# A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis

## Abstract

A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This *added-mass partitioned* (AMP) algorithm remains stable, without sub-iterations, for light and even zero mass rigid bodies when added-mass and viscous added-damping effects are large. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body. Added mass effects are handled in the Robin condition by inclusion of a boundary integral term that depends on the pressure. Added-damping effects due to the viscous shear forces on the body are treated by inclusion of added-damping tensors that are derived through a linearization of the integrals defining the force and torque. Added-damping effects may be important at low Reynolds number, or, for example, in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small. In this second part of a two-part series, the general formulation of the AMP scheme is presented including the form of the AMP interface conditions and added-damping tensors for general geometries. A fully second-order accurate implementation of the AMP scheme is developed in two dimensions basedmore »

- Authors:

- Rensselaer Polytechnic Inst., Troy, NY (United States)

- Publication Date:

- Research Org.:
- Rensselaer Polytechnic Inst., Troy, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- OSTI Identifier:
- 1353365

- Alternate Identifier(s):
- OSTI ID: 1439534

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 343; Journal Issue: C; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; fluid-structure interaction; moving overlapping; grids; incompressible Navier-Stokes; partitioned schemes; added-mass; added-damping; rigid bodies

### Citation Formats

```
Banks, J. W., Henshaw, W. D., Schwendeman, D. W., and Tang, Qi.
```*A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis*. United States: N. p., 2017.
Web. doi:10.1016/j.jcp.2017.01.015.

```
Banks, J. W., Henshaw, W. D., Schwendeman, D. W., & Tang, Qi.
```*A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis*. United States. doi:10.1016/j.jcp.2017.01.015.

```
Banks, J. W., Henshaw, W. D., Schwendeman, D. W., and Tang, Qi. Fri .
"A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis". United States.
doi:10.1016/j.jcp.2017.01.015. https://www.osti.gov/servlets/purl/1353365.
```

```
@article{osti_1353365,
```

title = {A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis},

author = {Banks, J. W. and Henshaw, W. D. and Schwendeman, D. W. and Tang, Qi},

abstractNote = {A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This added-mass partitioned (AMP) algorithm remains stable, without sub-iterations, for light and even zero mass rigid bodies when added-mass and viscous added-damping effects are large. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body. Added mass effects are handled in the Robin condition by inclusion of a boundary integral term that depends on the pressure. Added-damping effects due to the viscous shear forces on the body are treated by inclusion of added-damping tensors that are derived through a linearization of the integrals defining the force and torque. Added-damping effects may be important at low Reynolds number, or, for example, in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small. In this second part of a two-part series, the general formulation of the AMP scheme is presented including the form of the AMP interface conditions and added-damping tensors for general geometries. A fully second-order accurate implementation of the AMP scheme is developed in two dimensions based on a fractional-step method for the incompressible Navier-Stokes equations using finite difference methods and overlapping grids to handle the moving geometry. Here, the numerical scheme is verified on a number of difficult benchmark problems.},

doi = {10.1016/j.jcp.2017.01.015},

journal = {Journal of Computational Physics},

number = C,

volume = 343,

place = {United States},

year = {Fri Jan 20 00:00:00 EST 2017},

month = {Fri Jan 20 00:00:00 EST 2017}

}

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