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Least-squares finite element solution of Euler equations with adaptive mesh refinement
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Date
2012
Author
Akargün, Hayri Yiğit
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Least-squares finite element method (LSFEM) is employed to simulate 2-D and axisymmetric flows governed by the compressible Euler equations. Least-squares formulation brings many advantages over classical Galerkin finite element methods. For non-self-adjoint systems, LSFEM result in symmetric positive-definite matrices which can be solved efficiently by iterative methods. Additionally, with a unified formulation it can work in all flight regimes from subsonic to supersonic. Another advantage is that, the method does not require artificial viscosity since it is naturally diffusive which also appears as a difficulty for sharply resolving high gradients in the flow field such as shock waves. This problem is dealt by employing adaptive mesh refinement (AMR) on triangular meshes. LSFEM with AMR technique is numerically tested with various flow problems and good agreement with the available data in literature is seen.
Subject Keywords
Lagrange equations.
,
Finite element method.
,
Least squares.
URI
http://etd.lib.metu.edu.tr/upload/12614138/index.pdf
https://hdl.handle.net/11511/21414
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Graduate School of Natural and Applied Sciences, Thesis
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H. Y. Akargün, “Least-squares finite element solution of Euler equations with adaptive mesh refinement,” M.S. - Master of Science, Middle East Technical University, 2012.