Abstract
Fluid mechanics has emerged as a basic concept for nearly every field of technology. Despite there being a well-developed mathematical theory and available commercial software codes, the computation of solutions of the governing equations of motion is still challenging, especially due to the nonlinearity involved, and there are still open questions regarding the underlying physics of fluid flow, especially with respect to the continuum hypothesis and thermodynamic local equilibrium. The aim of this Special Issue is to reference recent advances in the field of fluid mechanics both in terms of developing sophisticated mathematical methods for finding solutions of the equations of motion, on the one hand, and on novel approaches to the physical modelling beyond the continuum hypothesis and thermodynamic local equilibrium, on the other.
Highlights
Fluid Mechanics has a long history, going back at least to the era of ancient Greece, when Archimedes [1] investigated fluid statics and buoyancy and formulated his famous law, known as Archimedes’ principle, which was published in his work, “On Floating Bodies”—generally considered to be the first major work on fluid mechanics
The focus is centred on two major approaches which are diametrically opposed in their origin: (i) the Clebsch transformation originally applies to inviscid flow (Re → ∞), while (ii) the classical complex variable method utilising Airy’s stress function applies to Stokes’ flow (Re → 0). It is shown how both methods have been generalised by successive advancements and applied to the full Navier-Stokes equation, requiring the extension of the complex variable method to a tensor potential method
Future work on the poroacoustic RRG theory is outlined by [16], who suggests the use of homogenisation methods in problems wherein the coefficients vary with position
Summary
Fluid Mechanics has a long history, going back at least to the era of ancient Greece, when Archimedes [1] investigated fluid statics and buoyancy and formulated his famous law, known as Archimedes’ principle, which was published in his work, “On Floating Bodies”—generally considered to be the first major work on fluid mechanics. Bernoulli [5] and developed further by the mathematicians d’Alembert, Lagrange, Laplace, and Poisson, resulting in the well-known potential flow theory, being nowadays an essential topic in standard fluid dynamics text books [6,7,8,9]. Prandtl’s boundary layer theory and its advancement by T. von Kármán was a keystone both in a mathematical and a physical sense. Another branch of research is related to the formation of chaotic turbulent flow structures due to the nonlinearity of the Navier–Stokes equation, beginning with the early studies of O. Water 2020, 12, 2199 mathematical theory and available commercial software codes, the computation of solutions of the governing equations of motion is still challenging, especially due to the nonlinearity involved, giving motivation for further research related to the mathematical and physical foundations
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