DAEs in Applications

Abstract

Differential-algebraic equations (DAEs) arise naturally in many technical and industrial applications. By incorporating the special structure of the DAE systems arising in certain physical domains, the general approach for the regularization of DAEs can be efficiently adapted to the system structure. We will present the analysis and regularization approaches for DAEs arising in mechanical multibody systems, electrical circuit equations, and flow problems. In each of these cases the DAEs exhibit a certain structure that can be used for an efficient analysis and regularization. Moreover, we discuss the numerical treatment of hybrid DAE systems, that also occur frequently in industrial applications. For such systems, the framework of DAEs provides essential information for a robust numerical treatment. IntroductionIn the simulation and control of constrained dynamical systems differential-algebraic equations (DAEs) are widely used, since they naturally arise in the modeling process. In particular, the automatic modeling using coupling of modularized subcomponents is frequently used in industrial applications yielding large-scale (but often sparse) DAE systems. An important aspect in the simulation of these systems is that conservation laws (e.g. conservation of mass or momentum, mass or population balances, etc.) included in the model equations should be preserved during the numerical integration. These algebraic relations pose constraints on the solution and may lead to so-called hidden constraints (for higher index DAEs). Also path-following constraints can be considered as additional algebraic constraints. The occurrence of hidden constraints leads to difficulties in the numerical solution as