Supersonic flows over both simple and complex geometries involve features over a
wide spectrum of spatial and temporal scales, whose resolution in a numerical
solution is of significant importance for accurate predictions in engineering
applications. While CFD has been greatly developed in the last 30 years, the
desire and necessity to perform more complex, high fidelity simulations still
remains.
The present thesis has introduced two major innovations regarding the fidelity
of numerical solutions of the compressible \ns equations. The first one is the
development of new a priori mesh quality measures for the Finite
Volume (FV) method on mixed-type (quadrilateral/triangular) element meshes.
Elementary types of mesh distortion were identified expressing grid distortion
in terms of stretching, skewness, shearing and non-alignment of the mesh.
Through a rigorous truncation error analysis, novel grid quality measures were
derived by emphasizing on the direct relation between mesh distortion and the
quality indicators. They were applied over several meshes and their ability was
observed to identify faithfully irregularly-shaped small or large distortions in
any direction. It was concluded that accuracy degradation occurs even for small
mesh distortions and especially at mixed-type element mesh interfaces the formal
order of the FV method is degraded no matter of the mesh geometry and local mesh
size.
Therefore, in the present work, the high-order Discontinuous Galerkin (DG)
discretization of the compressible flow equations was adopted as a means of
achieving and attaining high resolution of flow features on irregular mixed-type
meshes for flows with strong moving shocks. During the course of the
thesis a code was developed and named HoAc (standing for High Order Accuracy),
which can perform via the domain decomposition method parallel $p$-adaptive
computations for flows with strong shocks on mixed-type element meshes over
arbitrary geometries at a predefined arbitrary order of accuracy. In HoAc in
contrast to other DG developments, all the numerical operations are performed in
the computational space, for all element types. This choice constitutes the key
element for the ability to perform $p$-adaptive computations along with modal
hierarchical basis for the solution expansion. The time marching of the DG
discretized Navier-Stokes system is performed with the aid of explicit Runge-Kutta methods or with a matrix-free implicit approach.
The second innovation of the present thesis, which is also based on the choice
of implementing the DG method on the regular computational space, is the
development of a new $p$-adaptive limiting procedure for shock capturing of the
implemented DG discretization. The new limiting approach along with positivity
preserving limiters is suitable for computations of high speed flows with strong
shocks around complex geometries. The unified approach for $p$-adaptive limiting
on mixed-type meshes is achieved by applying the limiters on the transformed
canonical elements, and it is fully automated without the need of
ad hoc specification of parameters as it has been done with
standard limiting approaches and in the artificial dissipation method for shock
capturing.
Verification and validation studies have been performed, which prove the
correctness of the implemented discretization method in cases where the linear
elements are adequate for the tessellation of the computational domain both for
subsonic and supersonic flows. At present HoAc can handle only linear elements
since most grid generators do not provide meshes with curved elements.
Furthermore, p-adaptive computations with the implemented DG method were
performed for a number of standard test cases for shock capturing schemes to
illustrate the outstanding performance of the proposed $p$-adaptive limiting
approach. The obtained results are in excellent agreement with analytical
solutions and with experimental data, proving the excellent efficiency of the
developed shock capturing method for the DG discretization of the equations of
gas dynamics. / -
| Identifer | oai:union.ndltd.org:upatras.gr/oai:nemertes:10889/5839 |
| Date | 04 February 2013 |
| Creators | Κοντζιάλης, Κωνσταντίνος |
| Contributors | Αικατερινάρης, Ιωάννης, Καλλιντέρης, Ιωάννης, Γιαννάκογλου, Κυριάκος, Kontzialis, Konstantinos, Κωστόπουλος, Βασίλειος, Σαραβάνος, Δημήτριος, Καλλιντέρης, Ιωάννης, Γιαννάκογλου, Κυριάκος, Γαλόπουλος, Στρατής, Τσαμόπουλος, Ιωάννης |
| Source Sets | University of Patras |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Rights | 0 |
| Relation | Η ΒΚΠ διαθέτει αντίτυπο της διατριβής σε έντυπη μορφή στο βιβλιοστάσιο διδακτορικών διατριβών που βρίσκεται στο ισόγειο του κτιρίου της. |
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