An efficient semi-implicit method for three-dimensional non-hydrostatic flows in compliant arterial vessels

Area of Science:

• * Computational fluid dynamics
• * Biomedical engineering
• * Cardiovascular system modeling

Background:

• * Arterial blood flow is governed by complex three-dimensional Navier-Stokes equations.
• * Modeling requires accounting for the time-dependent, elastic nature of arterial walls.
• * Previous models often face challenges with numerical stability and computational cost.

Purpose of the Study:

• * To develop a robust and efficient computational model for simulating blood flow in compliant arterial systems.
• * To address numerical stability and reduce computational cost in three-dimensional fluid dynamics simulations.
• * To validate the model against known analytical solutions and previous results.

Main Methods:

• * A three-dimensional semi-implicit finite difference and finite volume model on a staggered grid.
• * A novel pressure-splitting technique: hydrostatic and non-hydrostatic components.
• * Sequential solution of quasi-1D and 3D nonlinear systems for pressure calculation.

Main Results:

• * The developed algorithm is robust, efficient, and mass-conservative (locally and globally).
• * Successfully applied to various flow dimensions (1D, 2D, 3D) and vessel types.
• * Validated against analytical solutions for circular and elliptical cross-sections and compared with prior studies on curved tubes.

Conclusions:

• * The pressure-splitting method provides a stable and computationally inexpensive approach for simulating arterial blood flow.
• * The model accurately captures complex flow phenomena, including axial velocity development and secondary flows.
• * This method offers a versatile tool for analyzing hemodynamics in realistic arterial geometries.