32 research outputs found
Accuracy of the Explicit Energy-Conserving Particle-in-Cell Method for Under-resolved Simulations of Capacitively Coupled Plasma Discharges
The traditional explicit electrostatic momentum-conserving Particle-in-cell
algorithm requires strict resolution of the electron Debye length to deliver
numerical accuracy. The explicit electrostatic energy-conserving
Particle-in-Cell algorithm alleviates this constraint with minimal modification
to the traditional algorithm, retaining its simplicity and ease of
parallelization and acceleration on modern supercomputing architectures. In
this article we apply the algorithm to model a one-dimensional radio-frequency
capacitively coupled plasma discharge relevant to industrial applications. The
energy-conserving approach closely matches the results from the
momentum-conserving algorithm and retains accuracy even for cell sizes up to 8x
the electron Debye length. For even larger cells the algorithm loses accuracy
due to poor resolution of steep gradients in the radio-frequency sheath. This
can be amended by introducing a non-uniform grid, which allows for accurate
simulations with 9.4x fewer cells than the fully resolved case, an improvement
that will be compounded in higher-dimensional simulations. We therefore
consider the explicit energy-conserving algorithm as a promising approach to
significantly reduce the computational cost of full-scale device simulations
and a pathway to delivering kinetic simulation capabilities of use to industry
Metriplectic Integrators for the Landau Collision Operator
We present a novel framework for addressing the nonlinear Landau collision
integral in terms of finite element and other subspace projection methods. We
employ the underlying metriplectic structure of the Landau collision integral
and, using a Galerkin discretization for the velocity space, we transform the
infinite-dimensional system into a finite-dimensional, time-continuous
metriplectic system. Temporal discretization is accomplished using the concept
of discrete gradients. The conservation of energy, momentum, and particle
densities, as well as the production of entropy is demonstrated algebraically
for the fully discrete system. Due to the generality of our approach, the
conservation properties and the monotonic behavior of entropy are guaranteed
for finite element discretizations in general, independently of the mesh
configuration.Comment: 24 pages. Comments welcom