## Details

Original language | English |
---|---|

Number of pages | 13 |

Journal | Computational mechanics |

Early online date | 25 May 2024 |

Publication status | E-pub ahead of print - 25 May 2024 |

## Abstract

We consider the aeroelastic simulation of flexible mechanical structures submerged in subsonic fluid flows at low Mach numbers. The nonlinear kinematics of flexible bodies are described in the total Lagrangian formulation and discretized by finite elements. The aerodynamic loads are computed using the unsteady vortex-lattice method wherein a free wake is tracked over time. Each implicit time step in the dynamic simulation then requires solving a nonlinear equation system in the structural variables with additional aerodynamic load terms. Our focus here is on the efficient numerical solution of this system by accelerating the Newton algorithm. The particular structure of the aeroelastic nonlinear system suggests the structural derivative as an approximation to the full derivative in the linear Newton system. We investigate and compare two promising algorithms based on this approximation, a quasi-Newton type algorithm and a novel inexact Newton algorithm. Numerical experiments are performed on a flexible plate and on a wind turbine. Our computational results show that the approximation can indeed accelerate the Newton algorithm substantially. Surprisingly, the theoretically preferable inexact Newton algorithm is much slower than the quasi-Newton algorithm, which motivates further research to speed up derivative evaluations.

## Keywords

- Aeroelastic simulation, Implicit time integration, Inexact Newton algorithms, Unsteady vortex-lattice method

## ASJC Scopus subject areas

- Engineering(all)
**Computational Mechanics**- Engineering(all)
**Ocean Engineering**- Engineering(all)
**Mechanical Engineering**- Computer Science(all)
**Computational Theory and Mathematics**- Mathematics(all)
**Computational Mathematics**- Mathematics(all)
**Applied Mathematics**

## Cite this

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- Harvard
- Apa
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- BibTeX
- RIS

**Accelerating aeroelastic UVLM simulations by inexact Newton algorithms.**/ Schubert, Jenny; Steinbach, Marc C.; Hente, Christian et al.

In: Computational mechanics, 25.05.2024.

Research output: Contribution to journal › Article › Research › peer review

*Computational mechanics*. https://doi.org/10.48550/arXiv.2403.15286, https://doi.org/10.1007/s00466-024-02484-2

*Computational mechanics*. Advance online publication. https://doi.org/10.48550/arXiv.2403.15286, https://doi.org/10.1007/s00466-024-02484-2

}

TY - JOUR

T1 - Accelerating aeroelastic UVLM simulations by inexact Newton algorithms

AU - Schubert, Jenny

AU - Steinbach, Marc C.

AU - Hente, Christian

AU - Märtins, David

AU - Schuster, Daniel

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/5/25

Y1 - 2024/5/25

N2 - We consider the aeroelastic simulation of flexible mechanical structures submerged in subsonic fluid flows at low Mach numbers. The nonlinear kinematics of flexible bodies are described in the total Lagrangian formulation and discretized by finite elements. The aerodynamic loads are computed using the unsteady vortex-lattice method wherein a free wake is tracked over time. Each implicit time step in the dynamic simulation then requires solving a nonlinear equation system in the structural variables with additional aerodynamic load terms. Our focus here is on the efficient numerical solution of this system by accelerating the Newton algorithm. The particular structure of the aeroelastic nonlinear system suggests the structural derivative as an approximation to the full derivative in the linear Newton system. We investigate and compare two promising algorithms based on this approximation, a quasi-Newton type algorithm and a novel inexact Newton algorithm. Numerical experiments are performed on a flexible plate and on a wind turbine. Our computational results show that the approximation can indeed accelerate the Newton algorithm substantially. Surprisingly, the theoretically preferable inexact Newton algorithm is much slower than the quasi-Newton algorithm, which motivates further research to speed up derivative evaluations.

AB - We consider the aeroelastic simulation of flexible mechanical structures submerged in subsonic fluid flows at low Mach numbers. The nonlinear kinematics of flexible bodies are described in the total Lagrangian formulation and discretized by finite elements. The aerodynamic loads are computed using the unsteady vortex-lattice method wherein a free wake is tracked over time. Each implicit time step in the dynamic simulation then requires solving a nonlinear equation system in the structural variables with additional aerodynamic load terms. Our focus here is on the efficient numerical solution of this system by accelerating the Newton algorithm. The particular structure of the aeroelastic nonlinear system suggests the structural derivative as an approximation to the full derivative in the linear Newton system. We investigate and compare two promising algorithms based on this approximation, a quasi-Newton type algorithm and a novel inexact Newton algorithm. Numerical experiments are performed on a flexible plate and on a wind turbine. Our computational results show that the approximation can indeed accelerate the Newton algorithm substantially. Surprisingly, the theoretically preferable inexact Newton algorithm is much slower than the quasi-Newton algorithm, which motivates further research to speed up derivative evaluations.

KW - Aeroelastic simulation

KW - Implicit time integration

KW - Inexact Newton algorithms

KW - Unsteady vortex-lattice method

UR - http://www.scopus.com/inward/record.url?scp=85194459885&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2403.15286

DO - 10.48550/arXiv.2403.15286

M3 - Article

AN - SCOPUS:85194459885

JO - Computational mechanics

JF - Computational mechanics

SN - 0178-7675

ER -