Commun. Comput. Phys., 11 (2012), pp. 1279-1299.


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

Yuqi Wu 1*, Xiao-Chuan Cai 2

1 Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO 80309, USA.
2 Department of Computer Science, University of Colorado at Boulder, Boulder, CO 80309, USA.

Received 15 May 2010; Accepted (in revised version) 15 May 2011
Available online 30 November 2011
doi:10.4208/cicp.060510.150511s

Abstract

We 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.

AMS subject classifications: 74F10, 65M55, 35R37, 65Y05, 68W10

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Key words: Fluid-structure interaction, blood flow, mesh movement, resistive boundary condition, additive Schwarz, domain decomposition, parallel computing.

*Corresponding author.
Email: yuqi.wu@colorado.edu (Y. Wu), cai@cs.colorado.edu (X.-C. Cai)
 

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