Well balanced Arbitrary-Lagrangian-Eulerian Finite Volume schemes on moving nonconforming meshes for non-conservative hyperbolic systems.
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.
and I am a finalist for the ECCOMAS PhD Awards 2018.
Next years research project
This grant promotes excellent researchers and encourages them to participate – as principal investigators or scientific coordinators – in competitive European and international calls.
with the Seal of Excellence for the (not funded) High Quality Project Proposal
Structure Preserving schemes for Conservation Laws on dynamic Space Time Manifolds,
submitted under the Horizon 2020’s Marie Skłodowska-Curie actions 2018. Certificate.
Ongoing research projects
Project 1: High order direct ALE schemes on moving Voronoi meshes with changing connectivity.
I am developing 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, I am coupling 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 and V. Springel.
Project 2: Angular momentum preserving strategies.
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 3: Well balancing for free surface flows.
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.