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arXiv · 2509.15900

A Flow-rate-conserving CNN-based Domain Decomposition Method for Blood Flow Simulations

Simon Klaes·Axel Klawonn·Natalie Kubicki·Martin Lanser·Kengo Nakajima·Takashi Shimokawabe·Janine Weber
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Abstract

This work aims to predict blood flow with non-Newtonian viscosity in stenosed arteries using convolutional neural network (CNN) surrogate models. An alternating Schwarz domain decomposition method is proposed which uses CNN-based subdomain solvers. A universal subdomain solver (USDS) is trained on a single, fixed geometry and then applied for each subdomain solve in the Schwarz method. Results for two-dimensional stenotic arteries of varying shape and length for different inflow conditions are presented and statistically evaluated. One key finding, when using a limited amount of training data, is that incorporating a physics-aware constraint, as, in our case, flow rate conservation, into the USDS improves the prediction accuracy and convergence behavior of the Schwarz method compared to a purely data-driven USDS. As the USDS is a data-driven, inexact subdomain solver, admissible parameter ranges for the geometry and inflow configurations must be defined and tested.

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Simon Klaes, Axel Klawonn, Natalie Kubicki, Martin Lanser, Kengo Nakajima, Takashi Shimokawabe, Janine Weber. 2025-09-19. A Flow-rate-conserving CNN-based Domain Decomposition Method for Blood Flow Simulations. https://arxiv.org/abs/2509.15900

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