Research activities

PhD thesis

Well balanced Arbitrary-Lagrangian-Eulerian Finite Volume schemes on moving nonconforming meshes for non-conservative hyperbolic systems. (Manuscript)
I defended my PhD thesis in June 2018.
My advisor was Michael Dumbser and my PhD committee was composed of Christian Klingenberg, Manuel J. Castro, Bruno Després, and Michael Dumbser.

My PhD thesis presents a novel second order accurate direct Arbitrary-Lagrangian-Eulerian (ALE) Finite Volume scheme for nonlinear hyperbolic systems, written both in conservative and non-conservative form, whose peculiarities are the nonconforming motion of interfaces, the exact preservation of equilibria and the conservation of angular momentum. It is especially well suited for modeling vortical flows affected by strong differential rotation: in particular, the novel combination with the well balancing make it possible to obtain great results for challenging astronomical phenomena as the rotating Keplerian disk. A large set of tests shows the greatly reduced dissipation and the significant improvements of the new scheme compared with well established software for astrophysical fluid dynamics.

A new HLL-type and a novel Osher-type flux have been formulated: they are able to maintain up to machine precision the equilibrium between pressure gradient, centrifugal force and gravity force that characterizes the Euler equations with gravity, and correspondingly capture with high accuracy even small perturbations. Moreover, to ensure a high quality of the moving mesh for long computational times, I have introduced a new and fully automatic nonconforming treatment of the sliding interfaces that appear due to the differential rotation.

In addition, it has been shown that the introduced techniques can be easily extended also to other contexts, such as steady vortex flows in the shallow water equations or complex free surface flows in compressible two-phase models, and a preliminary analysis on how to increase the accuracy of the method by exploiting the conservation of the angular momentum.

I have been awarded by GIMC/AIMETA as the Best PhD Thesis in Computational Fluid Mechanics in Italy (2018),
and I am a finalist for the ECCOMAS PhD Awards 2018.

Research projects

Long term project: Structure Preserving schemes for Conservation Laws on dynamic Space Time Manifolds

Open positions:
3 to 6 months internships and 1 to 2 years postdoctoral positions will be available soon.
Interested people can send an email to elena.gaburro@inria.fr including a detailed CV.
Possible research topics include: lagrangian schemes on moving meshes with topology changes (for example: parallelization, moving boundaries, adaptive mesh refinement, new applications, 3D extension ...) and well balancing for general relativity (using simplified or complete models, in 1D, 2D or 3D, with a theoretical and/or a numerical approach).

Funds and prizes:
In 2021: ... to be announced soon ...

In 2019: 14000 euros under the UniTN Starting Grant Programme

In 2019 and 2020: I have been awarded by the European Commission, under the Programme Horizon 2020, with the Seal of Excellence for this (not funded) High Quality Project Proposal, submitted under the Horizon 2020’s Marie Skłodowska-Curie actions 2018. Certificate.

Preliminary result:
Well-balanced vs not well-balanced simulation of a TOV netron star with GRMHD.
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RT Project 1: High order direct ALE schemes on moving Voronoi meshes with topology changes.

New directions as coupling with mesh adapting and shock tracking are now under investigations

Development of a new arbitrary high order accurate both Finite Volume (FV) and Discontinous Galerkin (DG) scheme on Voronoi meshes, in the framework of direct Arbitrary-Lagrangian-Eulerian (ALE) methods.
To do this, we have coupled the PnPm scheme (arbitrary high order unified framework for FV and DG introduced by M. Dumbser for unstructured triangular meshes) with AREPO (a massively parallel second order ALE code for Voronoi tessellations rebuilt at any time step, written by V. Springel for astrophysical applications).

The project requires a new space-time connection between old and new meshes and the adaptation of the PnPm scheme to Voronoi elements (even degenerating), as well as a C-Fortran interface.

In collaboration with W. Boscheri, S. Chiocchetti, M. Dumbser, C. Klingenberg, V. Springel, M. Ricchiuto and M. Ciallella.

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Project 2: Diffuse interface for compressible flows around moving solids.

We have proposed a new diffuse interface model (based on a simplified version of the seven-equation Baer-Nunziato model) for the simulation of inviscid compressible flows aroun fixed and moving solid bodies of arbitrary shape. The geometry of the solid bodies is simply specified via a scalar volume fraction function!

The PDE system is a nonlinear system of hyperbolic conservation laws with non-conservative products, that we solve via a high order path-conservative ADER-DG method.

We also prove that at the material interface, the normal component of the fluid velocity assumes the value of the normal component of the solid velocity.

In collaboration M. Dumbser, F. Thein, F. Kemm.
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Project 3: Angular momentum preserving strategies.

Kidder I am considering novel angular momentum preserving strategies in order to reduce the dissipation introduced with FV and DG schemes in the case of vortical phenomena.

In collaboration with M. Dumbser, B. Després, S. Del Pino.

Project 4: Well balancing for free surface flows.

SpinningSquare We have proposed a new well balanced FV scheme, written in parallel using CUDA, for complex nonhydrostatic free surface flows. It shows very little dissipation at the interface and high efficiency.

In collaboration M. Dumbser, M. Castro, C. Parés.

Preprint

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