Index analysis and reduction of systems of quasi-linear partial-differential and algebraic equations

•A new procedure for the systematic index reduction of PDAE systems is presented.•Supports the development of distributed models in a systematic modeling work flow.•Method yields low-index model and important insight into the PDAE system.•Supports the consistent specification of initial and boundary conditions.•Applied to tubular reactor, charge transport and incompressible fluid flow models.

To reliably solve PDAE models in established equation-oriented modeling environments (i) certain mathematical properties are to be fulfilled and (ii) the specified initial- and boundary conditions are to be consistent. For an assessment of both of these aspects an important theoretical framework is the concept of index. In this contribution we propose a new method for a systematic index reduction of quasi-linear PDAE systems. The general idea is to reveal quasi-linear combinations of the differential quantities in the high-index model which are invariant with respect to a specific independent variable. By using these quasi-linear combinations as templates for symbolic manipulations, additional algebraic constraints become explicit. These explicit constraints are then used for index reduction yielding low-index PDAE models. The procedure is demonstrated in the context of a typical modeling work-flow for modeling problems of a tubular reactor, diffusive charge transport in electrolyte mixtures and incompressible fluid flow.

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