

Title of Thesis
Boundary Elements Methods for Compressible Fluid Flow Problems 
Author(s)
Muhammad Mushtaq 
Institute/University/Department
Details Department of Mathematics / University of
Engineering & Technology, Lahore 
Session 2011 
Subject Mathematics 
Number of Pages 257 
Keywords (Extracted from title, table of contents and
abstract of thesis) Methods, System, Compressible,
Fluid, Technique, Compressible, Boundary, Flow, Calculation,
Problems, Potential, Elements, Dimensional 
Abstract The boundary element method is a numerical technique which consists of sub–
dividing the boundary of the body into a series of discrete elements, over which the
function can vary.This technique offers important advantages over domain type solutions
such as finite elements and finite differences.One of the most important features of this
method is the much smaller system of equations and the considerable reduction in data
required to run a program. Furthermore, the method is well–suited to problems with an
infinite domain.Boundary element methods can be formulated using two different
approaches called the ‘direct’ and the ‘indirect’ methods.
In this thesis, the direct and indirect boundary element methods have been used
for the calculation of the compressible fluid flow around arbitrary bodies.The results obtained using boundary element methods have been compared with
analytical solutions.These methods have been implemented with the help of computer
programming using FORTRAN 77.
In chapter (1), statement of the problem, literature survey and brief description of
the method of solution are discussed.In chapter (2) the fundamental equations for
compressible fluid are given and in chapter (3) mathematical formulation of the equation
for inviscid compressible fluid flow is given.In chapter (4) the constitutive equations for
the boundary element methods for the interior and exterior domains are derived, and in
chapter (5) the various types of boundary elements, the matrix formulation for the
equation of the direct method.The numerical evaluation of the integrals over an element
and the solution of the resultant system of equations are discussed.In chapter (6) the
direct and indirect boundary element methods are applied to the three – dimensional
potential flow problems and the comparisons of the analytical and computed results are
presented.In chapter (7) both the direct and indirect boundary element methods have
been used to calculate two dimensional inviscid compressible flow past a symmetric and
Joukowski aerofoils.It has been seen that the computed results in all the above
mentioned cases are in good agreement with the analytical results. Finally, conclusions
and suggestions for future work are given at the end.

