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arXiv · 2512.08207

Duct boundary conditions for incompressible fluid flows: finite element discretizations and parameter estimation in coronary blood flow

Jeremías Garay·David Nolte·Cristóbal Bertoglio
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Abstract

3D-0D coupled flow models are widely used across many application fields but remain challenging to solve. Implicit coupling introduces non-local terms, whereas explicit coupling results in only conditionally stable schemes. Furthermore, incorporating inertial effects alongside viscous resistance enlarges the parameter space, making calibration more difficult. In this work, we propose a new type of boundary condition based on the method of asymptotic partial decomposition of a domain (MAPDD), which we denote as the Duct Boundary Condition (DuBC). This approach enables the incorporation of geometrically reduced domains as a boundary term with only local coupling in the implicit case. Moreover, the DuBC accounts for both viscous and inertial effects simultaneously using a single physical parameter. Additionally, we derive a fractional-step time-marching scheme including the DuBC. We demonstrate the features of the DuBC in coronary artery blood flow simulations, including sequential parameter estimation from noisy velocity data.

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Jeremías Garay, David Nolte, Cristóbal Bertoglio. 2025-12-09. Duct boundary conditions for incompressible fluid flows: finite element discretizations and parameter estimation in coronary blood flow. https://arxiv.org/abs/2512.08207

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