Two dimensional finite volume weighted essentially non-oscillatory euler schemes with uniform and non-uniform grid coefficients

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2005

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Elfarra, Monier Ali

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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 idea lies at the high approximation level, where a convex combination of all the candidate stencils is used with certain weights. Those weights are used to eliminate the stencils, which contain discontinuity. WENO schemes have been quite successful in applications, especially for problems containing both shocks and complicated smooth solution structures. The applications tested in this thesis are the Diverging Nozzle, Shock Vortex Interaction, Supersonic Channel Flow, Flow over Bump, and supersonic Staggered Wedge Cascade. The numerical solutions for the diverging nozzle and the supersonic channel flow are compared with the analytical solutions. The results for the shock vortex interaction are compared with the Roe scheme results. The results for the bump flow and the supersonic staggered cascade are compared with results from literature.

Subject Keywords

Numerical analysis.

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http://etd.lib.metu.edu.tr/upload/2/12605898/index.pdf
https://hdl.handle.net/11511/14816

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

M. A. Elfarra, “Two dimensional finite volume weighted essentially non-oscillatory euler schemes with uniform and non-uniform grid coefficients,” M.S. - Master of Science, Middle East Technical University, 2005.