The Compressible euler system and its numerical analysis

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2019
Yılmaz, Eda
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In this thesis we analyze the compressible Euler equations in one and two dimensions. For this purpose, we firstly consider a particular form of this system, namely the inviscid Burgers equation, which can be derived by imposing vanishing pressure to the Euler system. The inviscid Burgers equation leads us to understand the idea behind discontinuous solutions such as shock and rarefaction waves. A brief analysis of smooth and weak solutions with necessary conditions for choosing physically meaningful solutions among the others, entropy and Rankine-Hugonoit conditions are studied in the first part of this work. In the second part, the derivation of the compressible Euler equations is demonstrated in one dimension where the thermodynamic aspects are given to understand the nature of the Euler system. Furthermore, in order to illustrate the model numerically, the stability analysis of three different methods, namely Lax Friedrich, two step Lax Wendroff, and two step MacCormack methods, are examined in one dimensional case. We use Sod shock tube problem to test numerical methods since analytic solution 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 equations., Finite differences., Numerical analysis.
http://etd.lib.metu.edu.tr/upload/12623041/index.pdf
https://hdl.handle.net/11511/27993
Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats
E. Yılmaz, “The Compressible euler system and its numerical analysis,” M.S. - Master of Science, Middle East Technical University, 2019.
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