Benchmark problems for numerical treatment of backflow at open boundaries

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Biomedical engineering

Background:

• Incoming velocity at open boundaries, known as backflow, frequently causes unphysical instabilities in computational fluid dynamics (CFD) simulations, even at moderate Reynolds numbers.
• Existing methods to address backflow instabilities lack comprehensive comparative analysis regarding their accuracy across different physiological regimes.
• Generating stable reference solutions for validation, beyond analytical forms, presents a significant challenge in this field.

Purpose of the Study:

• To establish a standardized set of benchmark problems for evaluating computational fluid dynamics methods.
• To facilitate a detailed comparison of various backflow treatment strategies.
• To assess the accuracy of different methods in diverse backflow conditions, including full flow reversal and propagating vortices.

Main Methods:

• Development and implementation of benchmark problems in FreeFem++.
• Simulation of backflow scenarios, including full flow reversal and post-stenosis vortex propagation.
• Comparative analysis of different numerical methods designed to handle backflow instabilities.

Main Results:

• The study provides a framework for comparing backflow treatment methods.
• Identifies challenges in generating stable reference solutions for validation.
• Demonstrates the utility of the benchmark problems in assessing method performance.

Conclusions:

• The developed benchmark problems offer a robust basis for future advancements in computational fluid dynamics methods.
• Openly available source code promotes reproducibility and further research.
• Standardized comparison is crucial for improving the accuracy of CFD simulations in physiological contexts.