Three-dimensional discontinuous spectral/hp element methods for compressible flows
File(s)
Thesis: final copy
Author(s)
De Grazia, Daniele
Type
Thesis
Abstract
In this thesis we analyse and develop two high-order schemes which belong to
the class of discontinuous spectral/hp element methods focusing on compressible
aerodynamic studies and, more specifically, on boundary-layer flows. We investigate
the discontinuous Galerkin method and the flux reconstruction approach
providing a detailed analysis of the connections between these methods. The connections
found enable a better understanding of the broader class of discontinuous
spectral/hp element methods.
From this perspective it was evident that some of the issues of the discontinuous
Galerkin method are also encountered in the flux reconstruction approach, and
in particular, the aliasing errors of the two schemes are identical. The techniques
applied in the more famous discontinuous Galerkin method for tackling these errors
can be also extended to the flux reconstruction approach. We present two
dealiasing strategies based on the concept of consistent integration of the nonlinear
terms. The first is a localised approach which targets in each element the
nonlinearities arising in the problem, while the second is a more global approach
which involves a higher quadrature of the overall right-hand side of the discretised
equation(s). Both the strategies have been observed to be effective in enhancing
the robustness of the schemes considered.
We finally present the direct numerical simulation of a high-speed subsonic
boundary-layer flow past a three-dimensional roughness element, achieved by means
of the compressible aerodynamic solver developed. This type of analyses have been
widely performed in the past with approximated theories. Only recently, has DNS
been used due to the improvement of numerical techniques and an increase in
computational resources for similar studies in low-speed subsonic, supersonic and
hypersonic regimes. This thesis takes a first step to close the gap between the results
for a high-speed subsonic regime and the results in supersonic and hypersonic
regimes.
the class of discontinuous spectral/hp element methods focusing on compressible
aerodynamic studies and, more specifically, on boundary-layer flows. We investigate
the discontinuous Galerkin method and the flux reconstruction approach
providing a detailed analysis of the connections between these methods. The connections
found enable a better understanding of the broader class of discontinuous
spectral/hp element methods.
From this perspective it was evident that some of the issues of the discontinuous
Galerkin method are also encountered in the flux reconstruction approach, and
in particular, the aliasing errors of the two schemes are identical. The techniques
applied in the more famous discontinuous Galerkin method for tackling these errors
can be also extended to the flux reconstruction approach. We present two
dealiasing strategies based on the concept of consistent integration of the nonlinear
terms. The first is a localised approach which targets in each element the
nonlinearities arising in the problem, while the second is a more global approach
which involves a higher quadrature of the overall right-hand side of the discretised
equation(s). Both the strategies have been observed to be effective in enhancing
the robustness of the schemes considered.
We finally present the direct numerical simulation of a high-speed subsonic
boundary-layer flow past a three-dimensional roughness element, achieved by means
of the compressible aerodynamic solver developed. This type of analyses have been
widely performed in the past with approximated theories. Only recently, has DNS
been used due to the improvement of numerical techniques and an increase in
computational resources for similar studies in low-speed subsonic, supersonic and
hypersonic regimes. This thesis takes a first step to close the gap between the results
for a high-speed subsonic regime and the results in supersonic and hypersonic
regimes.
Version
Open Access
Date Issued
2016-05
Date Awarded
2016-09
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Sherwin, Spencer
Sponsor
Airbus Industrie; EADS Innovation Works
Engineering and Physical Sciences Research Council
Grant Number
EP/I037946
Publisher Department
Aeronautics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)