A Fast Navier Stokes Flow Simulation Tool Forimage Based CFD

The objective of this paper is to present a fast parallel incompressible Navier Stokes (NS) simulator that has enough versatility to apply to various endovascular situations with ease in medical image integration. Our long term goal is to bring NS simulation to surgeons as an additional routine image modality that can complement existing medical imaging channels. Given a medical image describing the geometry of an artery, we are able to simulate the blood flow through an artery close to clinical conditions. To achieve this goal, our interface relies on the combination of the L2 penalty method to deal with complex geometry for solving the NS equations. We present here a high performance portable domain decomposition solver based on a tuning of the fastest linear solver depending on the subdomain and the processor architecture. This paper provides a detailed proof of concept in the two dimensional case. The three dimensional results will be reported in a companion paper.

[1]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[2]  William L. Briggs,et al.  A multigrid tutorial, Second Edition , 2000 .

[3]  Robert D. Falgout,et al.  hypre: A Library of High Performance Preconditioners , 2002, International Conference on Computational Science.

[4]  Hanif M. Ladak,et al.  Template-based finite-element mesh generation from medical images , 2005, Comput. Methods Programs Biomed..

[5]  H. Schwarz.  Gesammelte mathematische Abhandlungen , 1970 .

[6]  Marc Garbey,et al.  WIMI - web interface to medical information , 2007, SEDE.

[7]  Philippe Angot,et al.  A penalization method to take into account obstacles in incompressible viscous flows , 1999, Numerische Mathematik.

[8]  Barry F. Smith,et al.  Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations , 1996 .

[9]  D. Ku,et al.  Reduced blood flow accelerates intimal hyperplasia in endarterectomized canine arteries. , 1995, Cardiovascular surgery.

[10]  William L. Briggs,et al.  A multigrid tutorial , 1987 .

[11]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[12]  Marc Garbey,et al.  Numerically efficient solution techniques for computational fluid dynamics and heat transfer problems , 2004 .

[13]  Marc Garbey,et al.  A versatile incompressible Navier–Stokes solver for blood flow application , 2007 .

[14]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[15]  Tony F. Chan,et al.  Active contours without edges , 2001, IEEE Trans. Image Process..

[16]  Marc Garbey,et al.  On some Aitken-like acceleration of the Schwarz method , 2002 .

[17]  Rainald Löhner,et al.  Parallel Advancing Front Grid Generation , 1999, IMR.

[18]  James Demmel,et al.  SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems , 2003, TOMS.

[19]  M. Garbey,et al.  Operator Splitting and Domain Decomposition for Multiclusters , 2000 .

[20]  Marc Garbey,et al.  Parallel Image-Based Hemodynamic Simulator , 2007, 2007 Second International Conference on Systems and Networks Communications (ICSNC 2007).

[21]  Zi-Cai Li,et al.  Schwarz Alternating Method , 1998 .