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KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation

Donald Brown, Texas A&M University
Multiscale Methods for Fluid-Structure Interaction


In this poster we develop a multiscale formulation for Fluid-Structure Interaction (FSI) of elastic solid media with slowly creeping Newtonian fluids. Traditionally, the governing equations in solid mechanics are formulated in the Lagrangian, or fixed reference frame, while fluid mechanics equations are presented in the Eulerian, or moving frame. This poses a problem when attempting to utilize tools of homogenization to understand the dependence of microscopic quantities on macroscopic quantities. In addition, this difference in frame formulation makes analysis of related iterative algorithms exceedingly difficult and convoluted. We present the Arbitrary-Lagrange-Eulerian (ALE) formulation of the problem and the homogenized equations in this formulation. We highlight how this may alleviate these issues.

We also show results comparing results computed from a fine scale FSI and an iterative multiscale framework in the case of many small elastic circular inclusions. The deformation of the initially periodic media, makes the use of traditional periodic homogenization corrector estimates not feasible. We present recent related results to the generalization of corrector estimates for Stokesian flow in slowly varying media. We present two computational examples of the corrector estimates: one where we have precomputed elliptical inclusions and the other for fractured media with FSI driven deformation.