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

TL;DR

This paper introduces the Duct Boundary Condition (DuBC), a novel boundary condition for 3D-0D coupled flow models that simplifies coupling, incorporates inertial effects, and improves parameter estimation in coronary blood flow simulations.

Contribution

The paper presents the DuBC, a new boundary condition that enables local coupling, accounts for viscous and inertial effects with a single parameter, and facilitates parameter estimation.

Findings

DuBC simplifies coupling in flow models.

It effectively incorporates inertial effects.

Demonstrated improved parameter estimation in coronary flow.

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.