Numerical Computation of a Two-Dimensional Navier-Stokes Equation Using an Improved Finite Difference Method

Abstract

The two-dimensional Navier-Stokes equation is solved numerically using a finite differenced based method which essentially takes advantage of the best features of two well-established numerical formulations, the finite difference and the finite volume methods. The lid-driven cavity flow is validated using an improved finite difference method. It is found that within the family of the finite difference methods used for the solution of steady and incompressible flows, this new approach provides a viable alternative for handling the pressure of the flow. Keywords: Finite difference method; Navier-Stokes equations; incompressible flow; staggered grid; pressure correction equation 2010 Mathematics Subject Classification 76D04.