Institutional Repository
Technical University of Crete
Technical University of Crete
EN
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| URI | http://purl.tuc.gr/dl/dias/36A9C901-77FC-4599-AADA-8107F14F02F6 | - |
| Identifier | https://doi.org/10.26233/heallink.tuc.81821 | - |
| Language | en | - |
| Extent | 122 pages | en |
| Title | Validation of a high-order numerical discretization scheme for the solution of the 3-D Euler equations | en |
| Title | Πιστοποίηση αριθμητικού σχήματος διακριτοποίησης υψηλής τάξεως για την επίλυση των 3-Δ εξισώσεων Euler | el |
| Creator | Angelopoulos Dimitrios | en |
| Creator | Αγγελοπουλος Δημητριος | el |
| Contributor [Thesis Supervisor] | Nikolos Ioannis | en |
| Contributor [Thesis Supervisor] | Νικολος Ιωαννης | el |
| Contributor [Committee Member] | Delis Anargyros | en |
| Contributor [Committee Member] | Δελης Αναργυρος | el |
| Contributor [Committee Member] | Arampatzis Georgios | en |
| Contributor [Committee Member] | Αραμπατζης Γεωργιος | el |
| Publisher | Πολυτεχνείο Κρήτης | el |
| Publisher | Technical University of Crete | el |
| Academic Unit | Technical University of Crete::School of Production Engineering and Management | en |
| Academic Unit | Πολυτεχνείο Κρήτης::Σχολή Μηχανικών Παραγωγής και Διοίκησης | el |
| Content Summary | In this study, the application and evaluation of a high-order spatial and time discretization method for the numerical solution of 2-dimensional Euler equations is reported. An alternative high-order approach enhances the in-house academic solver, named EU2, employing the dimensionless Euler equations, discretized with a node-centered finite volume method on triangular unstructured girds, to simulate inviscid compressible flows. Most methodologies that have been developed during the past years, e.g. the discontinuous Galerkin and K-exact scheme, necessitate a non-trivial increase of the DoFs (Degrees of Freedom) and consequently a considerable increase of computational resources. Moreover, major modifications to existing CFD codes are required for their implementation. The adopted high-order scheme is based on the incorporation of additional high order terms to the reconstructed nodal values, used for the computation of the inviscid fluxes. The required higher-order derivatives are computed with the corresponding lower-order ones on the existing DoFs via a successive differentiation technique. As a result, the connectivity requirements are restricted to the first neighbouring points, overcoming the inherent constraint of the unstructured solvers to retrieve information from a wider computational stencil. The aforementioned technique was incorporated with a variable extrapolation numerical scheme, named U-MUSCL, which closely resembles the traditional MUSCL one, and was coupled with a high-order time discretization that employs a Strong Stability Preserving Runge-Kutta method (SSPRK). To assess the effectiveness of the aforementioned numerical scheme, the EU2 solver is used against a benchmark problem having analytic solution. A satisfactory agreement is obtained, demonstrating the proposed scheme’s potential to increase the solution’s accuracy for a given grid density. Furthermore, a corresponding high-order formulation is extended to a 3-dimensional numerical fluid model. An elaborate construction method of 3-d computational meshes for various grid types is presented in detail for future exploitation on the numerical evaluation of equivalent 3-d high-order schemes. | en |
| Type of Item | Μεταπτυχιακή Διατριβή | el |
| Type of Item | Master Thesis | en |
| License | http://creativecommons.org/licenses/by/4.0/ | en |
| Date of Item | 2019-05-16 | - |
| Date of Publication | 2019 | - |
| Subject | Computational physics | en |
| Subject | Computational fluid dynamics | en |
| Bibliographic Citation | Dimitrios Angelopoulos, "Validation of a high-order numerical discretization scheme for the solution of the 3-D Euler equations", Master Thesis, School of Production Engineering and Management, Technical University of Crete, Chania, Greece, 2019 | en |
| Bibliographic Citation | Δημήτριος Αγγελόπουλος, "Πιστοποίηση αριθμητικού σχήματος διακριτοποίησης υψηλής τάξεως για την επίλυση των 3-Δ εξισώσεων Euler", Μεταπτυχιακή Διατριβή, Σχολή Μηχανικών Παραγωγής και Διοίκησης, Πολυτεχνείο Κρήτης, Χανιά, Ελλάς, 2019 | el |
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