Reconstructing Fluid Dynamics with Micro–Finite Elements

ABSTRACT: In the theory of Navier–Stokes (N–S) equations, an incompressible fluid in motion is modeled as a homogeneous and dense assemblage of constituent “fluid particles” with viscous stress proportional to the rate of strain. The crucial concept in fluid flow is the velocity of a particle, which is accelerated by the pressure and viscous interactions around it. In this paper, by virtue of an alternative constituent “micro-finite element”, we introduce a set of new intrinsic quantities, called the vortex fields, to characterize the relative orientation between elements and the feature of micro-eddies in the element, while the description of viscous interaction in the fluid returns to that the interlayer friction is proportional to the slip strength, more matching Newton’s original intuition. Such a framework enables us to reconstruct the dynamics theory of viscous fluid, in which the fluid can be modeled as a finite covering of elements and consequently its flow is indicated by a space-time differential manifold that admits complex topological evolution.