Thesis (M.Sc.) - Cairo University - Faculty of Engineering - Department of Aerospace Engineering

In this thesis, the traditional {uFB01}nite volume method is compared to the spectral volume method. First, the convergence order of each scheme is studied. The results show that the traditional {uFB01}nite volume scheme has smaller error for the same order as the spectral volume method. Furthermore, the {uFB01}nite volume schemes are always computationally more e{uFB03}cient and less time consuming. Second, the Taylor series expansion was used to verify the numerical results obtained from the scheme. The results for the SVM show that the scheme is only higher-order on the spectral volume scale, with lower orders elsewhere. The classical {uFB01}nite volume method has uniform order everywhere. This results in a higher cost of the SVM compared to the FVM for the same number of degrees of freedom. Third, a steady formulation for the SVM is presented. Traditionally, the SVM is only applied to unsteady problems and integrated using di{uFB00}erent time marching schemes. This enables the usage of the P- multigrid algorithm. Finally, a P- multigrid technique was applied to both classical {uFB01}nite volume method and the spectral volume method. The numerical tests show that the classical {uFB01}nite volume method is superior and converges faster for the same model problem

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