197 research outputs found
Multi-Moment Advection scheme for Vlasov simulations
We present a new numerical scheme for solving the advection equation and its
application to Vlasov simulations. The scheme treats not only point values of a
profile but also its zeroth to second order piecewise moments as dependent
variables, for better conservation of the information entropy. We have
developed one- and two-dimensional schemes and show that they provide quite
accurate solutions within reasonable usage of computational resources compared
to other existing schemes. The two-dimensional scheme can accurately solve the
solid body rotation problem of a gaussian profile for more than hundred
rotation periods with little numerical diffusion. This is crucially important
for Vlasov simulations of magnetized plasmas. Applications of the one- and
two-dimensional schemes to electrostatic and electromagnetic Vlasov simulations
are presented with some benchmark tests.Comment: 52 pages, 18 figures, accepted for the publication in Journal of
Computational Physic
Mini-Workshop: Innovative Trends in the Numerical Analysis and Simulation of Kinetic Equations
In multiscale modeling hierarchy, kinetic theory plays a vital role in connecting microscopic Newtonian mechanics and macroscopic continuum mechanics. As computing power grows, numerical simulation of kinetic equations has become possible and undergone rapid development over the past decade. Yet the unique challenges arising in these equations, such as highdimensionality, multiple scales, random inputs, positivity, entropy dissipation, etc., call for new advances of numerical methods. This mini-workshop brought together both senior and junior researchers working on various fastpaced growing numerical aspects of kinetic equations. The topics include, but were not limited to, uncertainty quantification, structure-preserving methods, phase transitions, asymptotic-preserving schemes, and fast methods for kinetic equations
PolyPIC: the Polymorphic-Particle-in-Cell Method for Fluid-Kinetic Coupling
Particle-in-Cell (PIC) methods are widely used computational tools for fluid
and kinetic plasma modeling. While both the fluid and kinetic PIC approaches
have been successfully used to target either kinetic or fluid simulations,
little was done to combine fluid and kinetic particles under the same PIC
framework. This work addresses this issue by proposing a new PIC method,
PolyPIC, that uses polymorphic computational particles. In this numerical
scheme, particles can be either kinetic or fluid, and fluid particles can
become kinetic when necessary, e.g. particles undergoing a strong acceleration.
We design and implement the PolyPIC method, and test it against the Landau
damping of Langmuir and ion acoustic waves, two stream instability and sheath
formation. We unify the fluid and kinetic PIC methods under one common
framework comprising both fluid and kinetic particles, providing a tool for
adaptive fluid-kinetic coupling in plasma simulations.Comment: Submitted to Frontier
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