The Compressible Euler System and Its Numerical Analysis


Thesis Type: Postgraduate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Graduate School of Natural and Applied Sciences, Graduate School of Natural and Applied Sciences, Turkey

Approval Date: 2019

Thesis Language: English

Student: Eda Yılmaz

Principal Consultant (For Co-Consultant Theses): Baver Okutmuştur

Abstract:

In this thesis we analyze the compressible Euler equations in one and two dimen-sions. For this purpose, we firstly consider a particular form of this system, namelythe inviscid Burgers equation, which can be derived by imposing vanishing pressureto the Euler system. The inviscid Burgers equation leads us to understand the ideabehind discontinuous solutions such as shock and rarefaction waves. A brief analy-sis of smooth and weak solutions with necessary conditions for choosing physicallymeaningful solutions among the others, entropy and Rankine-Hugonoit conditionsare studied in the first part of this work.In the second part, the derivation of the compressible Euler equations is demonstratedin one dimension where the thermodynamic aspects are given to understand the na-ture of the Euler system. Furthermore, in order to illustrate the model numerically,the stability analysis of three different methods, namely Lax Friedrich, two step LaxWendroff, and two step MacCormack methods, are examined in one dimensionalcase. We use Sod shock tube problem to test numerical methods since analytic so-lution of this problem exists. We finalize this work by a particular illustration of the Euler model in two dimensional case by applying the Lax Friedrich’s method with a short concluding remark. Euler model in two dimensional case by applying the Lax Friedrich’s method with a short concluding remark.