Annals of Mathematical Sciences and Applications

Volume 9 (2024)

Number 1

A 3D DLM/FD method for simulating the motion of an ellipsoid in a bounded shear flow of viscoelastic fluids

Pages: 91 – 121

DOI: https://dx.doi.org/10.4310/AMSA.2024.v9.n1.a3

Authors

Shang-Huan Chiu (Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania, U.S.A.)

Tsorng-Whay Pan (Department of Mathematics, University of Houston, Texas, U.S.A.)

Abstract

$\def\De{\operatorname{De}}$We present a novel distributed Lagrange multiplier/fictitious domain (DLM/FD) method for simulating fluid-particle interaction in viscoelastic fluids in Stokes regime. The results concerning an ellipsoid rotating in a three dimensional (3D) bounded shear flow are obtained for Deborah number $(De$) up to $4$. The averaged angular velocities of a prolate ellipsoid rotating only in the shear plane have been validated in Giesekus fluid and its period of rotation becomes larger when increasing the value of $De$. For a freely rotating prolate ellipsoid placed in the middle between two moving walls in Oldroyd‑B fluids, kayaking motion is stable for lower $De$ and then tilted log-rolling becomes stable when $De$ exceeds a critical value. Similar results are also obtained for a rotating oblate ellipsoid.

Keywords

Oldroyd-B fluid, Giesekus fluid, shear flow, neutrally buoyant ellipsoid, distributed Lagrange multiplier/fictitious domain methods

2010 Mathematics Subject Classification

Primary 65M60, 76M10. Secondary 76T20.

Received 1 June 2023

Accepted 2 January 2024

Published 5 April 2024