Flow problem in three-dimensional geometry

TL;DR

This paper presents a method to reduce complex 3D hydrodynamic equations to surface equations, enabling efficient analysis of viscous flow and stress distribution around solid bodies.

Contribution

It introduces a novel dimension reduction technique for over-determined differential systems in 3D hydrodynamics, providing a closed surface equation system.

Findings

Derivation of surface equations for 3D viscous flow

Ability to determine stress distribution on solid surfaces

Simplification of hydrodynamic analysis around bodies

Abstract

It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of over-determined systems of differential equations. These systems of equations allow determining the surface distribution of the resulting stresses on the surface of this body as well as all other quantities characterizing the hydrodynamic flow around it.