The Simulation of a Physical Process and Analogous Computers

The simulation of a physical process consists in analysing the phenomena of the whole process or of a part of it. This is based on the use of a reduced-scale plant. 

At the same time, when we impose the dimensions of the plant, we can focus on obtaining one or more of the optimal solutions (maximum degree of species transformation, minimum chemical consumption, maximum degree of species transformation with minimum chemical consumption etc.) For this purpose, it is recommended to use both mathematical and physical simulations. 

For physical process simulation, as well as for mathematical model development, we can use the isomorphism principle. This is based on the formal analogy of the mathematical and physical descriptions of different phenomena. We can detail this principle by considering the conductive flux transport of various properties, which can be written as follows  

It is not difficult to observe that in all of these expressions we have a multiplication between the property gradient and a constant that characterizes the medium in which the transport occurs. As a consequence, with the introduction of a transformation coefficient we can simulate, for example, the momentum flow, the heat flow or species flow by measuring only the electric current flow. So, when we have the solution of one precise transport property, we can extend it to all the cases that present an analogous physical and mathematical description. Analogous computers [1.27] have been developed on this principle. The analogous computers, able to simulate mechanical, hydraulic and electric micro-laboratory plants, have been experimented with and used successfully to simulate heat [1.28] and mass [1.29] transport. 

Zeigler, The Theory of Modelling and Simulation, Wiley, New York, 1976. 

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