Clifford Algebraic Computational Fluid Dynamics: A New Class of Experiments.
Though some influentially critical objections have been raised during the ‘classical’ pre-computational simulation philosophy of science (PCSPS) tradition, suggesting a more nuanced methodological category for experiments , it safe to say such critical objections have greatly proliferated in philosophical studies dedicated to the role played by computational simulations in science. For instance, Eric Winsberg (1999-2003) suggests that computer simulations are methodologically unique in the development of a theory’s models suggesting new epistemic notions of application. This is also echoed in Jeffrey Ramsey’s (1995) notions of “transformation reduction,”—i.e., a notion of reduction of a more highly constructive variety. Computer simulations create a broadly continuous arena spanned by normative and descriptive aspects of theory-articulation, as entailed by the notion of transformation reductions occupying a continuous region demarcated by Ernest Nagel’s (1974) logical-explanatory “domain-combining reduction” on the one hand, and Thomas Nickels’ (1973) heuristic “domain-preserving reduction,” on the other.
I extend Winsberg’s and Ramsey’s points here, by arguing that in the field of computational fluid dynamics (CFD) as well as in other branches of applied physics, the computer plays a constitutively experimental role—supplanting in many cases the more traditional experimental methods such as flow-visualization, etc. In this case, however CFD algorithms act as substitutes, not supplements (as the notions “simulation” suggests) when it comes to experimental practices. I bring up the constructive example involving the Clifford-Algebraic algorithms for modeling singular phenomena (i.e., vortex formation, etc.) in CFD by Gerik Scheuermann (2000) and Steven Mann & Alyn Rockwood (2003) who demonstrate that their algorithms offer greater descriptive and explanatory scope than the standard Navier-Stokes approaches. The mathematical distinction between Navier-Stokes-based and Clifford-Algebraic based CFD (i.e., NSCFD and CACFD) has essentially to do with the regularization features (i.e., overcoming and conditioning singularities) exhibited to a far greater extent by the latter, than the former. Hence, CACFD indicate that the utilization of computational techniques can be based on principled reasons (i.e., the ability to characterize singular phenomena in ways that traditional experimental methodologies are too coarse-grained to meet the explanatory demands suggested by CFD), as opposed to merely practical (i.e., that such computational procedures better fit the bill-literally!-in terms of contingent resource allocation). CACFD hence exhibit a new generative role in the field of fluid mechanics, by offering categories of experimental evidence that are optimally descriptive and explanatory—i.e., pace Batterman (2005) can be both ontologically and epistemically fundamental.
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