scholarly journals Some Numerical Approaches to Solve Fluid Structure Interaction Problems in Blood Flow

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Aik Ying Tang ◽  
Norsarahaida Amin
Keyword(s):  
Blood Flow ◽  
Fluid Structure Interaction ◽  
Computational Cost ◽  
Mass Effect ◽  
Rigid Wall ◽  
Added Mass ◽  
Multiscale Approach ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Numerical Approaches

Some numerical approaches to solve fluid structure interaction problems in blood flow are reviewed. Fluid structure interaction is the interaction between a deformable structure with either an internal or external flow. A discussion on why the compliant artery associated with fluid structure interaction should be taken into consideration in favor of the rigid wall model being included. However, only the Newtonian model of blood is assumed, while various structure models which include, amongst others, generalized string models and linearly viscoelastic Koiter shell model that give a more realistic representation of the vessel walls compared to the rigid structure are presented. Since there exists a strong added mass effect due to the comparable densities of blood and the vessel wall, the numerical approaches to overcome the added mass effect are discussed according to the partitioned and monolithic classifications, where the deficiencies of each approach are highlighted. Improved numerical methods which are more stable and offer less computational cost such as the semi-implicit, kinematic splitting, and the geometrical multiscale approach are summarized, and, finally, an appropriate structure and numerical scheme to tackle fluid structure interaction problems are proposed.

Speeding Up Fluid-Structure Interaction Simulation of the Blood Flow in a Flexible Artery Using Sub-Cycling: Stability and Accuracy

2013 ◽  
Author(s):  
L. Taelman ◽  
J. Degroote ◽  
J. Vierendeels ◽  
P. Segers
Keyword(s):  
Blood Flow ◽  
Fluid Structure Interaction ◽  
Computational Cost ◽  
Rigid Wall ◽  
Driving Mechanism ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Flexible Wall ◽  
Mechanism Of Wave Propagation ◽  
Stability And Accuracy

In the cardiovascular system, the distensibility of the blood vessels is the driving mechanism of wave propagation. As the blood flow interacts mechanically with the flexible vessel walls, this phenomenon gives rise to complex fluid-structure interaction (FSI) problems. Several studies comparing rigid wall with FSI simulations in settings with large deformations demonstrate the importance of including the flexible wall modeling, in particular with respect to the simulation of wall shear stress. As both the equations governing the flow and the arterial deformation (and their interaction) need to be solved, FSI simulations are characterized by a high computational cost. To make them applicable to a broader range of cardiovascular problems, efforts to reduce the calculation time (such as the use of so-called ‘sub-cycling’) should be made.

Natural Frequencies of Centrifugal Compressor Impellers for High Density Gas Applications

2008 ◽  
Author(s):  
Yohei Magara ◽  
Mitsuhiro Narita ◽  
Kazuyuki Yamaguchi ◽  
Naohiko Takahashi ◽  
Tetsuya Kuwano
Keyword(s):  
Centrifugal Compressor ◽  
Natural Frequencies ◽  
Fluid Structure Interaction ◽  
Mass Effect ◽  
Added Mass ◽  
High Density ◽  
Experimental Results ◽  
Density Condition ◽  
Fluid Structure ◽  
Structure Interaction

Characteristics of natural frequencies of an impeller and an equivalent disc were investigated in high-density gas to develop a method for predicting natural frequencies of centrifugal compressor impellers for high-density gas applications. The equivalent disc had outer and inner diameters equal to those of the impeller. We expected that natural frequencies would decrease with increasing the gas density because of the added-mass effect. However, we found experimentally that some natural frequencies of the impeller and the disc in high-density gas decreased but others increased. Moreover, we observed, under high-density condition, some resonance frequencies that we did not observe under low-density condition. These experimental results cannot be explained by only the added-mass effect. For simplicity, we focused on the disc to understand the mechanism of the behavior of natural frequencies. We developed a theoretical analysis of fluid-structure interaction considering not only the mass but also stiffness of gas. The analysis gave a qualitative explanation of the experimental results. In addition, we carried out a fluid-structure interaction analysis using the finite element method. The behavior of natural frequencies of the disc in high-density gas was predicted with errors less than 6%.

scholarly journals A SEMI-IMPLICIT APPROACH FOR FLUID-STRUCTURE INTERACTION BASED ON AN ALGEBRAIC FRACTIONAL STEP METHOD

2007 ◽  
Vol 17 (06) ◽  
pp. 957-983 ◽  
Author(s):  
A. QUAINI ◽  
A. QUARTERONI
Keyword(s):  
Fluid Structure Interaction ◽  
Mass Effect ◽  
Added Mass ◽  
Fractional Step ◽  
Step Method ◽  
Fractional Step Method ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Wide Range ◽  
Structure Problem

We address the numerical simulation of fluid-structure interaction problems characterized by a strong added-mass effect. We propose a semi-implicit coupling scheme based on an algebraic fractional-step method. The basic idea of a semi-implicit scheme consists in coupling implicitly the added-mass effect, while the other terms (dissipation, convection and geometrical nonlinearities) are treated explicitly. Thanks to this kind of explicit–implicit splitting, computational costs can be reduced (in comparison to fully implicit coupling algorithms) and the scheme remains stable for a wide range of discretization parameters. In this paper we derive this kind of splitting from the algebraic formulation of the coupled fluid-structure problem (after finite-element space discretization). From our knowledge, it is the first time that algebraic fractional step methods, used thus far only for fluid problems in computational domains with rigid boundaries, are applied to fluid-structure problems. In particular, for the specific semi-implicit method presented in this work, we adapt the Yosida scheme to the case of a coupled fluid-structure problem. This scheme relies on an approximate LU block factorization of the matrix obtained after the discretization in time and space of the fluid-structure system. We analyze the numerical performances of this scheme on 2D fluid-structure simulations performed with a simple 1D structure model.

scholarly journals A semi-implicit coupling technique for fluid–structure interaction problems with strong added-mass effect

2018 ◽  
Vol 80 ◽  
pp. 94-112 ◽  
Author(s):  
Alireza Naseri ◽  
Oriol Lehmkuhl ◽  
Ignacio Gonzalez ◽  
Eduard Bartrons ◽  
Carlos David Pérez-Segarra ◽  
...  
Keyword(s):  
Fluid Structure Interaction ◽  
Mass Effect ◽  
Added Mass ◽  
Fluid Structure ◽  
Coupling Technique ◽  
Structure Interaction

scholarly journals Fluid-structure interaction problems with strong added-mass effect

2009 ◽  
Vol 80 (10) ◽  
pp. 1261-1294 ◽  
Author(s):  
S. R. Idelsohn ◽  
F. Del Pin ◽  
R. Rossi ◽  
E. Oñate
Keyword(s):  
Fluid Structure Interaction ◽  
Mass Effect ◽  
Added Mass ◽  
Fluid Structure ◽  
Structure Interaction

scholarly journals Numerical modeling in arterial hemodynamics incorporating fluid-structure interaction and microcirculation

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Fan He ◽  
Lu Hua ◽  
Tingting Guo
Keyword(s):  
Numerical Modeling ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Fluid Structure Interaction ◽  
Rigid Wall ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Arterial Hemodynamics ◽  
Wall Compliance ◽  
Wall Shear

Abstract Background The effects of arterial wall compliance on blood flow have been revealed using fluid-structure interaction in last decades. However, microcirculation is not considered in previous researches. In fact, microcirculation plays a key role in regulating blood flow. Therefore, it is very necessary to involve microcirculation in arterial hemodynamics. Objective The main purpose of the present study is to investigate how wall compliance affects the flow characteristics and to establish the comparisons of these flow variables with rigid wall when microcirculation is considered. Methods We present numerical modeling in arterial hemodynamics incorporating fluid-structure interaction and microcirculation. A novel outlet boundary condition is employed to prescribe microcirculation in an idealised model. Results The novel finding in this work is that wall compliance under the consideration of microcirculation leads to the increase of wall shear stress in contrast to rigid wall, contrary to the traditional result that wall compliance makes wall shear stress decrease when a constant or time dependent pressure is specified at an outlet. Conclusions This work provides the valuable study of hemodynamics under physiological and realistic boundary conditions and proves that wall compliance may have a positive impact on wall shear stress based on this model. This methodology in this paper could be used in real model simulations.

Modeling of aortic valve stenosis using fluid-structure interaction method

Perfusion ◽  
2021 ◽  
pp. 026765912199854
Author(s):  
Mohammad Javad Ghasemi Pour ◽  
Kamran Hassani ◽  
Morteza Khayat ◽  
Shahram Etemadi Haghighi
Keyword(s):  
Blood Flow ◽  
Aortic Valve ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Relaxation Phase ◽  
Exercise Condition ◽  
Time Dependent Domain ◽  
Comparison Of The Results

Background and objectives: Fluid structure interaction (FSI) is defined as interaction of the structures with contacting fluids. The aortic valve experiences the interaction with blood flow in systolic phase. In this study, we have tried to predict the hemodynamics of blood flow through a normal and stenotic aortic valve in two relaxation and exercise conditions using a three-dimensional FSI method. Methods: The aorta valve was modeled as a three-dimensional geometry including a normal model and two others with 25% and 50% stenosis. The geometry of the aortic valve was extracted from CT images and the models were generated by MMIMCS software and then they were implemented in ANSYS software. The pulsatile flow rate was used for all cases and the numerical simulations were conducted based on a time-dependent domain. Results: The obtained results including the velocity, pressure, and shear stress contours in different systolic time sequences were explained and discussed. The maximum blood flow velocity in relaxation phase was obtained 1.62 m/s (normal valve), 3.78 m/s (25% stenosed valve), and 4.73 m/s (50% stenosed valve). In exercise condition, the maximum velocities are 2.86, 4.32, and 5.42 m/s respectively. The maximum blood pressure in relaxation phase was calculated 111.45 mmHg (normal), 148.66 mmHg (25% stenosed), and 164.21 mmHg (50% stenosed). However, the calculated values in exercise situation were 129.57, 163.58, and 191.26 mmHg. The validation of the predicted results was also conducted using existing literature. Conclusions: We believe that such model are useful tools for biomechanical experts. The further studies should be done using experimental data and the data are implemented on the boundary conditions for better comparison of the results.

scholarly journals Optimal Pressure Boundary Control of Steady Multiscale Fluid-Structure Interaction Shell Model Derived from Koiter Equations

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 149
Author(s):  
Andrea Chierici ◽  
Leonardo Chirco ◽  
Sandro Manservisi
Keyword(s):  
Optimal Control ◽  
Solid Wall ◽  
Fluid Structure Interaction ◽  
Computational Cost ◽  
Robin Boundary Condition ◽  
Design Parameters ◽  
Fluid Structure ◽  
Control Approach ◽  
Structure Interaction ◽  
Fluid Boundary

Fluid-structure interaction (FSI) problems are of great interest, due to their applicability in science and engineering. However, the coupling between large fluid domains and small moving solid walls presents numerous numerical difficulties and, in some configurations, where the thickness of the solid wall can be neglected, one can consider membrane models, which are derived from the Koiter shell equations with a reduction of the computational cost of the algorithm. With this assumption, the FSI simulation is reduced to the fluid equations on a moving mesh together with a Robin boundary condition that is imposed on the moving solid surface. In this manuscript, we are interested in the study of inverse FSI problems that aim to achieve an objective by changing some design parameters, such as forces, boundary conditions, or geometrical domain shapes. We study the inverse FSI membrane model by using an optimal control approach that is based on Lagrange multipliers and adjoint variables. In particular, we propose a pressure boundary optimal control with the purpose to control the solid deformation by changing the pressure on a fluid boundary. We report the results of some numerical tests for two-dimensional domains to demonstrate the feasibility and robustness of our method.

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