Reference : Order reduction in time integration caused by velocity projection
Scientific congresses and symposiums : Paper published in a book
Engineering, computing & technology : Mechanical engineering
http://hdl.handle.net/2268/167843
Order reduction in time integration caused by velocity projection
English
Arnold, Martin []
Cardona, Alberto []
Bruls, Olivier mailto [Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire des Systèmes Multicorps et Mécatroniques >]
Jul-2014
Proceedings of the 3rd Joint International Conference on Multibody System Dynamics and the 7th Asian Conference on Multibody Dynamics
10 pages
No
Yes
International
3rd Joint International Conference on Multibody System Dynamics and the 7th Asian Conference on Multibody Dynamics
July 2014
Busan
Corea
[en] Lie group methods ; differential-algebraic equation ; time integration
[en] Holonomic constraints restrict the configuration of a multibody system to a subset of the configuration space. They imply so called hidden constraints at the level of velocity coordinates that may formally be obtained from time derivatives of the original holonomic constraints. A numerical solution that satisfies hidden constraints as well as the original constraint equations may be obtained considering both types of constraints simultaneously in each time step (stabilized index-2 formulation) or using projection techniques. Both approaches are well established in the time integration of differential-algebraic equations. Recently, we have introduced a generalized- alpha Lie group time integration method for the stabilized index-2 formulation that achieves second order convergence for all solution components. In the present paper, we show that a separate velocity projection would be less favourable since it may result in an order reduction and in large transient errors after each projection step. This undesired numerical behaviour is analysed by a one-step error recursion that considers the coupled error propagation in differential and algebraic solution components. This one-step error recursion has been used before to prove second order convergence for the application of generalized-alpha methods to constrained systems. As a technical detail, we discuss the extension of these results from symmetric, positive definite mass matrices to the rank deficient case.
Researchers ; Professionals ; Students
http://hdl.handle.net/2268/167843

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