Consistency Analysis of Systems of Partial and Ordinary Differential and Algebraic Equations
This thesis is concerned with process simulation of mathematical models comprising mixed systems of ordinary and partial differential and algebraic equations and the correct formulation thereof. The first part of the thesis considers general point conditions imposed on nonlinear DAE systems, e.g. problems involving periodic conditions or problems, where a degree of 'shaping' of the transient behaviour of a particular system is desired. A necessary condition for consistency is derived that permits the formulation of a structural algorithm that is applicable to large nonlinear DAE systems of index-1. The second part of the thesis considers the determination of consistent variations of the dependent variables over the boundary of the domain of definition of a PDAE system. Specifications ('boundary conditions') imposed on overlapping parts of the boundary (e.g. faces with common edges, or edges with common vertices) often lead to inconsistencies that are not trivial to detect, especially in PDAEs involving three or more dimensions. A general algorithmic framework is introduced that facilitates the consistent specification of PDAE systems.