Numerical Solution of One-Dimensional Incompressible Steady Flow Burgers’ equation Research Report in Mathematics, Number 04, 2018

Abstract

The aim of this project is to nd the numerical solution of one dimensional ,steady incompressible Burgers’ equation by using the Runge-Kutta method. We shall solve the equation by rst converting the non-linear Navier Stokes equation into the non-linear viscous burgers equation by using the Orlowski and Sobczyk transformation(OST).After solving we will represent the solutions graphically. In chapter one,we look at the historical background of Burgers’Equations(BE) and its applications, ways in which uid motion is described how uid motion is classi ed.We will also consider the concept of Dimensional Analysis with the main focus on similarity and dimensionless numbers.We shall derive some common non-dimensional numbers as well. In this chapter ,we consider the equations that govern uid ow,the momentum equations and the Navier -Stokes equations (NSE) in the various coordinate systems and their derivations. In chapter two, we will look at some literature review on Burgers’Equations. We shall look at the methodology in chapter three with emphasis on the Orlowski and Sobczyk transformation(OST)as a method of transforming the Navier-Stokes equation to Burgers’ Equation.We will also discuss some types of Runge-Kutta methods. Finally chapter four we will solve the one-dimensional Burgers’Equation for steady incompressible ow numerically using fourth order Runge-Kutta method(RK4) and represent the solutions graphically.