Spinoff Challenges for Computational Fluid Dynamics

Abstract

This paper describes extensions of computational fluid dynamics (CFD) to fields of analysis lying well beyond their current realms of application. In particular, three examples are presented. The first is to the collective behavior of mobs of people interacting with sources of danger and/or opportunity to which each individual responds by actions that depend strongly on the inducement of fear and/or excitement, depending on the intrinsic susceptibilities of the person. This behavior results in both individual activities (agent-based) and collective behaviors (crowd-based stochastic) with consequences of potentially great significance. Extensions are also described for which various other emotional developments are important to the behavior of a mob. The second example is to the processes of biological evolution, in particular to the driving forces that influence the directions of species alterations through a succession of characteristics that are tested for survivability in classical Darwinian fashion. The key to the analysis lies in the newly emerging field of epigenetics, in which numerous important experimental studies are producing astonishing results leading to major challenges to the creation of computational models of the collective fluid-like dynamics of interacting biological species. The third example explores an alternative to the Big Bang theory for describing the origin of our universe. The idea is that a parent universe exists, being composed of energy, matter, and antimatter in various forms. In some region a perturbation occurs, which locally has an excess of matter over antimatter. An enormous gravitational buildup of matter and energy in the region leads to a black hole, in which there is distortion in the fourth dimension. The result then leads to an offspring entity (universe) that becomes completely detached from the parent. To apply computational fluid dynamics to the analysis of this process requires formulations that include a major component of relevant physical representations. In all three of these examples, instabilities, fluctuations, and turbulence play major roles. These arise naturally in agent-based numerical formulations (the first and second of our examples), but are much more challenging to describe in a stochastic representation (e.g., the Navier–Stokes equations). Some promising spectral analysis extensions for stochastic formulations are included in this paper.