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Adaptive Algorithms and High Order Stabilization for Finite Element Computation of Turbulent Compressible Flow
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
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.
Series
Trita-CSC-A, ISSN 1653-5723 ; 2011:13
Keyword [en]
Compressible flow, adaptivity, finite element method, a posteriori error estimates, Implicit LES
National Category
Computational Mathematics Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-34532ISBN: 978-91-7501-053-3 (print)OAI: oai:DiVA.org:kth-34532DiVA: diva2:421860
Public defence
2011-09-01, F3, Entre plan,, Lindstedtsvägen 26, KTH, Stockholm, 17:58 (English)
Opponent
Supervisors
Funder
Swedish Research Council
Note
QC 20110627Available from: 2011-06-27 Created: 2011-06-09 Last updated: 2011-07-21Bibliographically approved
List of papers
1. Implementation of the entropy viscosity method
Open this publication in new window or tab >>Implementation of the entropy viscosity method
2011 (English)Report (Other academic)
Series
KTH-CTL, 4015
Identifiers
urn:nbn:se:kth:diva-36914 (URN)
Note
QC 20110720Available from: 2011-07-20 Created: 2011-07-20 Last updated: 2011-07-21Bibliographically approved
2. Convergence of a residual based artificial viscosity finite element method
Open this publication in new window or tab >>Convergence of a residual based artificial viscosity finite element method
2011 (English)Report (Other academic)
Series
KTH-CTL, 4016
Identifiers
urn:nbn:se:kth:diva-36915 (URN)
Note
QC 20110720Available from: 2011-07-20 Created: 2011-07-20 Last updated: 2011-07-21Bibliographically approved
3. An adaptive finite element method for the compressible Euler equations
Open this publication in new window or tab >>An adaptive finite element method for the compressible Euler equations
2010 (English)In: INT J NUMER METHOD FLUID, 2010, Vol. 64, no 10-12, 1102-1128 p.Conference paper, Published paper (Refereed)
Abstract [en]

We present an adaptive finite element method for the compressible Euler equations, based on a posteriori error estimation of a quantity of interest in terms of a dual problem for the linearized equations. Continuous piecewise linear approximation is used in space and time, with componentwise weighted least-squares stabilization of convection terms and residual-based shock-capturing. The adaptive algorithm is demonstrated numerically for the quantity of interest being the drag force on a body.

Keyword
adaptive finite element method, a posteriori error estimation, dual problem, compressible euler equations, circular cylinder, wedge, sphere
National Category
Computer and Information Science
Identifiers
urn:nbn:se:kth:diva-25412 (URN)
Conference
15th International Conference on Finite Elements in Flow Problems Tokyo, JAPAN, APR 01-03, 2009
Note
QC 20101020Available from: 2010-10-20 Created: 2010-10-20 Last updated: 2012-01-16Bibliographically approved
4. A posteriori error estimation for the compressible Euler equations using entropy viscosity
Open this publication in new window or tab >>A posteriori error estimation for the compressible Euler equations using entropy viscosity
2011 (English)Report (Other academic)
Series
KTH-CTL, 4017
Identifiers
urn:nbn:se:kth:diva-36917 (URN)
Note
QC 20110720Available from: 2011-07-20 Created: 2011-07-20 Last updated: 2011-07-21Bibliographically approved
5. On the stability of the dual problem for high Reynolds number flow past a circular cylinder in two dimensions
Open this publication in new window or tab >>On the stability of the dual problem for high Reynolds number flow past a circular cylinder in two dimensions
2011 (English)Report (Other academic)
Series
KTH-CTL, 4018
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-36918 (URN)
Note
QC 20110720Available from: 2011-07-20 Created: 2011-07-20 Last updated: 2011-11-30Bibliographically approved
6. Residual based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods
Open this publication in new window or tab >>Residual based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods
2011 (English)Report (Other academic)
Series
KTH-CTL, 4019
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-36919 (URN)
Note
QC 20110720Available from: 2011-07-20 Created: 2011-07-20 Last updated: 2011-11-18Bibliographically approved

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