the LSC and boundary layer thickness is proposed and examined. 相似文献
2.
Subrata Mukhopadhyay Mani Shankar Mandal Swati Mukhopadhyay 《Mathematical Methods in the Applied Sciences》2019,42(2):488-504
The objective of the present study is to investigate the effects of variable viscosity on incompressible laminar pulsatile flow of blood through an overlapping doubly constricted tapered artery. To mimic the realistic situation, wall of the artery is taken to be flexible, and physiologically relevant pulsatile flow is introduced. The governing equations of blood flow are made dimensionless. A coordinate transformation is used to make the overlapping doubly constricted wall geometry of tube to a straight tube. Taking advantage of the Stream function–Vorticity formulation, the system of partial differential equations is then solved numerically by finite difference approximations. Effects of Reynolds number, Strouhal number, degree of contraction, tapering angle, and viscosity parameters are presented graphically and analyzed. The results show that formation of stenosis and tapering disturb the flow field significantly, and degree of stenosis is more important in influencing blood flow compared with tapering. 相似文献
3.
Determination of arterial wall shear stress 总被引：4，自引：0，他引：4
The arteries can remodel their structure and function to adapt themselves to the mechanical environment. In various factors
that lead to vascular remodeling, the shear stress on the arterial wall induced by the blood flow is of great importance.
However, there are many technique difficulties in measuring the wall shear stress directly at present. In this paper, through
analyzing the pulsatile blood flow in arteries, a method has been proposed that can determine the wall shear stress quantitatively
by measuring the velocity on the arterial axis, and that provides a necessary means to discuss the influence of arterial wall
shear stress on vascular remodeling. 相似文献
4.
In this paper, we propose a spectral method for the vorticity‐stream function form of the Navier–Stokes equations with slip boundary conditions. The numerical solutions fulfill the incompressibility and the physical boundary conditions automatically. The stability and convergence of the proposed methods are proven. Numeric results demonstrate the efficiency of suggested algorithm. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
5.
Jian Li 《计算数学(英文版)》1999,17(4):419-424
1.IntroductionFOrsemi-periodicincompressiblefluidflows,S.C.R.Dennisandco-workers[1--4]solvethevorticity-streamfunctionformulationofthegoverningequationsbytheseriestruncationandfinitedifferencemethod.Sincenoboundaryconditionforthevorticity,theypropose... 相似文献
6.
Physiological pulsatile flow in a 3D model of arterial stenosis is investigated by using large eddy simulation (LES) technique. The computational domain chosen is a simple channel with a biological type stenosis formed eccentrically on the top wall. The physiological pulsation is generated at the inlet using the first harmonic of the Fourier series of pressure pulse. In LES, the large scale flows are resolved fully while the unresolved subgrid scale (SGS) motions are modelled using a localized dynamic model. Due to the narrowing of artery the pulsatile flow becomes transition-to-turbulent in the downstream region of the stenosis, where a high level of turbulent fluctuations is achieved, and some detailed information about the nature of these fluctuations are revealed through the investigation of the turbulent energy spectra. Transition-to-turbulent of the pulsatile flow in the post stenosis is examined through the various numerical results such as velocity, streamlines, velocity vectors, vortices, wall pressure and shear stresses, turbulent kinetic energy, and pressure gradient. A comparison of the LES results with the coarse DNS are given for the Reynolds number of 2000 in terms of the mean pressure, wall shear stress as well as the turbulent characteristics. The results show that the shear stress at the upper wall is low just prior to the centre of the stenosis, while it is maximum in the throat of the stenosis. But, at the immediate post stenotic region, the wall shear stress takes the oscillating form which is quite harmful to the blood cells and vessels. In addition, the pressure drops at the throat of the stenosis where the re-circulated flow region is created due to the adverse pressure gradient. The maximum turbulent kinetic energy is located at the post stenosis with the presence of the inertial sub-range region of slope −5/3. 相似文献
7.
T. Abboud M. Salaün S. Salmon 《Numerical Methods for Partial Differential Equations》2004,20(5):765-788
We consider the bidimensional Stokes problem for incompressible fluids in stream function‐vorticity form. The classical finite element method of degree one usually used does not allow the vorticity on the boundary of the domain to be computed satisfactorily when the meshes are unstructured and does not converge optimally. To better approach the vorticity along the boundary, we propose that harmonic functions obtained by integral representation be used. Numerical results are very satisfactory, and we prove that this new numerical scheme leads to an optimal convergence rate of order 1 for the natural norm of the vorticity and, under higher regularity assumptions, from 3/2 to 2 for the quadratic norm of the vorticity. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004. 相似文献
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动脉中的血液流动被分解为平衡状态(相当于平均压定常流状态)和叠加在平衡状态上的周期脉动流,利用Fung的血管应变能密度函数分析血管壁在平衡状态下的应力-应变关系,确定相对于平衡状态血管作微小变形所对应的周向弹性模量和轴向弹性模量,并建立在脉动压力作用下相应的管壁运动方程,与线性化Navier-Stokes方程联立,求得血液流动速度和血管壁位移的分析表达式,详细讨论血管壁周向和轴向弹性性质差异对脉博波、血液脉动流特性以及血管壁运动的影响. 相似文献
11.
Biyue Liu 《高等学校计算数学学报(英文版)》2008,1(2):165-175
Pulsatile blood flows in curved atherosclerotic arteries are studied by com- puter simulations.Computations are carried out with various values of physiological parameters to examine the effects of flow parameters on the disturbed flow patterns downstream of a curved artery with a stenosis at the inner wall.The numerical re- suits indicate a strong dependence of flow pattern on the blood viscosity and inlet flow rate,while the influence of the inlet flow profile to the flow pattem in downstream is negligible. 相似文献
12.
Alternating‐Direction Explicit (A.D.E.) finite‐difference methods make use of two approximations that are implemented for computations proceeding in alternating directions, e.g., from left to right and from right to left, with each approximation being explicit in its respective direction of computation. Stable A.D.E. schemes for solving the linear parabolic partial differential equations that model heat diffusion are well‐known, as are stable A.D.E. schemes for solving the first‐order equations of fluid advection. Several of these are combined here to derive A.D.E. schemes for solving time‐dependent advection‐diffusion equations, and their stability characteristics are discussed. In each case, it is found that it is the advection term that limits the stability of the scheme. The most stable of the combinations presented comprises an unconditionally stable approximation for computations carried out in the direction of advection of the system, from left to right in this case, and a conditionally stable approximation for computations proceeding in the opposite direction. To illustrate the application of the methods and verify the stability conditions, they are applied to some quasi‐linear one‐dimensional advection‐diffusion problems. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
13.
针对冠状动脉狭窄的情况,采用数值模拟方法求解了牛顿流体与非牛顿流体(幂次律流体和Casson流体)的定常与脉动的流场。在此基础上,求解了LDL(低密度脂肪蛋白)和Albumin(血清白蛋白)的浓度场。根据计算结果,详细讨论了壁面剪应力、非牛顿流效应、分子大小等因素对大分子传质的影响;并对牛顿流体与非牛顿流体、定常流动与脉动流动的大分子浓度场进行了比较,这些结果对于了解动脉硬化成因与流动特性和大分子传质的联系提供了较为丰富的信息。 相似文献
14.
The aim of this paper is to propose mixed two‐grid finite difference methods to obtain the numerical solution of the one‐dimensional and two‐dimensional Fitzhugh–Nagumo equations. The finite difference equations at all interior grid points form a large‐sparse linear system, which needs to be solved efficiently. The solution cost of this sparse linear system usually dominates the total cost of solving the discretized partial differential equation. The proposed method is based on applying a family of finite difference methods for discretizing the spatial and time derivatives. The obtained system has been solved by two‐grid method, where the two‐grid method is used for solving the large‐sparse linear systems. Also, in the proposed method, the spectral radius with local Fourier analysis is calculated for different values of h and Δt. The numerical examples show the efficiency of this algorithm for solving the one‐dimensional and two‐dimensional Fitzhugh–Nagumo equations. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
15.
Harun Selvitopi Muhammet Yaz&#x;c&#x; 《Mathematical Methods in the Applied Sciences》2019,42(16):5446-5454
We consider the initial value problem for the Klein‐Gordon equation in de Sitter spacetime. We use the central difference scheme on the temporal discretization. We also discretize the spatial variable using the finite element method with implicit and the Crank‐Nicolson schemes for the numerical solution of the initial value problem. In order to show the accuracy for the results of the solutions, we also examine the finite difference methods. We observe that the numerical results obtained by using these methods are compatible. 相似文献
16.
The aim of this paper is to propose a multigrid method to obtain the numerical solution of the one‐dimensional nonlinear sine‐Gordon equation. The finite difference equations at all interior grid points form a large sparse linear system, which needs to be solved efficiently. The solution cost of this sparse linear system usually dominates the total cost of solving the discretized partial differential equation. The proposed method is based on applying a compact finite difference scheme of fourth‐order for discretizing the spatial derivative and the standard second‐order central finite difference method for the time derivative. The proposed method uses the Richardson extrapolation method in time variable. The obtained system has been solved by V‐cycle multigrid (VMG) method, where the VMG method is used for solving the large sparse linear systems. The numerical examples show the efficiency of this algorithm for solving the one‐dimensional sine‐Gordon equation. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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A. Serghini Mounim 《Numerical Methods for Partial Differential Equations》2008,24(2):368-382
A space‐time finite element method is introduced to solve the linear damped wave equation. The scheme is constructed in the framework of the mixed‐hybrid finite element methods, and where an original conforming approximation of H(div;Ω) is used, the latter permits us to obtain an upwind scheme in time. We establish the link between the nonstandard finite difference scheme recently introduced by Mickens and Jordan and the scheme proposed. In this regard, two approaches are considered and in particular we employ a formulation allowing the solution to be marched in time, i.e., one only needs to consider one time increment at a time. Numerical results are presented and compared with the analytical solution illustrating good performance of the present method. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 相似文献
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A. Serghini Mounim B.M. de Dormale 《Numerical Methods for Partial Differential Equations》2006,22(4):761-775
We are interested in numerical methods for the Liouville‐Bratu‐Gelfand problem. The ideas and techniques developed here to construct the schemes are inspired from the fitted method and the so‐called compact exponentially fitted method. Some of those schemes can be viewed as extensions of both the Buckmire scheme and the standard scheme which results from the use of the standard finite‐difference procedures. We study and compare computationally the accuracy of methods introduced here. It is also mentioned that the Buckmire's techniques and the standard scheme are a particular case of the fitted method. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
20.
Norzieha Mustapha Prashanta K. Mandal Ilyani Abdullah Norsarahaida NAmin Tasawar Hayat 《Numerical Methods for Partial Differential Equations》2011,27(4):960-981
This paper looked at the numerical investigations of the generalized Newtonian blood flow through a couple of irregular arterial stenoses. The flow is treated to be axisymmetric, with an outline of the stenoses obtained from a three dimensional casting of a mild stenosed artery, so that the flow effectively becomes two‐dimensional. The Marker and Cell (MAC) method is developed for the governing unsteady generalized Newtonian equations in staggered grid for viscous incompressible flow in the cylindrical polar co‐ordinates system. The derived pressure‐Poisson equation was solved using Successive‐Over‐Relaxation (S.O.R.) method and the pressure‐velocity correction formulae have been derived. Computations are performed for the pressure drop, the wall shear stress distribution and the separation region. The presented computations show that in comparison to the corresponding Newtonian model the generalized Newtonian fluid experiences higher pressure drop, lower peak wall shear stress and smaller separation region. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 960–981, 2011 相似文献