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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