A strongly-coupled immersed-boundary formulation for thin deforming surfaces, with application to elastic beams

TL;DR

This paper introduces a stable, strongly-coupled immersed-boundary method for simulating flow interactions with thin, deforming surfaces like elastic beams, capable of handling large motions and various mass ratios.

Contribution

The paper presents a novel nonlinear algebraic system solution approach for immersed-boundary methods that avoids heuristic parameters and scales efficiently with surface discretization.

Findings

Method is stable for arbitrary mass ratios and large motions

Converges in few iterations without heuristic regularization

Validated with nonlinear beam flapping simulations

Abstract

We present a strongly-coupled immersed-boundary method for flow-structure interaction problems involving thin deforming bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large body motions. As with many strongly-coupled immersed-boundary methods, our method requires the solution of a nonlinear algebraic system at each time step. The system is solved through iteration, where the iterates are obtained by linearizing the system and performing a block LU factorization. This restricts all iterations to small-dimensional subsystems that scale with the number of discretization points on the immersed surface, rather than on the entire flow domain. Moreover, the iteration procedure we propose does not involve heuristic regularization parameters, and has converged in a small number of iterations for all problems we have considered. We derive our method for general deforming surfaces, and verify the method with two-dimensional test problems of geometrically nonlinear beams undergoing large amplitude flapping behavior.