arXiv subjects

Luis Chacon

Publications and source records attributed to Luis Chacon.

23 records · Page 2Linked to original sources

arXiv2017

An Adaptive, Implicit, Conservative 1D-2V Multi-Species Vlasov-Fokker-Planck Multiscale Solve in Planar Geometry

We consider a 1D-2V Vlasov-Fokker-Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we extend the conservative adaptive velocity-space discretization scheme proposed in [Taitano et al., J. Comp. Phys., 318, 391-420, (2016)] to a spatially inhomogeneous system. In this approach, we normalize the velocity-space coordinate to a temporally and spatially varying local characteristic speed per species. We explicitly consider the resulting inertial terms in the Vlasov equation, and derive a discrete formulation that conserves mass, momentum, and energy up to a prescribed nonlinear tolerance upon convergence. Our conservation strategy employs nonlinear constraints to enforce these properties discretely for both the Vlasov operator and the Fokker-Planck collision operator. Numerical examples of varying degrees of complexity, including shock-wave propagation, demonstrate the favorable efficiency and accuracy properties of the scheme.

physics.plasm-ph↗

arXiv2017

Deciphering the Kinetic Structure of Multi-Ion Plasma Shocks

Strong collisional shocks in multi-ion plasmas are featured in many high-energy-density environments, including Inertial Confinement Fusion (ICF) implosions. However, their basic structure and its dependence on key parameters (e.g., the Mach number and the plasma ion composition) are poorly understood, and controversies in that regard remain in the literature. Using a high-fidelity Vlasov-Fokker-Planck code, iFP, and direct comparisons to multi-ion hydrodynamic simulations and semi-analytic predictions, we critically examine steady-state planar shocks in D-3He plasmas and put forward a resolution to these controversies.

physics.plasm-ph↗

arXiv2015

A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell algorithm

For decades, the Vlasov-Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. Here, we explore a fully implicit PIC algorithm for the Vlasov-Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space-time-centered, employing particle sub-cycling and orbit-averaging. The algorithm conserves total energy, local charge, canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large time steps and cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D-3V.

physics.comp-ph↗

arXiv2013

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov-Darwin particle-in-cell algorithm

A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen, Chacon, Barnes, J. Comput. Phys. 230 (2011) 7018). The algorithm employs a kinetically enslaved Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to numerical round-off. In this study, we generalize the method to electromagnetic simulations in 1D using the Darwin approximation of Maxwell's equations, which avoids radiative aliasing noise issues by ordering out the light wave. An implicit, orbit-averaged time-space-centered finite difference scheme is applied to both the 1D Darwin field equations (in potential form) and the 1D-3V particle orbit equations to produce a discrete system that remains exactly charge- and energy-conserving. Furthermore, enabled by the implicit Darwin equations, exact conservation of the canonical momentum per particle in any ignorable direction is enforced via a suitable scattering rule for the magnetic field. Several 1D numerical experiments demonstrate the accuracy and the conservation properties of the algorithm.

physics.plasm-ph↗

arXiv2013

Fluid preconditioning for Newton-Krylov-based, fully implicit, electrostatic particle-in-cell simulations

A recent proof-of-principle study proposes an energy- and charge-conserving, nonlinearly implicit electrostatic particle-in-cell (PIC) algorithm in one dimension [Chen et al, J. Comput. Phys., 230 (2011) 7018]. The algorithm in the reference employs an unpreconditioned Jacobian-free Newton-Krylov method, which ensures nonlinear convergence at every timestep (resolving the dynamical timescale of interest). Kinetic enslavement, which is one key component of the algorithm, not only enables fully implicit PIC a practical approach, but also allows preconditioning the kinetic solver with a fluid approximation. This study proposes such a preconditioner, in which the linearized moment equations are closed with moments computed from particles. Effective acceleration of the linear GMRES solve is demonstrated, on both uniform and non-uniform meshes. The algorithm performance is largely insensitive to the electron-ion mass ratio. Numerical experiments are performed on a 1D multi-scale ion acoustic wave test problem.

physics.plasm-ph↗