Approximating the Navier-Stokes Equations with the Explicit Finite Difference Method to Solve the Lid-driven Cavity Flow Problem

Abstract

The Navier-Stokes equations, one of the seven Millennium Problems, are a set of 2nd-order partial differential equations that are near impossible to solve. Instead of solving it, this paper uses the finite difference method to convert the differential terms in the Navier-Stokes Equations into algebraic equations to generate approximate solutions. The procedure to use the explicit finite difference method is outlined and proved in the context of solving the lid-driven cavity flow problem. The solution discussed is then applied in Mat lab and its accuracy and speed is evaluated. The finite difference method is then evaluated and its applications are outlined.