Stochastic Galerkin particle methods for kinetic equations of plasmas with uncertainties

Particle Simulation Methods for the Landau-Fokker-Planck Equation with Uncertain Data

“…for any I z ∈ R dz . The vector z characterizes the uncertainties of the system due, e.g., to missing information on the initial state, measurement of the model parameters and, boundary conditions [27,46].…”

“…Once established the DSMC solver of interest we seek to derive the related sG particle approach. These methods have been previously studied for mean-field model for emerging phenomena [9,10,28], and subsequently extended to the space-homogeneous Boltzmann equation in [36] and to a non-homogeneous plasma dynamics with BGK collision operator in [27].…”

“…To overcome this issue, a different approach based on projecting the particle dynamics through generalized polynomial chaos was pro-posed in [9,10,28,36]. Recently, the methodology has been extended to plasma simulations with BGK collisions in [27].…”

Orbits and chaos of a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback

“…Considering that the system studied in the paper is a delayed differential system, the DDE23 algorithm is adopted as a basic algorithm. On this basis, several numerical simulations for system (7) are given in the section. The simulated parameters are dimensionless.…”

“…In recent years, there are numerous innovative, challenging, and meaningful research continuously emerging in the fields of plasma science and plasma dynamics. Medaglia et al [7] proposed a novel stochastic Galerkin particle method for collisional kinetic models of plasmas under the effect of uncertainties. In plasma physics simulations, Medaglia's method is able to capture the correct behavior of the system in all test cases.…”