Open Access

ARTICLE

An IB Method for Non-Newtonian-Fluid Flexible-Structure Interactions in Three-Dimensions

Luoding Zhu^1,∗

1 Indiana University-Purdue University Indianapolis, USA.

*Corresponding Author: Luoding Zhu. Email: .

(This article belongs to the Special Issue: Recent Developments of Immersed Methods for Fluid-structure Interactions)

Computer Modeling in Engineering & Sciences 2019, 119(1), 125-143. https://doi.org/10.32604/cmes.2019.04828

Abstract

Problems involving fluid flexible-structure interactions (FFSI) are ubiquitous in engineering and sciences. Peskin’s immersed boundary (IB) method is the first framework for modeling and simulation of such problems. This paper addresses a three-dimensional extension of the IB framework for non-Newtonian fluids which include power-law fluid, Oldroyd-B fluid, and FENE-P fluid. The motion of the non-Newtonian fluids are modelled by the lattice Boltzmann equations (D3Q19 model). The differential constitutive equations of Oldroyd-B and FENE-P fluids are solved by the D3Q7 model. Numerical results indicate that the new method is first-order accurate and conditionally stable. To show the capability of the new method, it is tested on three FFSI toy problems: a power-law fluid past a flexible sheet fixed at its midline, a flexible sheet being flapped periodically at its midline in an Oldroyd-B fluid, and a flexible sheet being rotated at one edge in a FENE-P fluid.

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