A characteristic mapping method to study kinetic equations
Date(s) : 14/05/2024 iCal
11h00 - 12h00
In this talk, I will present a novel semi-Lagrangian approach to solve kinetic equations numerically. I will
demonstrate its efficacy for kinetic equation by tackling the Vlasov–Poisson equation. The approach makes
use of the characteristic mapping method (CMM) that allows evolving fine-scaled quantities on coarse
grids. The advected quantities are constructed as the function composition of the initial condition with
the characteristic map. This flow map is a one-parameter semi-group structure, which allows decomposing
the map into sub-maps. In contrast to other refinement methods we thus use compositional refinement.
Therefore the numerical solution can be in principle evaluated at any given resolution at any given time,
preserving the features of the initial condition like positivity.
In the presentation, I will showcase the global third-order convergence in both spatial and temporal
domains as well as the method’s exceptional ability to surpass the limitations of current schemes by
highlighting its capacity for extreme fine-scale resolution, as depicted in fig. 1. Our approach represents
a significant step forward in addressing computational challenges inherent in kinetic theories, offering a
pathway towards unprecedented precision in kinetic simulations. The talk is based on the preprint [P. Krah, X.-Y. Yin, J. Bergmann, J.-C. Nave, and K. Schneider. A characteristic mapping method
for Vlasov-Poisson with extreme resolution properties. arXiv preprint arXiv:2311.09379, 2023].
Emplacement
Saint-Charles - FRUMAM (2ème étage)
Catégories
