A semi-Lagrangian AMR scheme for 2D transport problems in conservation form
Presented by Mr. Francesco VECIL
Type: Oral presentation
Track: Numerical Methods for Partial Differential Equations
We propose a numerical instrument to solve, in 1D and 2D, transport problems written in conservation form. The integrand function evolves following the laws described by an advection field, whose expression depends on the nature of the system studied. Common issues in the simulation of such problems are the appearance or movement of large gradients, the filamentation of the phase space or the presence of vortices, in which cases many discretization points are required, while smooth zones could be given less resolution. If a Fixed-Mesh (FM) discretization is used, then the choice of meshing the whole domain at the highest resolution is forced, which makes the numerical method time-consuming. Adaptive-Mesh-Renement (AMR) schemes describe different zones of the domain with different resolutions; the grid hierarchy is updated after each time step depending on the features of integrand function. The transport stages are solved by means of a PWENO-semi-Lagrangian (SL) strategy, extended to the 2D setting by means of a second-order Strang splitting. We show several 2D benchmark tests (Vlasov-Poisson, deformation flows, guiding-center and Kelvin-Helmholtz instabilities) of which we discuss the quality and the speedup with respect to a FM strategy. We show the preliminary results relative to the application of our strategy to a Vlasov-Maxwell system for the description of a laser penetrating into a plasma.