Reconstructing fluid dynamics with micro-finite element

TL;DR

This paper introduces a novel micro-finite element framework to model viscous fluid dynamics, incorporating vortex fields and complex topology, offering a new perspective on fluid flow and interactions.

Contribution

It proposes a new micro-finite element approach with vortex fields to reconstruct fluid dynamics, emphasizing topological evolution and intrinsic quantities.

Findings

Reconstruction of viscous fluid dynamics using micro-finite elements.

Introduction of vortex fields to characterize micro-eddies.

Modeling fluid flow as a space-time manifold with complex topology.

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.