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Convergence of a residual based artificial viscosity finite element method
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
2011 (English)Report (Other academic)
Place, publisher, year, edition, pages
, KTH-CTL, 4016
URN: urn:nbn:se:kth:diva-36915OAI: diva2:431535
QC 20110720Available from: 2011-07-20 Created: 2011-07-20 Last updated: 2011-07-21Bibliographically approved
In thesis
1. Adaptive Algorithms and High Order Stabilization for Finite Element Computation of Turbulent Compressible Flow
Open this publication in new window or tab >>Adaptive Algorithms and High Order Stabilization for Finite Element Computation of Turbulent Compressible Flow
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This work develops finite element methods with high order stabilization, and robust and efficient adaptive algorithms for Large Eddy Simulation of turbulent compressible flows.

The equations are approximated by continuous piecewise linear functions in space, and the time discretization is done in implicit/explicit fashion: the second order Crank-Nicholson method and third/fourth order explicit Runge-Kutta methods. The full residual of the system and the entropy residual, are used in the construction of the stabilization terms. These methods are consistent for the exact solution, conserves all the quantities, such as mass, momentum and energy, is accurate and very simple to implement. We prove convergence of the method for scalar conservation laws in the case of an implicit scheme. The convergence analysis is based on showing that the approximation is uniformly bounded, weakly consistent with all entropy inequalities, and strongly consistent with the initial data. The convergence of the explicit schemes is tested in numerical examples in 1D, 2D and 3D.

To resolve the small scales of the flow, such as turbulence fluctuations, shocks, discontinuities and acoustic waves, the simulation needs very fine meshes. In this thesis, a robust adjoint based adaptive algorithm is developed for the time-dependent compressible Euler/Navier-Stokes equations. The adaptation is driven by the minimization of the error in quantities of interest such as stresses, drag and lift forces, or the mean value of some quantity.

The implementation and analysis are validated in computational tests, both with respect to the stabilization and the duality based adaptation.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. xii, 54 p.
Trita-CSC-A, ISSN 1653-5723 ; 2011:13
Compressible flow, adaptivity, finite element method, a posteriori error estimates, Implicit LES
National Category
Computational Mathematics Computational Mathematics
urn:nbn:se:kth:diva-34532 (URN)978-91-7501-053-3 (ISBN)
Public defence
2011-09-01, F3, Entre plan,, Lindstedtsvägen 26, KTH, Stockholm, 17:58 (English)
Swedish Research Council
QC 20110627Available from: 2011-06-27 Created: 2011-06-09 Last updated: 2011-07-21Bibliographically approved

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Nazarov, Murtazo
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Numerical Analysis, NA

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ReferencesLink to record
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