This paper addresses the critical need for the development of
intelligent or assisting software tools for the scientist who is
working in the initial problem formulation and mathematical model
representation stage of research. In particular, examples of that
representation in fluid dynamics and instability theory are
discussed. The creation of a mathematical model that is ready for
application of certain solution strategies requires extensive
symbolic manipulation of the original mathematical model. These
manipulations can be as simple as term reordering or as complicated
as discovery of various symmetry groups embodied in the equations,
whereby Backlund-type transformations create new determining
equations and integrability conditions or create differential
Grobner bases that are then solved in place of the original
nonlinear PDEs. Several examples are presented of the kinds of
problem formulations and transforms that can be frequently
encountered in model representation for fluids problems. The
capability of intelligently automating these types of transforms,
available prior to actual mathematical solution, is advocated.
Physical meaning and assumption-understanding can then be
propagated through the mathematical transformations, allowing for
explicit strategy development.
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