2019/10/07 by José A. Carrillo, Carrillo, Jose A., Jingwei Hu +5 · 6 citations
Mathematics · Physics and Astronomy · #65M75 #82B40 #82D10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1910.03080
openalex publication_date 2019/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a novel deterministic particle method to numerically approximate the Landau equation for plasmas. Based on a new variational formulation in terms of gradient flows of the Landau equation, we regularize the collision operator to make sense of the particle solutions. These particle solutions solve a large coupled ODE system that retains all the important properties of the Landau operator, namely the conservation of mass, momentum and energy, and the decay of entropy. We illustrate our new method by showing its performance in several test cases including the physically relevant case of the Coulomb interaction. The comparison to the exact solution and the spectral method is strikingly good maintaining 2nd order accuracy. Moreover, an efficient implementation of the method via the treecode is explored. This gives a proof of concept for the practical use of our method when coupled with the classical PIC method for the Vlasov equation.