Least-squares finite element solution of Euler equations with adaptive mesh refinement

Akargün, Hayri Yiğit
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.


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Least-squares finite element solution of Euler equations with H-type mesh refinement and coarsening on triangular elements
AKARGUN, Hayri Yigit; Sert, Cüneyt (2014-01-01)
Purpose - The purpose of this paper is to demonstrate successful use of least-squares finite element method (LSFEM) with h-type mesh refinement and coarsening for the solution of two-dimensional, inviscid, compressible flows.
Optimal boundary control of the unsteady Burgers equation with simultaneous space-time discretization
Karasözen, Bülent (2014-07-01)
The optimality system for boundary controlled unsteady Burgers equation is transformed after linearization into a biharmonic equation in the space-time domain. It is then discretized in space and time simultaneously, so that standard finite element software can be easily implemented. Numerical experiments with and without control constraint problems confirm the applicability of this approach. Copyright (C) 2013 John Wiley & Sons, Ltd.
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Citation Formats
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.