(588g) The Five Levels of Modelling

Preisig, H. A., Norwegian University of Science and Technology (NTNU)
Haug-Warberg, T., Norwegian University of Science and Technology

The ProcessModeller project distinguishes between five main items:

1) Abstraction: The modelled process is represented as a network lumped and distributed systems that communicate extensive quantity.

2) Description: Causality is the main concept for mimicking the behaviour of the modelled system: The concept of conservation laws stating that the change of the system is caused by the exchange of the conserved quantity in all forms across the boundary and the possible internal transposition of the conserved quantity. On the macroscopic scale, the driving forces for the transfer are continuous across the boundaries, whilst some of the intensive quantities exhibit jump-behaviour. The complete description thus incorporates the network, the conservation laws for all systems, all transfers, all transpositions and all links between the quantities that provide the information of the driving forces both for the transport and the transposition. Latter incorporates thermodynamics and geometry as the two main components besides some simple definitions such as density and composition measures. The physical description must be accompanied by a unique internal representation of the involved equations. It is important to bear in mind that, even though the aforementioned concepts are believed to be correct at all time and space scales, their mathematical representations are quite limited. This brings simplification to our minds.

3) Simplification: Four cases dominate models of physical systems: distributed vs lumped and dynamic vs steady state. The first pair contrasts spatial considerations in which at least some intensities are a function of the position vs all being uniform over the viewed spatial domain. The second pair deals with two extremes of the time scale in which the dynamic systems describe the change of the state with time, whilst in the steady state the state of the system is defined by the conditions on the boundary. In mathematical terms, the pairs are represented by partial differential equations vs ordinary differential and the second pair by partial or ordinary differential equations vs algebraic or differential equations is patial co-ordinates. All of them augmented with the algebraic equations representing transport, transposition and state variable transformations. The second member in each pair also represents an approximation of the first. Thus lumped systems are approximations of distributed systems and steady state systems are approximations of dynamic system either on the very short time scale (event dynamic) or on the very long time scale (constant).

4) Encapsulation: All equations admissible for the description of the process must be available in a containment. Traditionally such a generic model does not exist. Instead the equations are distributed in instances of modelled process components. The strength of successful industrial packages lies in their process-unit packages. The aim here is to encapsulate the theory as a superstructure representing all alternatives of modelled systems. The actual equations are only generated at the time the instantiated model of a particular system is being generated. Even on this level, the model can be split into a simple graph of the super model and a description of the network and a list of lists of parameters.

5) Exportation: The programming languages used for the implementation of physical models have changed very little over the years, at least compared to what languages are available today. It started with FORTRAN some 40-50 years ago, went through C/C++ 20-30 years ago, and is now come to a point that scripting languages like Matlab and Python have become viable options. This trend is likely to continue and it is important to make the modelling process independent of the target language. Most of the operations needed to do modelling (hashes, structs, vectors and matrices) are available in all modern languages and it is possible to export different target codes for different languages from within the modelling tool without actually rewriting the model itself. Only the syntactic and semantic rules of the target language must be known. In addition the solver's required structure must be woven with the equations: earlier called splicing today it is a wrapper.