Adaptive Mesh Refinement in Computational Biofluid Dynamics: Applications and Algorithmic Advances

Abstract

Computational biofluid dynamics has emerged as a critical tool for modeling complex physiological flows, yet traditional uniform mesh methods struggle to balance accuracy and computational cost. Adaptive mesh refinement (AMR) addresses this challenge by dynamically adjusting spatial resolution based on localized flow features, enabling high-fidelity simulations of multiscale phenomena such as turbulent blood flow, respiratory aerosol transport, and cerebrospinal fluid dynamics. This paper presents a systematic analysis of AMR's algorithmic evolution within biofluid applications, focusing on recent advances in error estimation, parallel scalability, and topology-aware adaptation strategies. We evaluate three dominant AMR paradigms—block-structured, octree-based, and unstructured mesh adaptation—against biomechanical benchmarks including pulsatile arterial flow and alveolar ventilation. Comparative studies reveal that hybrid AMR approaches combining implicit gradient tracking with Lagrangian marker particles reduce temporal overhead by 37\% compared to classical Berger-Oliger methods while maintaining physiological accuracy. Furthermore, we demonstrate that machine learning-driven error predictors can cut mesh optimization cycles by 50\% through anticipatory load balancing. The study also identifies persistent challenges in handling moving boundaries within deformable biological tissues, proposing a coupled immersed boundary-AMR framework validated against in vitro particle image velocimetry data. These results establish quantitative guidelines for selecting AMR strategies based on flow regime complexity, available computational resources, and required biological fidelity.