A multibody approach in granular dynamics simulations

Abstract

A plane model of a granular system made out of interconnected disks is treated as a multibody system with variable topology and one-sided constraints between the disks. The motion of such a system is governed by a set of nonlinear algebraic and differential equations. In the paper two formalisms (Lagrangian and Newton-Euler) and two solvers (Runge-Kutta and iterative) are discussed. It is shown numerically that a combination of the Newton-Euler formalism and an iterative method allows to maintain the accuracy of the fourth order Runge-Kutta solver while reducing substantially the CPU time. The accuracy and efficiency are achieved by integrating the error control into the iterative process. Two levels of error control are introduced: one, based on satisfying the position, velocity and acceleration constraints, and another, on satisfying the energy conservation requirement. An adaptive time step based on the rate of convergence at the previous time step is introduced which also allows to reduce the simulation time. The efficiency and accuracy is investigated on a physically unstable vertical stack of disks and on multibody pendulums with 50, 100, 150 and 240 masses. An application to the problem of jamming in a two-phase flow is presented.