A monolithic localized high-order ALE finite element method for multi-scale fluid-structure interaction problems

Abstract: This paper presents MLH-ALE, a monolithic localized high-order arbitrary Lagrangian-Eulerian finite element method for multi-scale fluid-structure interaction (FSI). The framework employs isoparametric $\mathcal{P}_2$ elements for geometric fidelity and an implicit-explicit partitioned Runge-Kutta (IMEX-PRK) scheme for temporal discretization. To address scale disparity, a localized updating strategy is integrated to focus computational resolution on the moving structure. Numerical benchmarks confirm the optimal high-order convergence of the underlying ALE scheme. Furthermore, simulations of particle focusing in spiral microchannels demonstrate that the MLH-ALE approach provides reliable numerical results in good agreement with experimental observations, confirming its feasibility for complex multi-scale applications.