الفهرس 
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Abstract
PREFACE AND SUMMERY
One ot the most important topics in comput,tional
Fluid Dynamics is the study ot shock and rarefa~tion
waves. In most practical applications, the rel~vant
.equations are coupled and non_linear and numeri’cal methods
must be used to solve these equations. Moreover,
additional techniques ( Artiticial Viscosity)at
e
needed
to get rid ot the non-linear oscillations that take
place in treating shock waves numerically.
Tbe aim of this thesis is to study such techniques
and lntroduC.eit in the numerical solutions without adding
it explicitly.
In cha.pter I, }l’ediscuss physical and mathematical
pictures ot shock waves and the Rankine-Hugoniont relations.
The Eulerian, Lagrangian approaches and discretization
in computational Fluid Dynamics are also discussed.
In chapter II, we express the quasi-linear hyperbolic
system, that describe the unsteady compressible floY of
a polytropic. gas, in a non_dimensional Eulerian form. We
also review some otthe eXplicit, first, second, third
and tourth order accurate method, tha.t. ·are frequently .
used to solve the system numerically. The stability of
some ot these methods. using both Hirt and von_Neumann
approaches ifla~so discussed. In,the ~ast-part ot chapter
II. ye revieY tbe ditterent artiticia~ viscosity torms
that, are used to e~iminate PQst shock osci~~ations.
In,chapter III. we moditied an ,iterative sche’lle.
origina~~y devised by Abarbane~ and Zyas in ~969. as
a rep~acement to the artitica~ viscosity. ~he same
scheme vas used by E~_Fayoumi and Fkirin (~978) to iterate
tirst order numerica~ so~utions otthe quasi-~inear system
that represent the compressib~e one dimensiona~ t~ow
ot a pO~ytropic gas in cartizian coordinates.
Here. ye iterate second order Lax~wendrott so~ution
of the system that represent the compressib~e one di~en-
, siona~ t~ow ot a pO~ytropic gas in ct~il;ldrica~co~rdinates’.
Chapter III has been pup~ished in the preoceeding ot titth
international”~ongress ~or statistics. computer science.
socia~ ,and demographiC res~arch” (pp. 433-
448
)”~rganized
by Ain ShamS University. 29 March-3 Apri~ ~980.
~he same article has been accep”ted”to~ Jl1Jb:l:t
c
”t”to
n
in the EgyptlanComputer Journa~.
{ ~o appear in June ~980 Ii-lfiu.1e.