A parallel two-level method for simulating blood flows in branching arteries with the resistive boundary condition

Wu, Yuqi; Cai, Xiao‐Chuan

doi:10.1016/j.compfluid.2010.11.015

Cited by 19 publications

(16 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…donde, la deformaciónû f , del dominioΩ f , satisface la ecuación armónica ( [1], [9], [15], [19], [21], [22], [23])…”

Section: Definamos Una Transformaciónâunclassified

“…La gran mayoría de trabajos han abarcado problemas referentes a la hemodinámica ( [1], [8], [19] [22], [23], [24], [25]), y a la dinámica del fluido en el sistema respiratorio humano ( [4], [5]). Los problemas de interacción fluido-estructura, se originan por el acoplamiento de las ecuaciones que modelan la dinámica del fluido, junto con las del movimiento y deformación de la estructura; así como también, de ciertas condiciones impuestas sobre la zona de contacto del fluido con la estructura, a la cual se le llama interfaz.…”

Section: Introductionunclassified

See 1 more Smart Citation

Arbitrary Lagrangian - Eulerian formulation of the equations system which modeling the interaction of airflow with the pulmonary alveolus

Vallejos¹,

Rubio²,

Rodriguez³

et al. 2017

Sel.mat

View full text Add to dashboard Cite

In this article, we formulate a physiological process through a two-dimensional fluid-structure interaction problem between the airflow and the pulmonary alveolus in the Eulerian-Lagrangian Arbitrary (ALE) frame. This problem arises by coupling the equations of the fluid and the structure, described by the Navier-Stokes equations of evolution for incompressible flows, and an equilibrium equation, respectively.Keywords. Fluid-Estructure interaction, airflow, pulmonary alveolus, Arbitrary Lagrangian-Eulerian (ALE) framework , Navier-Stokes equations, equilibrium equation. Introducción.En la última década, los problemas de interacción fluido-estructura han logrado gran interés en el campo de la Fisiología Humana; ya que estos modelan de forma casi realista el funcionamiento de los órganos y tejidos del ser humano. La gran mayoría de trabajos han abarcado problemas referentes a la hemodinámica ( Los problemas de interacción fluido-estructura, se originan por el acoplamiento de las ecuaciones que modelan la dinámica del fluido, junto con las del movimiento y deformación de la estructura; así como también, de ciertas condiciones impuestas sobre la zona de contacto del fluido con la estructura, a la cual se le llama interfaz. Tradicionalmente, existen dos sistemas de coordenadas que se utilizan para estudiar la dinámica del fluido y la mecánica de sólidos, a saber: las coordenadas Eulerianas, centradas en el espacio; y las Lagrangianas, centradas en la partícula. El marco Lagrangiano, es apropiado para materiales, cuyas deformaciones son pequeñas, como por ejemplo los sólidos, y no para cuerpos con grandes deformaciones como son los fluidos. Para estos el marco Euleriano es el indicado. Desde el punto de vista de los métodos numéricos, el marco Euleriano se caracteriza porque mientras el cuerpo está en movimiento, la malla permanece fija, por lo que no aparecen deformaciones de la malla; mientras que en el marco Lagrangiano, la malla se mueve junto a las partículas, quedando deformada también la malla.

show abstract

“…donde, la deformaciónû f , del dominioΩ f , satisface la ecuación armónica ( [1], [9], [15], [19], [21], [22], [23])…”

Section: Definamos Una Transformaciónâunclassified

Section: Introductionunclassified

Arbitrary Lagrangian - Eulerian formulation of the equations system which modeling the interaction of airflow with the pulmonary alveolus

Vallejos¹,

Rubio²,

Rodriguez³

et al. 2017

Sel.mat

View full text Add to dashboard Cite

show abstract

“…We show numerically that the proposed version of the parallel algorithm is scalable to thousands of processor cores for large‐scale problems with hundreds of millions of unknowns. We also mention that the NKS method has been successfully applied to several classes of problems including the Bidomain reaction‐diffusion system in Munteanu et al, some elasticity problems in Kong and Cai, and fluid‐structure interaction problems in other works …”

Section: Introductionmentioning

confidence: 99%

“…We also mention that the NKS method has been successfully applied to several classes of problems including the Bidomain reaction-diffusion system in Munteanu et al, 24 some elasticity problems in Kong and Cai,25 and fluid-structure interaction problems in other works. [12][13][14]21 The remainder of this paper is organized as follows. In Section 2, we first introduce a partitioning strategy to subdivide the large artery tree into a large number of small artery trees that will be handled by different processor cores in parallel, and then the discretization of the incompressible Navier-Stokes equations in time and space.…”

Section: Introductionmentioning

confidence: 99%

An efficient parallel simulation of unsteady blood flows in patient‐specific pulmonary artery

Kong

Kheyfets

Finol

et al. 2018

Numer Methods Biomed Eng

View full text Add to dashboard Cite

Simulation of blood flows in the pulmonary artery provides some insight into certain diseases by examining the relationship between some continuum metrics, eg, the wall shear stress acting on the vascular endothelium, which responds to flow-induced mechanical forces by releasing vasodilators/constrictors. V. Kheyfets, in his previous work, studies numerically a patient-specific pulmonary circulation to show that decreasing wall shear stress is correlated with increasing pulmonary vascular impedance. In this paper, we develop a scalable parallel algorithm based on domain decomposition methods to investigate an unsteady model with patient-specific pulsatile waveforms as the inlet boundary condition. The unsteady model offers tremendously more information about the dynamic behavior of the flow field, but computationally speaking, the simulation is a lot more expensive since a problem which is similar to the steady-state problem has to be solved many times, and therefore, the traditional sequential approach is not suitable anymore. We show computationally that simulations using the proposed parallel approach with up to 10 000 processor cores can be obtained with much reduced compute time. This makes the technology potentially usable for the routine study of the dynamic behavior of blood flows in the pulmonary artery, in particular, the changes of the blood flows and the wall shear stress in the spatial and temporal dimensions.

show abstract

“…In this paper, we introduce a special interpolation method and a new two-level method that works well for shape optimization problems. Some scalability studies of multilevel preconditioners for boundary control problems and fluid-structure interaction problems can be found in [4,38,40], but as far as we know, this kind of study has not been performed for shape optimization problems. Although both boundary control and shape optimization problems are PDE-constrained optimization problems, shape optimization problems are often more difficult due to the deformation of the computational domain.…”

Section: Introductionmentioning

confidence: 99%

A parallel two‐level domain decomposition based one‐shot method for shape optimization problems

Chen

Cai

2014

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

A two-level domain decomposition method is introduced for general shape optimization problems constrained by the incompressible Navier-Stokes equations. The optimization problem is first discretized with a finite element method on an unstructured moving mesh that is implicitly defined without assuming that the computational domain is known and then solved by some one-shot Lagrange-Newton-Krylov-Schwarz algorithms. In this approach, the shape of the domain, its corresponding finite element mesh, the flow fields and their corresponding Lagrange multipliers are all obtained computationally in a single solve of a nonlinear system of equations. Highly scalable parallel algorithms are absolutely necessary to solve such an expensive system. The one-level domain decomposition method works reasonably well when the number of processors is not large. Aiming for machines with a large number of processors and robust nonlinear convergence, we introduce a two-level inexact Newton method with a hybrid two-level overlapping Schwarz preconditioner. As applications, we consider the shape optimization of a cannula problem and an artery bypass problem in 2D. Numerical experiments show that our algorithm performs well on a supercomputer with over 1000 processors for problems with millions of unknowns. that is, Here,ˇD 10, Re D 500, N h D 1:1 10 6 , and N H D 7:0 10 4 . In algorithm One-One: ı D 8; in algorithm Two-One: ı h D 8, and ı H D 4; in algorithm Two-Two: ı h D 0 and ı H D 2.

show abstract

A parallel two-level method for simulating blood flows in branching arteries with the resistive boundary condition

Cited by 19 publications

References 21 publications

Arbitrary Lagrangian - Eulerian formulation of the equations system which modeling the interaction of airflow with the pulmonary alveolus

Arbitrary Lagrangian - Eulerian formulation of the equations system which modeling the interaction of airflow with the pulmonary alveolus

An efficient parallel simulation of unsteady blood flows in patient‐specific pulmonary artery

A parallel two‐level domain decomposition based one‐shot method for shape optimization problems

Contact Info

Product

Resources

About