An implicit solver for 1D arterial network models

Area of Science:

• Computational fluid dynamics
• Biomedical engineering
• Numerical analysis

Background:

• Accurate simulation of blood flow is crucial for understanding cardiovascular diseases.
• Existing numerical methods for 1D blood flow models often face limitations in stability or computational efficiency.

Purpose of the Study:

• To introduce and evaluate a novel enhanced trapezoidal rule method (ETM) for solving 1D blood flow equations.
• To assess the ETM's performance against benchmark arterial network and dam break problems.

Main Methods:

• The enhanced trapezoidal rule method (ETM) was developed as an extension of the simplified trapezoidal rule.
• Conservation laws for mass and total pressure at vessel junctions were enforced using Lagrange multipliers.
• The ETM scheme was validated using established arterial network and dam break benchmark problems.

Main Results:

• The ETM demonstrated simplicity, intuitive connection to lumped parameter models, and no restrictive stability criteria (e.g., Courant-Friedrichs-Lewy number).
• The method efficiently handled vessel junctions and boundary conditions without requiring characteristics.
• Simulations of a 56-vessel arterial network yielded satisfactory results, with computation times significantly reduced by increasing time step and element size.

Conclusions:

• The ETM provides an accurate, stable, and computationally efficient approach for 1D blood flow modeling.
• The method's robustness and speed make it suitable for complex physiological simulations, even with larger time steps.
• ETM offers a promising alternative for researchers and clinicians in cardiovascular modeling.