Simulating Arterial Blood Flow Using Finite Volume Conservation Element and Solution Element Scheme (European Journal of Pure and Applied Mathematics, 2025)
This article explores the numerical approximation of blood flow in arteries with spatially varying stiffness and resting cross-sectional areas. The underlying model is designed to maintain steady-state solutions by accurately balancing non-zero fluxes with corresponding source terms. The study primarily addresses the numerical difficulties arising from the model’s complexity. To tackle these challenges, a Conservation Element and Solution Element (CE/SE) scheme is employed, ensuring the preservation of the steady-state condition associated with zero discharge. The proposed scheme effectively reduces numerical oscillations and dissipation, offering enhanced accuracy and robustness over conventional methods. Its performance is validated through several benchmark cases drawn from existing literature, with comparisons made against results obtained using the Central Scheme.
Keywords: 1-D blood flow, CE/SE scheme, Central scheme, KFVS scheme, Non-conservative, Hyperbolic systems.