A Parallel Domain Decomposition Algorithm for Simulating Blood Flow with Incompressible Navier-Stokes Equations with Resistive Boundary Condition

2012 ◽  
Vol 11 (4) ◽  
pp. 1279-1299
Author(s):  
Yuqi Wu ◽  
Xiao-Chuan Cai
Keyword(s):  
Boundary Condition ◽  
Blood Flow ◽  
Domain Decomposition ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Outflow Boundary Condition ◽  
Outflow Boundary ◽  
Domain Decomposition Algorithm ◽  
Fully Coupled

AbstractWe introduce and study a parallel domain decomposition algorithm for the simulation of blood flow in compliant arteries using a fully-coupled system of nonlinear partial differential equations consisting of a linear elasticity equation and the incompressible Navier-Stokes equations with a resistive outflow boundary condition. The system is discretized with a finite element method on unstructured moving meshes and solved by a Newton-Krylov algorithm preconditioned with an overlapping restricted additive Schwarz method. The resistive outflow boundary condition plays an interesting role in the accuracy of the blood flow simulation and we provide a numerical comparison of its accuracy with the standard pressure type boundary condition. We also discuss the parallel performance of the implicit domain decomposition method for solving the fully coupled nonlinear system on a supercomputer with a few hundred processors.

Structured tree outflow condition for blood flow in larger systemic arteries

1999 ◽  
Vol 276 (1) ◽  
pp. H257-H268 ◽  
Author(s):  
Mette S. Olufsen
Keyword(s):  
Boundary Condition ◽  
Blood Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Phase Lag ◽  
Tree Model ◽  
Arterial Tree ◽  
Windkessel Model ◽  
Navier Stokes Equations ◽  
Systemic Arteries

A central problem in modeling blood flow and pressure in the larger systemic arteries is determining a physiologically based boundary condition so that the arterial tree can be truncated after a few generations. We have used a structured tree attached to the terminal branches of the truncated arterial tree in which the root impedance is estimated using a semianalytical approach based on a linearization of the viscous axisymmetric Navier-Stokes equations. This provides a dynamic boundary condition that maintains the phase lag between blood flow and pressure as well as the high-frequency oscillations present in the impedance spectra. Furthermore, it accommodates the wave propagation effects for the entire systemic arterial tree. The result is a model that is physiologically adequate as well as computationally feasible. For validation, we have compared the structured tree model with a pure resistance and a windkessel model as well as with measured data.

Iterative method for solving fully-coupled fluid solid systems

2010 ◽  
pp. 653-670
Author(s):  
Elisabeth Longatte
Keyword(s):  
Stokes Equations ◽  
Cross Flow ◽  
Elastic Cylinder ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Ale Formulation ◽  
Volume Method ◽  
Fully Coupled ◽  
Solid System

This work is concerned with the modelling of the interaction of a fluid with a rigid or a flexible elastic cylinder in the presence of axial or cross-flow. A partitioned procedure is involved to perform the computation of the fully-coupled fluid solid system. The fluid flow is governed by the incompressible Navier-Stokes equations and modeled by using a fractional step scheme combined with a co-located finite volume method for space discretisation. The motion of the fluid domain is accounted for by a moving mesh strategy through an Arbitrary Lagrangian-Eulerian (ALE) formulation. Solid dyncamics is modeled by a finite element method in the linear elasticity framework and a fixed point method is used for the fluid solid system computation. In the present work two examples are presented to show the method robustness and efficiency.

Sign in / Sign up

Export Citation Format

Share Document