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Numerical simulation of shockpropagation in one and twodimensional domains

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  1. Tez No: 614489
  2. Yazar: HATİCE KURŞUNGEÇMEZ
  3. Danışmanlar: PROF. DR. NOEL SMYTH
  4. Tez Türü: Doktora
  5. Konular: Matematik, Mathematics
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 2015
  8. Dil: İngilizce
  9. Üniversite: The University of Edinburgh
  10. Enstitü: Yurtdışı Enstitü
  11. Ana Bilim Dalı: Matematik Ana Bilim Dalı
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 179

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Özet (Çeviri)

The objective of this dissertation is to develop robust and accurate numerical meth-ods for solving the compressible, non-linear Euler equations of gas dynamics in one andtwo space dimensions. In theory, solutions of the Euler equations can display variouscharacteristics including shock waves, rarefaction waves and contact discontinuities. Tocapture these features correctly, highly accurate numerical schemes are designed. Inthis thesis, two different projects have been studied to show the accuracy and utility ofthese numerical schemes.Firstly, the compressible, non-linear Euler equations of gas dynamics in one spacedimension are considered. Since the non-linear partial differential equations (PDEs)can develop discontinuities (shock waves), the numerical code is designed to obtain sta-ble numerical solutions of the Euler equations in the presence of shocks. Discontinuoussolutions are defined in a weak sense, which means that there are many different solu-tions of the initial value problems of PDEs. To choose the physically relevant solutionamong the others, the entropy condition was applied to the problem. This conditionis then used to derive a bound on the solution in order to satisfyL2-stability. Also,it provides information on how to add an adequate amount of diffusion to smooth thenumerical shock waves. Furthermore, numerical solutions are obtained using far-fieldand no penetration (wall) boundary conditions. Grid interfaces were also included inthese numerical computations.Secondly, the two dimensional compressible, non-linear Euler equations are consid-ered. These equations are used to obtain numerical solutions for compressible flow ina shock tube with a 90◦circular bend for two channels of different curvatures. Thecell centered finite volume numerical scheme is employed to achieve these numericaliv solutions. The accuracy of this numerical scheme is tested using two different methods.In the first method, manufactured solutions are used to the test the convergence rate ofthe code. Then, Sod's shock tube test case is implemented into the numerical code toshow the correctness of the code in both flow directions. The numerical method is thenused to obtain numerical solutions which are compared with experimental data avail-able in the literature. It is found that the numerical solutions are in a good agreementwith these experimental results.

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