On the representation of balance equations in a knowledge based process modeling tool

Abstract:
A methodology for the representation and generation of arbitrary balance equations in a knowledge-based modeling tool is presented. Balance equations form the core of any process model. A crude estimation of the number of geometrical set-ups for variants of balance equations (one-, two- and three-dimensional spatial domains in different coordinate systems, macroscopic and ideally mixed system descriptions) denies the explicit declarative representations of all equation types in a knowledge base. Therefore a hybrid declarative / procedural representation is suggested in this contribution. A single generic balance equation for either scalar or vector quantities in general orthogonal coordinates is derived. In addition, procedures are introduced which allow the generation of balance equation variants in arbitrary orthogonal coordinate systems of arbitrary spatial dimensions. The introduced procedures involve formal integration over spatial domains, the specialization of different spatial operators and the specification of the generic terms of the balance equation. Consistency and extensibility of this representation is guaranteed since new types of equations can be easily incorporated into the developed methodology by specifying a new set of data for the generic procedures.

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