# An added-mass partition algorithm for fluid–structure interactions of compressible fluids and nonlinear solids

## Abstract

We describe an added-mass partitioned (AMP) algorithm for solving fluid–structure interaction (FSI) problems involving inviscid compressible fluids interacting with nonlinear solids that undergo large rotations and displacements. The computational approach is a mixed Eulerian–Lagrangian scheme that makes use of deforming composite grids (DCG) to treat large changes in the geometry in an accurate, flexible, and robust manner. The current work extends the AMP algorithm developed in Banks et al. [1] for linearly elasticity to the case of nonlinear solids. To ensure stability for the case of light solids, the new AMP algorithm embeds an approximate solution of a nonlinear fluid–solid Riemann (FSR) problem into the interface treatment. The solution to the FSR problem is derived and shown to be of a similar form to that derived for linear solids: the state on the interface being fundamentally an impedance-weighted average of the fluid and solid states. Numerical simulations demonstrate that the AMP algorithm is stable even for light solids when added-mass effects are large. The accuracy and stability of the AMP scheme is verified by comparison to an exact solution using the method of analytical solutions and to a semi-analytical solution that is obtained for a rotating solid disk immersed inmore »

- Authors:

- Publication Date:

- OSTI Identifier:
- 22570219

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 305; Other Information: Copyright (c) 2015 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; ACCURACY; ALGORITHMS; ANALYTICAL SOLUTION; COMPUTERIZED SIMULATION; DEFORMATION; ELASTICITY; EXACT SOLUTIONS; FLUIDS; FLUID-STRUCTURE INTERACTIONS; IMPACT SHOCK; IMPEDANCE; NONLINEAR PROBLEMS; SOLIDS; VELOCITY

### Citation Formats

```
Banks, J.W., E-mail: banksj3@rpi.edu, Henshaw, W.D., E-mail: henshw@rpi.edu, Kapila, A.K., E-mail: kapila@rpi.edu, and Schwendeman, D.W., E-mail: schwed@rpi.edu.
```*An added-mass partition algorithm for fluid–structure interactions of compressible fluids and nonlinear solids*. United States: N. p., 2016.
Web. doi:10.1016/J.JCP.2015.10.043.

```
Banks, J.W., E-mail: banksj3@rpi.edu, Henshaw, W.D., E-mail: henshw@rpi.edu, Kapila, A.K., E-mail: kapila@rpi.edu, & Schwendeman, D.W., E-mail: schwed@rpi.edu.
```*An added-mass partition algorithm for fluid–structure interactions of compressible fluids and nonlinear solids*. United States. https://doi.org/10.1016/J.JCP.2015.10.043

```
Banks, J.W., E-mail: banksj3@rpi.edu, Henshaw, W.D., E-mail: henshw@rpi.edu, Kapila, A.K., E-mail: kapila@rpi.edu, and Schwendeman, D.W., E-mail: schwed@rpi.edu. Fri .
"An added-mass partition algorithm for fluid–structure interactions of compressible fluids and nonlinear solids". United States. https://doi.org/10.1016/J.JCP.2015.10.043.
```

```
@article{osti_22570219,
```

title = {An added-mass partition algorithm for fluid–structure interactions of compressible fluids and nonlinear solids},

author = {Banks, J.W., E-mail: banksj3@rpi.edu and Henshaw, W.D., E-mail: henshw@rpi.edu and Kapila, A.K., E-mail: kapila@rpi.edu and Schwendeman, D.W., E-mail: schwed@rpi.edu},

abstractNote = {We describe an added-mass partitioned (AMP) algorithm for solving fluid–structure interaction (FSI) problems involving inviscid compressible fluids interacting with nonlinear solids that undergo large rotations and displacements. The computational approach is a mixed Eulerian–Lagrangian scheme that makes use of deforming composite grids (DCG) to treat large changes in the geometry in an accurate, flexible, and robust manner. The current work extends the AMP algorithm developed in Banks et al. [1] for linearly elasticity to the case of nonlinear solids. To ensure stability for the case of light solids, the new AMP algorithm embeds an approximate solution of a nonlinear fluid–solid Riemann (FSR) problem into the interface treatment. The solution to the FSR problem is derived and shown to be of a similar form to that derived for linear solids: the state on the interface being fundamentally an impedance-weighted average of the fluid and solid states. Numerical simulations demonstrate that the AMP algorithm is stable even for light solids when added-mass effects are large. The accuracy and stability of the AMP scheme is verified by comparison to an exact solution using the method of analytical solutions and to a semi-analytical solution that is obtained for a rotating solid disk immersed in a fluid. The scheme is applied to the simulation of a planar shock impacting a light elliptical-shaped solid, and comparisons are made between solutions of the FSI problem for a neo-Hookean solid, a linearly elastic solid, and a rigid solid. The ability of the approach to handle large deformations is demonstrated for a problem of a high-speed flow past a light, thin, and flexible solid beam.},

doi = {10.1016/J.JCP.2015.10.043},

url = {https://www.osti.gov/biblio/22570219},
journal = {Journal of Computational Physics},

issn = {0021-9991},

number = ,

volume = 305,

place = {United States},

year = {2016},

month = {1}

}