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 -