The Compressible euler system and its numerical analysis

Download
index.pdf
2019
Yılmaz, Eda
Show full item record
219
views
80
downloads
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

Suggestions

A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations
Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01)
In this paper we provide an error analysis of a subgrid scale eddy viscosity method using discontinuous polynomial approximations for the numerical solution of the incompressible Navier-Stokes equations. Optimal continuous in time error estimates of the velocity are derived. The analysis is completed with some error estimates for two fully discrete schemes, which are first and second order in time, respectively.
Two dimensional finite volume weighted essentially non-oscillatory euler schemes with uniform and non-uniform grid coefficients
Elfarra, Monier Ali; Akmandor, İbrahim Sinan; Department of Aerospace Engineering (2005)
In this thesis, Finite Volume Weighted Essentially Non-Oscillatory (FV-WENO) codes for one and two-dimensional discretised Euler equations are developed. The construction and application of the FV-WENO scheme and codes will be described. Also the effects of the grid coefficients as well as the effect of the Gaussian Quadrature on the solution have been tested and discussed. WENO schemes are high order accurate schemes designed for problems with piecewise smooth solutions containing discontinuities. The key ...
The relativistic Burgers equation on a Friedmann–Lemaître–Robertson–Walker (FLRW) background and its finite volume approximation
Ceylan, Tuba; Okutmuştur, Baver; LeFloch, Philippe G.; Department of Mathematics (2015)
In this thesis, applications of generalized integral inequalities especially on biomathematics and physics are studied. Application on Biomathematics is about the predatorprey dynamic systems with Beddington DeAngelis type functional response and application on physics is about water percolation equation. This thesis consists 6 chapters. Chapter 1 is introductory and contains the thesis structure. Chapter 2 is about under which conditions the two dimensional predator-prey dynamic system with Beddington DeAn...
Inverse Sturm-Liouville Systems over the whole Real Line
Altundağ, Hüseyin; Taşeli, Hasan; Department of Mathematics (2010)
In this thesis we present a numerical algorithm to solve the singular Inverse Sturm-Liouville problems with symmetric potential functions. The singularity, which comes from the unbounded domain of the problem, is treated by considering the limiting case of the associated problem on the symmetric finite interval. In contrast to regular problems which are considered on a finite interval the singular inverse problem has an ill-conditioned structure despite of the limiting treatment. We use the regularization t...
Solution of helmholtz type equations by differential quadrature method
Kuruş, Gülay; Tezer, Münevver; Department of Mathematics (2004)
This thesis presents the Differential Quadrature Method (DQM) for solving Helmholtz, modified Helmholtz and Helmholtz eigenvalue-eigenvector equations. The equations are discretized by using Polynomial-based and Fourier-based differential quadrature technique wich use basically polynomial interpolation for the solution of differential equation.
Citation Formats
E. Yılmaz, “The Compressible euler system and its numerical analysis,” M.S. - Master of Science, Middle East Technical University, 2019.
METU IIS - Integrated Information Service open@metu.edu.tr