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.
Publisher
University of Nairobi
Rights
Attribution-NonCommercial-NoDerivs 3.0 United StatesUsage Rights
http://creativecommons.org/licenses/by-nc-nd/3.0/us/Collections
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