• PhD,

PhD Defense - Hashim Elzaabalawy - LHEEA/ED SPI

You are cordially invited to attend the Ph.D. defense by Hashim Elzaabalawy on the subject "Towards High-Order Compact Discretization of Unsteady Navier-Stokes Equations for Incompressible Flows on Unstructured Grids". Due to the specific sanitary conditions, the defense will take place by videoconference on Friday, November 6th at 14:00.

On November 6, 2020 from 14:00 To 18:00


The Ph.D. defense will be organised via Zoom:
Meeting ID: 939 3684 3042
Passcode: 2u?NhRbW

The defense will start at 14:00 CET, the conference room will be open from 13:30 if you wish to test your connection.
To save bandwidth, all audience members are kindly requested to keep their camera and microphone shut off at all times until the defense is finished. Also, please connect around 13:45 or before so we will have time to sort out technical problems before the start of the defense. Thank you!


The thesis will be defended before the following committee:
- Ruben SEVILLA, Professeur, Université de Swansea, Grande-Bretagne (rapporteur)
- Jean-François REMACLE, Professeur, Université Catholique de Louvain, Belgique (rapporteur)
- Rémi ABGRALL, Professeur, Université de Zurich, Suisse (président du jury)
- Sonia FERNANDEZ MENDEZ, Professeur, Université Polytechnique de Catalogne, Espagne (examinateur)
- Carlos TIAGO, Professeur, Université de Lisbonne, Portugal (examinateur)
- José C. FERNANDES PEREIRA, Professeur, Université de Lisbonne, Portugal (examinateur)
- Michel VISONNEAU, Directeur de recherche CNRS, École Centrale de Nantes/CNRS, France (directeur de thèse)
- Luis ECA, Professeur, Université de Lisbonne, Portugal (co-directeur de thèse)
- Ganbo DENG, Ingénieur de recherche, Ecole Centrale de Nantes, France (co-encadrant)


The Ph.D. defense will occur mostly as usual. The president of the committee will open the defense, followed by 45 minutes of presentation. Afterwards, the president will allow the jury members one by one to ask questions. After this session, the jury will retreat to a separate conference room for discussion; the main conference room will remain open for the audience (cameras / microphones allowed). The committee will then return to the main room to announce its decision. Afterwards, the room will remain open for a general discussion where, depending on the result, we will be able to congratulate Hashim.



A high-order energy-stable method for solving the incompressible Navier-Stokes equations based on hybrid discontinuous Galerkin method is presented for which the mass and momentum are conserved. The formulation computes exactly pointwise divergence-free velocity fields for standard element types without post-processing operators nor using H(div)-conforming spaces. This is achieved by proposing a simple and novel definition to the functional space of the pressure, such that it contains the divergence of the approximate velocity. Specific focus is given on applying this method on different element shapes by introducing the concept of reduced-order elements for all standard shapes in 2D and 3D. Further, the incompressibility constraint is handled via the static condensation to solve the saddle point problem. Furthermore, with the aim to simulate high Reynolds numbers flows, the significance of the diffusion stabilization in the hybridizable discontinuous Galerkin framework is analyzed. Referring to literature, the diffusion stabilization term is directly proportional to the diffusivity or the viscosity for the Navier-Stokes equations. In this work, a new expression for the diffusion stabilization term is mathematically derived, where the term is inversely proportional to the diffusivity or viscosity. Its importance for convection dominated flows is emphasized and supported by numerical examples. Moreover, the proposed formulation for the incompressible Navier-Stokes is extended to solve the RANSE for the TNT, BSL, and SST k-ω models for Reynolds numbers up to 10e9. Solving RANSE is a resilient task for high-order methods, due to the non-smooth profiles of the turbulence quantities. In the discontinuous Galerkin framework, the polynomial approximation for these quantities leads to large oscillations that obstruct the non-linear solver. Taking into account the complexity with high-order methods and the fairly large modeling errors of the RANS modeling, low-order methods are believed to be more pragmatic. However, it is illustrated that solving RANSE with high-order methods leads to significantly smaller error magnitudes compared with second-order finite volume based solvers. Additionally, there is a remarkable improvement regarding the number of iterations to obtain a converged solution. Attention is given to the treatment of the specific rate of turbulence dissipation ω in the high-order framework. The possibilities and limitations of simulating industrial incompressible flows using discontinuous Galerkin based methods are assessed in order to draw some general conclusions for industrial applications.

Published on November 3, 2020 Updated on November 3, 2020