39 research outputs found
Exactly energy-conserving electromagnetic Particle-in-Cell method in curvilinear coordinates
In this paper, we introduce and discuss an exactly energy-conserving
Particle-in-Cell method for arbitrary curvilinear coordinates. The flexibility
provided by curvilinear coordinates enables the study of plasmas in
complex-shaped domains by aligning the grid to the given geometry, or by
focusing grid resolution on regions of interest without overresolving the
surrounding, potentially uninteresting domain. We have achieved this through
the introduction of the metric tensor, the Jacobian matrix, and contravariant
operators combined with an energy-conserving fully implicit solver. We
demonstrate the method's capabilities using a Python implementation to study
several one- and two-dimensional test cases: the electrostatic two-stream
instability, the electromagnetic Weibel instability, and the geomagnetic
environment modeling (GEM) reconnection challenge. The test results confirm the
capability of our new method to reproduce theoretical expectations (e.g.
instability growth rates) and the corresponding results obtained with a
Cartesian uniform grid when using curvilinear grids. Simultaneously, we show
that the method conserves energy to machine precision in all cases.Comment: 14 pages, 5 figure
Topics in Magnetohydrodynamics
To understand plasma physics intuitively one need to master the MHD behaviors. As sciences advance, gap between published textbooks and cutting-edge researches gradually develops. Connection from textbook knowledge to up-to-dated research results can often be tough. Review articles can help. This book contains eight topical review papers on MHD. For magnetically confined fusion one can find toroidal MHD theory for tokamaks, magnetic relaxation process in spheromaks, and the formation and stability of field-reversed configuration. In space plasma physics one can get solar spicules and X-ray jets physics, as well as general sub-fluid theory. For numerical methods one can find the implicit numerical methods for resistive MHD and the boundary control formalism. For low temperature plasma physics one can read theory for Newtonian and non-Newtonian fluids etc
Energy-conserving discontinuous Galerkin methods for the Vlasov-Amp\`{e}re system
In this paper, we propose energy-conserving numerical schemes for the
Vlasov-Amp\`{e}re (VA) systems. The VA system is a model used to describe the
evolution of probability density function of charged particles under self
consistent electric field in plasmas. It conserves many physical quantities,
including the total energy which is comprised of the kinetic and electric
energy. Unlike the total particle number conservation, the total energy
conservation is challenging to achieve. For simulations in longer time ranges,
negligence of this fact could cause unphysical results, such as plasma self
heating or cooling. In this paper, we develop the first Eulerian solvers that
can preserve fully discrete total energy conservation. The main components of
our solvers include explicit or implicit energy-conserving temporal
discretizations, an energy-conserving operator splitting for the VA equation
and discontinuous Galerkin finite element methods for the spatial
discretizations. We validate our schemes by rigorous derivations and benchmark
numerical examples such as Landau damping, two-stream instability and
bump-on-tail instability
Comparison of Preconditioning Strategies in Energy Conserving Implicit Particle in Cell Methods
This work presents a set of preconditioning strategies able to significantly
accelerate the performance of fully implicit energy-conserving Particle-in-Cell
methods to a level that becomes competitive with semi-implicit methods. We
compare three different preconditioners. We consider three methods and compare
them with a straight unpreconditioned Jacobian Free Newton Krylov (JFNK)
implementation. The first two focus, respectively, on improving the handling of
particles (particle hiding) or fields (field hiding) within the JFNK iteration.
The third uses the field hiding preconditioner within a direct Newton iteration
where a Schwarz-decomposed Jacobian is computed analytically. Clearly, field
hiding used with JFNK or with the direct Newton-Schwarz (DNS) method
outperforms all method. We compare these implementations with a recent
semi-implicit energy conserving scheme. Fully implicit methods are still lag
behind in cost per cycle but not by a large margin when proper preconditioning
is used. However, for exact energy conservation, preconditioned fully implicit
methods are significantly easier to implement compared with semi-implicit
methods and can be extended to fully relativistic physics
Geometry Modeling for Unstructured Mesh Adaptation
The quantification and control of discretization error is critical to obtaining reliable simulation results. Adaptive mesh techniques have the potential to automate discretization error control, but have made limited impact on production analysis workflow. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic mesh adaptation mechanics. However, the poor integration of initial mesh generation and adaptive mesh mechanics to typical sources of geometry has hindered adoption of adaptive mesh techniques, where these geometries are often created in Mechanical Computer- Aided Design (MCAD) systems. The difficulty of this coupling is compounded by two factors: the inherent complexity of the model (e.g., large range of scales, bodies in proximity, details not required for analysis) and unintended geometry construction artifacts (e.g., translation, uneven parameterization, degeneracy, self-intersection, sliver faces, gaps, large tolerances be- tween topological elements, local high curvature to enforce continuity). Manual preparation of geometry is commonly employed to enable fixed-grid and adaptive-grid workflows by reducing the severity and negative impacts of these construction artifacts, but manual process interaction inhibits workflow automation. Techniques to permit the use of complex geometry models and reduce the impact of geometry construction artifacts on unstructured grid workflows are models from the AIAA Sonic Boom and High Lift Prediction are shown to demonstrate the utility of the current approach
Verification of Unstructured Grid Adaptation Components
Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. Laminar flow over a delta wing and turbulent flow over an ONERA M6 wing are verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and a moment. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. The wing adaptation cases in the current study document a clear improvement to existing grid adaptation procedures. The stage is set for the infusion of verified grid adaptation into production fluid flow simulations