Analysis of Navier-Stokes Equation from the Viewpoint of Advection Diffusion

Abstract

We propose a highly accurate approximate solution for Navier-Stokes Equation (NSE) based on the similarity between NSE and Advection Diffusion Equation (ADE). First, we present the analytical exact solution of ADE using a Green function (integral kernel) that is obtained from the diffusion equation over uniform flow field (or velocity field) in three dimensional (3D) boundless region under arbitrary initial condition. Next, from the explicit similarity between NSE and ADE, we derive the approximate solution of NSE using the analytical solution of ADE.