Title: Reconstructing fluid dynamics with micro-finite element,
Abstract: In the theory of the Navier-Stokes equations, the viscous fluid in
incompressible flow is modelled as a homogeneous and dense assemblage of
constituent "fluid particles" with viscous stress proportional to rate of
strain. The crucial concept of fluid flow is the velocity of the particle that
is accelerated by the pressure and viscous interaction around it. In this
paper, by virtue of the alternative constituent "micro-finite element", we
introduce a set of new intrinsic quantities, called the vortex fields, to
characterise the relative orientation between elements and the feature of
micro-eddies in the element, while the description of viscous interaction in
fluid returns to the initial intuition that the interlayer friction is
proportional to the slip strength. Such a framework enables us to reconstruct
the dynamics theory of viscous fluid, in which the flowing fluid can be
modelled as a finite covering of elements and consequently indicated by a
space-time differential manifold that admits complex topological evolution.