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J. Houbolt, G. Brooks (1957)
Differential equations of motion for combined flapwise bending, chordwise bending, and torsion of twisted nonuniform rotor blades
W Johnson (2013)
Rotorcraft Aeromechanics. Cambridge Aerospace Series
C. Moler, C. Loan (1978)
Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years LaterSIAM Rev., 45
L. Sanches, G. Michon, A. Berlioz, D. Alazard (2011)
Instability zones for isotropic and anisotropic multibladed rotor configurationsMechanism and Machine Theory, 46
M. Arnold, K. Strehmel, R. Weiner (1993)
Half-explicit Runge-Kutta methods for semi-explicit differential-algebraic equations of index 1Numerische Mathematik, 64
W. Steeb (2014)
Solving Ordinary Differential Equations
W. Johnson (2013)
Rotorcraft Aeromechanics: Frontmatter
U. Leiss, S. Wagner (1987)
Toward a unified representation of rotor blade airloads with emphasis
M. Hochbruck, A. Ostermann (2005)
Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic ProblemsSIAM J. Numer. Anal., 43
(2006)
Geometric Numerical Integration, Springer Series in Computational Mathematics, vol
E. Hairer, G. Wanner (2010)
Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems
M. Hochbruck, A. Ostermann (2010)
Exponential integratorsActa Numerica, 19
G. Beylkin, J. Keiser, L. Vozovoi (1998)
A New Class of Time Discretization Schemes for the Solution of Nonlinear PDEsJournal of Computational Physics, 147
S. Cox, P. Matthews (2002)
Exponential Time Differencing for Stiff SystemsJournal of Computational Physics, 176
Elena Kohlwey (2017)
Towards Helicopter Simulation with an Index-1 Differential-Algebraic Equations System - Efficient Time Integration Methods
M. Condon, Jing Gao, A. Iserles (2016)
On asymptotic expansion solvers for highly oscillatory semi-explicit DAEsDiscrete and Continuous Dynamical Systems, 36
M. Hochbruck, A. Ostermann (2005)
Exponential Runge--Kutta methods for parabolic problemsApplied Numerical Mathematics, 53
J. Butcher (1996)
A history of Runge-Kutta methodsApplied Numerical Mathematics, 20
E. Hairer, C. Lubich, M. Roche (1989)
The numerical solution of differential-algebraic systems by Runge-Kutta methods
BV Minchev (2004)
Exponential Integrators for Semilinear Problems
J. Butcher, G. Wanner (1996)
Runge-Kutta methods: some historical notesApplied Numerical Mathematics, 22
In this paper we suggest a combination of exponential integrators and half-explicit Runge–Kutta methods for solving index-1 DAE systems with a stiff linear part in their differential equations. We discuss the behavior of the resulting half-explicit exponential Runge–Kutta (HEERK) methods for a simple numerical example and for a coupled rotor simulation. The coupled rotor simulation is based on a modular software design where all subsystems are modeled by ODEs in state-space form. By connecting the subsystems’ inputs and outputs we obtain an index-1 DAE system. Large terms in the system can be expressed as a stiff linear part which includes strong damping or oscillation terms as well as coefficients for the discretization of the rotor blades (3d beam equations). We show that the proposed HEERK methods can solve the resulting system efficiently with a reasonable timestep size.
Mathematics in Computer Science – Springer Journals
Published: Jul 4, 2019
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