Συντάχθηκε 13-05-2019 12:26
ΠΟΛΥΤΕΧΝΕΙΟ ΚΡΗΤΗΣ
ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΑΡΑΓΩΓΗΣ ΚΑΙ ΔΙΟΙΚΗΣΗΣ
Ονοματεπώνυμο: Αγγελόπουλος Δημήτριος
Αριθμός Μητρώου: 2014019040
Θέμα
Τίτλος στα Ελληνικά: Πιστοποίηση αριθμητικού σχήματος διακριτοποίησης υψηλής τάξεως για την επίλυση των 3-Δ εξισώσεων Euler
Τίτλος στα Αγγλικά: Validation of a High-Order Numerical Discretization Scheme for the Solution of the 3-D Euler Equations
Επιτροπή:
Επιβλέπων: Ιωάννης Κ. Νικολός
Πρώτο Μέλος: Ανάργυρος Ι. Δελής
Δεύτερο Μέλος: Γεώργιος Αραμπατζής
Περίληψη της εργασίας στα Αγγλικά:
In this study, the application and evaluation of a high-0rder spatial and time discretization method for the numerical solution of 2-dimensional Euler equations is reported. An alternative high-order approach [Yan14] 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.
Ημερομηνία Εξέτασης
Ημέρα/Μήνας/Έτος: 14/05/2019
Ώρα: 17:00
Χώρος Εξέτασης
Αίθουσα: Β1004
Κτίριο: ………………………………………
Τόπος: Β1 - Αίθουσες Β, Β1.004
Έναρξη: 14/05/2019 17:00
Λήξη: 14/05/2019 17:30
