Combining existing numerical models with data assimilation using weighted least-squares finite element methods.

Area of Science:

• Computational fluid dynamics
• Biomedical engineering
• Numerical analysis

Background:

• Limited experimental blood velocity data in the left ventricle and inexact numerical models pose challenges for accurate flow simulation.
• Existing data assimilation methods often struggle with noisy experimental measurements and lack flexibility in numerical model integration.

Purpose of the Study:

• To develop a new, flexible approach for combining computational fluid dynamics (CFD) model results with experimental data.
• To enhance the assimilation of noisy, limited experimental data into numerical simulations of fluid flow, specifically blood flow in the left ventricle.

Main Methods:

• Utilized the weighted least-squares finite element method (WLSFEM) for data assimilation.
• Developed a flexible framework allowing various numerical methods for solving Navier-Stokes equations before WLSFEM integration.
• Implemented dynamic adjustment of experimental data influence based on data accuracy.

Main Results:

• The new approach successfully integrates experimental data with CFD models, accommodating noisy and limited datasets.
• Demonstrated significantly reduced computational costs compared to previous data assimilation techniques.
• Showcased the method's ability to dynamically weigh data accuracy, improving the final numerical solution.

Conclusions:

• The developed WLSFEM-based approach offers a flexible and computationally efficient solution for data assimilation in CFD.
• This method enhances the accuracy of numerical simulations by effectively incorporating experimental measurements, even with inherent noise and limitations.
• The findings have significant implications for improving the fidelity of computational fluid dynamics models in various scientific and engineering applications.