Well balanced Arbitrary-Lagrangian-Eulerian Finite Volume schemes on moving nonconforming meshes for non-conservative Hyperbolic systems

Venue: Seminar Room "-1" – Via Sommarive, 14 Povo - Trento
Hour: 10.00 a.m.

• Elena Gaburro - PhD in Mathematics

Abstract:
In this talk we present 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. Our nonconforming ALE scheme 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 our new scheme compared with well established software for astrophysical fluid dynamics.
Indeed, we have formulated a new HLL-type and a novel Osher-type flux 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, we have adopted a nonconforming treatment of the sliding interfaces that appear due to the differential rotation.
In addition, we show the ease with which the introduced techniques can be extended to other contexts, as steady vortex flows in shallow water equations or complex free surface flows in two-phase models, and a preliminary analysis on how to increase the accuracy of the method by exploiting the conservation of the angular momentum.

Supervisors: Michael Dumbser