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Related Experiment Videos

First-order system least-squares (FOSLS) for modeling blood flow.

J J Heys1, C G DeGroff, T A Manteuffel

  • 1Chemical and Materials Engineering Department, Arizona State University, Tempe, AZ 85287-6006, USA. jheys@asu.edu

Medical Engineering & Physics
|November 9, 2005
PubMed
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This study presents a new computational method for modeling blood flow in compliant vessels. The first-order system least-squares (FOSLS) approach achieves optimal scalability for complex 3D fluid-structure interaction problems.

Area of Science:

  • Computational fluid dynamics
  • Biomedical engineering
  • Numerical analysis

Background:

  • Modeling blood flow in compliant vessels involves complex, coupled nonlinear partial differential equations (PDEs).
  • Traditional numerical methods for solving these PDEs often exhibit suboptimal computational scalability.
  • Advances like multigrid algorithms and first-order system least-squares (FOSLS) formulations offer improved scalability.

Purpose of the Study:

  • To present and validate a FOSLS finite-element formulation for solving a 3D model of blood flow in a compliant vessel.
  • To demonstrate the optimal computational scalability of this new approach for realistic geometries.

Main Methods:

  • Utilized a first-order system least-squares (FOSLS) finite-element formulation.
  • Modeled blood as a Newtonian fluid and the vessel wall as a linear elastic material.

Related Experiment Videos

  • Applied the method to three distinct 3D vessel geometries.

    • Main Results:

    • The FOSLS approach demonstrated optimal computational scalability across a range of problem sizes for the 3D blood flow model.
    • The formulation provides a sharp, a posteriori error measure, aiding in solution verification.
    • Successfully applied to multiple complex geometries, indicating broad applicability.

    Conclusions:

    • The FOSLS method offers an efficient and scalable solution for simulating 3D blood flow in compliant vessels.
    • This approach advances the computational modeling of cardiovascular biomechanics.
    • The inherent error estimation provides a valuable tool for assessing solution accuracy.