A time-stepping scheme for inelastic collisions |
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Authors: | B Maury |
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Institution: | (1) Laboratoire de Mathématiques, Université Paris Sud, Batiment 425, 91405, ORSAY, France |
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Abstract: | We propose here a numerical scheme to compute the motion of rigid bodies with a non-elastic impact law. The method is based
on a global computation of the reaction forces between bodies. Those forces, whose direction is known since we neglect friction
effects, are identified at the discrete level with a scalar which plays the role of a Kuhn-Tucker multiplier associated to
a first-order approximation of the non-overlapping constraint, expressed in terms of velocities. Since our original motivation
is the handling of the non-overlapping constraint in fluid-particle direct simulations, we paid a special attention to stability
and robustness. The scheme is proved to be stable and robust. As regards its asymptotic behaviour, a convergence result is
established in the case of a single contact. Some numerical tests are presented to illustrate the properties of the algorithm.
Firstly, we investigate its asymptotic behaviour in a situation of non-uniqueness, for a single particle. The two other sets
of results show the good behaviour of the scheme for large time steps. |
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Keywords: | |
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