Stability of Sequential Modular Time Integration Methods for Coupled Multibody System Models

The interacting components of complex technical systems are often described by coupled systems of differential equations. In dynamical simulation, these coupled differential equations have to be solved numerically. Cosimulation techniques, multirate methods, and other approaches that exploit the modular structure of coupled systems are frequently used as alternatives to classical time integration methods. The numerical stability and convergence of such modular time integration methods is studied for a class of sequential modular methods for coupled multibody system models. Theoretical investigations and numerical test results show that the stability of these sequential modular methods may be characterized by a contractivity condition. A linearly implicit stabilization of coupling terms is proposed to guarantee numerical stability and convergence.

NUMERICAL STABILITY AND CONVERGENCE OF APPROXIMATE METHODS FOR CONSERVATION LAWS

We present the new approach to background of approximate methods convergence based on functional solutions theory for conservation laws. The applications to physical kinetics, gas and fluid dynamics are considered.