# A 3D DLM/FD method for simulating the motion of spheres and ellipsoids under creeping flow conditions

## Abstract

We present in this article a novel distributed Lagrange multiplier/fictitious domain (DLM/FD) method for simulating fluid-particle interaction in three-dimensional (3D) Stokes flow. The methodology is validated by comparing the numerical results for a neutrally buoyant particle, of either spherical or prolate shape, with the associated Jeffrey's solutions for a simple shear flow. The results concerning two balls, interacting under creeping flow conditions in a bounded shear flow, are consistent with those available in the literature. We will discuss also the interactions of two balls in a bounded shear flow, when these balls are very close initially. For a prolate ellipsoid rotating in a shear flow under the sole effect of the particle inertia, shear plane tumbling is stable, while log-rolling is unstable. For two prolate ellipsoids interacting in a bounded shear flow, the results are similar to those for two balls if the major axes are initially orthogonal to the shear plane (a result not at all surprising considering that the intersections of the ellipsoids with the shear pane are circular).

- Authors:

- Department of Mathematics, University of Houston, Houston, TX 77204 (United States)
- (China)

- Publication Date:

- OSTI Identifier:
- 22701649

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 352; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CREEP; INTERACTIONS; MATHEMATICAL SOLUTIONS; MOMENT OF INERTIA; SHEAR; SPHERICAL CONFIGURATION; THREE-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Pan, Tsorng-Whay, Guo, Aixia, Chiu, Shang-Huan, Glowinski, Roland, and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.
```*A 3D DLM/FD method for simulating the motion of spheres and ellipsoids under creeping flow conditions*. United States: N. p., 2018.
Web. doi:10.1016/J.JCP.2017.09.042.

```
Pan, Tsorng-Whay, Guo, Aixia, Chiu, Shang-Huan, Glowinski, Roland, & Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.
```*A 3D DLM/FD method for simulating the motion of spheres and ellipsoids under creeping flow conditions*. United States. doi:10.1016/J.JCP.2017.09.042.

```
Pan, Tsorng-Whay, Guo, Aixia, Chiu, Shang-Huan, Glowinski, Roland, and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong. Mon .
"A 3D DLM/FD method for simulating the motion of spheres and ellipsoids under creeping flow conditions". United States. doi:10.1016/J.JCP.2017.09.042.
```

```
@article{osti_22701649,
```

title = {A 3D DLM/FD method for simulating the motion of spheres and ellipsoids under creeping flow conditions},

author = {Pan, Tsorng-Whay and Guo, Aixia and Chiu, Shang-Huan and Glowinski, Roland and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong},

abstractNote = {We present in this article a novel distributed Lagrange multiplier/fictitious domain (DLM/FD) method for simulating fluid-particle interaction in three-dimensional (3D) Stokes flow. The methodology is validated by comparing the numerical results for a neutrally buoyant particle, of either spherical or prolate shape, with the associated Jeffrey's solutions for a simple shear flow. The results concerning two balls, interacting under creeping flow conditions in a bounded shear flow, are consistent with those available in the literature. We will discuss also the interactions of two balls in a bounded shear flow, when these balls are very close initially. For a prolate ellipsoid rotating in a shear flow under the sole effect of the particle inertia, shear plane tumbling is stable, while log-rolling is unstable. For two prolate ellipsoids interacting in a bounded shear flow, the results are similar to those for two balls if the major axes are initially orthogonal to the shear plane (a result not at all surprising considering that the intersections of the ellipsoids with the shear pane are circular).},

doi = {10.1016/J.JCP.2017.09.042},

journal = {Journal of Computational Physics},

issn = {0021-9991},

number = ,

volume = 352,

place = {United States},

year = {2018},

month = {1}

}