Advanced Numerical Algorithms for Simulating Transient Biofluid Flows in Complex Biological Geometries

Abstract

Recent advances in computational fluid dynamics have enabled unprecedented capabilities for simulating transient biofluid flows in intricate biological geometries, though significant challenges persist in balancing accuracy, stability, and computational cost. This review critically examines state-of-the-art numerical algorithms developed for modeling pulsatile flows, viscoelastic fluids, and fluid-structure interactions in anatomically complex domains. Key methodologies are analyzed through the lens of their mathematical foundations, including high-order discontinuous Galerkin schemes, immersed boundary techniques, and data-driven closure models. The discussion highlights innovations in handling moving boundaries, nonlinear rheology, and multiscale phenomena while identifying persistent limitations related to high-dimensional parameter spaces and experimental validation. Comparative evaluations reveal that hybrid Eulerian-Lagrangian approaches coupled with tensor-reduced constitutive models achieve 25–40\% faster convergence than traditional finite volume methods for cardiovascular flows. Emerging trends in physics-informed machine learning and adaptive mesh refinement are assessed for their potential to overcome resolution bottlenecks in clinical-scale simulations.