FINITE DIFFERENCE SOLUTIONS FOR NAVIER-STOKES EQUATIONS

Abstract

ABSTRACT : The aim of this thesis is to present different finite difference methods to solve Navier-Stokes equations in one, two or three-dimensions. In chapter one an introduction to finite difference methods using two different formula's connecting difference and differential operator's are given. Chapter two presents a derivation of Navier-Stokes equations from first principle using a control volume. The first section of chapter three discusses the linearization of Navier-Stokes equations using the perturbation method, while the other sections introduce the solutions of Navier-Stokes using explicit and implicit finite difference approximations for different space dimensions. In chapter four several results are presented and various graphs for comparisons have been plotted.