A Direct Numerical Simulation of a Computational Fluid Dynamics Application Using the Navier-Stokes Equations and Finite Differences

Abstract

When engineers design objects that interact with fluids, they must spend a considerable amount of time understanding the relationship between the fluid and the object. One method is to perform scale tests that involve a complicated apparatus to simulate the fluid flow and provide a way of obtaining measurements. This procedure is expensive and time consuming, sometimes costing thousands of dollars an hour and taking many weeks. As a result, engineers use Computational Fluid Dynamics (CFD) so that an object and a fluid flow can be simulated, thus minimizing time and cost. I will explore a method used to make a two dimensional CFD program using the Navier-Stokes equations for fluid flow, and the Finite Differences Method for CFD. I will then use my program to demonstrate how an airfoil and air interact to produce lift and drag.