Modeling 3-D compliant blood flow with FOSLS

Area of Science:

• Computational fluid dynamics
• Biomedical engineering
• Numerical analysis

Background:

• Modeling blood flow in large vessels involves complex fluid-solid interactions.
• Deforming vessel walls necessitate computationally intensive re-mapping techniques.
• Existing iterative methods for fluid-structure interaction can be inefficient and lack optimal scalability.

Purpose of the Study:

• To present a novel multilevel least-squares (LS) finite element approach for blood flow modeling.
• To overcome limitations of traditional iterative methods in terms of computational cost and scalability.
• To provide an a posteriori error measure for the finite element approximation.

Main Methods:

• Developed a multilevel minimization technique for finite element approximation error using a least-squares norm.
• Applied the method to the coupled system of fluid (Navier-Stokes) and solid (elasticity) equations.
• Compared the LS finite element approach against the commercial package CFD-ACE.

Main Results:

• The multilevel LS finite element approach demonstrates linear computational cost growth with degrees of freedom.
• This method achieves optimal scalability, particularly in serial environments.
• Significant degradation in performance was observed with other methods as problem size increased.

Conclusions:

• The multilevel LS finite element method offers a more efficient and scalable solution for blood flow modeling.
• This approach provides superior accuracy and computational performance compared to conventional numerical methods.
• The technique's flexibility and inherent error measure enhance its utility in complex biomechanical simulations.