Toward higher order event--capturing schemes and adaptive time--step strategies for nonsmooth multibody systems

Vincent Acary (1)

1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems

The report is devoted to the study of higher order time integration methods for multibody systems with unilateral constraints. After a brief presentation of the mathematical modelling of nonsmooth multibody systems, several estimates on the local error of consistency of the Moreau time--stepping scheme are given. Based on these estimates, an attempt at an adaptive time--step strategy is presented on academic examples. Finally, higher order event--capturing methods are designed by coupling implicit Runge--Kutta schemes and the Moreau's time--stepping scheme.

Mots clés: Multibody systems; nonsmooth Mechanics; unilateral constraints; impact; Moreau's sweeping process; numerical integration scheme; Adaptive time--step strategy; order of accuracy; error estimates.; error estimates

Domaines: Systèmes dynamiques [math.DS]; Modélisation et simulation; Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Vincent Acary. Toward higher order event--capturing schemes and adaptive time--step strategies for nonsmooth multibody systems. [Research Report] RR-7151, 2009, pp.31. ⟨inria-00440771v1⟩