Adaptation of mathematical models for use in complex physics problems

• 02/24/2010
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Frequently, physical processes which need to be understood include significant intrinsic complexity. As is in all generic problems, in order to find a solution systematically, it is advisable to divide the problem into a group of smaller problems and subsequently, divide each one of those into smaller groups until a unique complex problem is transformed into a system of simpler small problems, which is now possible, or efficient to solve.

However, problems can arise subsequently if the procedure used to resolve one of the smaller issues is not compatible with the others, i.e., it is necessary to establish general working rules, particularly when such smaller problems relate to different areas of physics (flow of groundwater, transport of substances or heat, heat transfer between liquids and solids, performance of machines or energy consumption, to mention a few which could be linked, for example, in the dimensioning of a geothermal plant).
 
Some practices are surmised easily: the use of a standardized system of units, or at least a homogenous system, in order to avoid errors seems obvious. Other matters to be considered are not as apparent and, nevertheless, their effect on the results can be significant, such as the numerical methodology used in each module, the steps used in calculation (e.g., not to combine intraday estimates with annual or monthly averages), the assumptions on which each of the models are based, etc.

Lastly, it is advisable, as a general rule, to establish or implement specific methodologies focused on the evaluation of the sensitivity of each module (and, as a result, the group), the system inputs and the uncertainty associated with the results, both arising from the procedure and those associated with the entry parameters (due to errors in their estimation, their measurement, etc.). The valuation, quantification or definition of the uncertainty in the context of a result is a necessary piece of information in order to interpret its meaning.