COOKIE

This program aims at making progress in the numerical simulation of multidimensional kinetic equations.

Our proposal centers on the advanced numerical simulation and thorough analysis of kinetic equations and their underlying systems. These models have wide-ranging applications across numerous fields, notably in plasma physics and gas dynamics. A key feature of these systems is their formulation within phase space (position and velocity), capturing phenomena across multiple physical scales. This multi-scale nature presents significant computational challenges, demanding substantial processing resources and posing a major obstacle to effective modeling and simulation in applied physical sciences.

Our objective is to develop and rigorously analyze efficient numerical methods that can accurately and feasibly handle the complex multi-scale dynamics inherent in high-dimensional kinetic models. The project focuses on two classes of numerical schemes:

• Lagrangian methods, which offer enhanced robustness and flexibility in handling complex, multi-dimensional geometries;
• Eulerian methods, known for their high accuracy, particularly when solutions are near thermodynamic equilibrium.

Numerical simulations are performed with HOPE, the project's C++ library for kinetic equations.

Hermite spectral simulations in an interval

Watch the video — A. Blaustein, M. Bessemoulin-Chatard, F. Filbet.

Particle-in-cell simulations in a torus

Watch the video — F. Filbet, L. M. Rodrigues, K.-H. Trinh.

Publications related to the project are listed on HAL.

Project document (administrative material)