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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
Summary
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.
- 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.
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