Incompressible Flows About an Object In a Driven Vertically Repeating Rectangular Domain
Forrest Bullard · 2020
IntroductionIn this report we will discuss how the Navier-Stokes momentum equation for incompressible flows can be adapted to a numerical solution so that analysis of fluid flow around a fixed object can be made. We will discuss a simplification of the Navier-Stokes equation by a change of variable from velocity to vorticity, the curl of velocity, and the stream function who's spatial derivatives will return the components of our velocity for each section of flow. As well we will examine what boundary conditions are necessary in order to create a flow through our domain and other conditions which will define the boundaries of our object. Finally we will discuss some of the limitations of this examination.MathIn our derivation we began with the incompressible Navier-Stokes equation of the form,