# Magneto-Fluid Dynamics Seminar

#### A Multiscale, Conservative, Adaptive Implicit Algorithm for the Multispecies Vlasov-Fokker-Planck-Landau Equation

**Speaker:**
Luis Chacon, Los Alamos National Laboratory

**Location:**
Warren Weaver Hall 905

**Date:**
Tuesday, February 12, 2019, 11 a.m.

**Synopsis:**

The Vlasov-Fokker-Planck-Landau (VFP) model is considered a first-principles model for the simulation of collisional plasmas. It has real-world applications in the simulation of many laboratory and natural plasma systems of interest, including the Sun, Earth’s magnetosphere, and thermonuclear fusion experiments. As a mathematical model, however, VFP presents notable challenges for its efficient solution, including high dimensionality (6D+time), nonlinearity, extreme temporal and spatial scale disparity, as well as scale disparity in velocity space due to the presence of multiple species with disparate masses and temperatures. To address these challenges, we propose a novel algorithmic framework in 1D-2V based on implicit timestepping with optimal multigrid-based solvers, spatial and velocity-space adaptivity via mesh motion, and a new discrete treatment of both the collision operator (in the Rosenbluth form) and the Vlasov equation that ensures exact conservation of mass, momentum, and energy. As a result, this new treatment achieves optimal O(N) computational complexities while delivering unprecedented long-term simulation capabilities with moderate computational resources (<1000 cores). We demonstrate the utility of our approach with the simulation of a real Inertial Confinement Fusion (ICF) capsule in spherical geometry, where we show the impact of kinetic effects on the fusion reactivity of the capsule.