Engineering topics
Chacón, Luis
Publications and source records attributed to Chacón, Luis.
An asymptotic-preserving semi-Lagrangian algorithm for the anisotropic heat transport equation with arbitrary magnetic fields
Here, we extend the recently proposed semi-Lagrangian algorithm for the extremely anisotropic heat transport equation [Chacón et al., J. Comput. Phys ., 272 (2014)] to deal with arbitrary magnetic field topologies. The original scheme (which showed remarkable numerical properties) was valid for the so-called tokamak-ordering regime, in which the magnetic field magnitude was not allowed to vary much along field lines. The proposed extension maintains the attractive features of the original scheme (including the analytical Green's function, which is critical for tractability) with minor modifications, while allowing for completely general magnetic fields. The accuracy and generality of the approach are demonstrated by numerical experiment with an analytical manufactured solution.
Asymptotic-preserving gyrokinetic implicit particle-orbit integrator for arbitrary electromagnetic fields
We extend the asymptotic preserving and energy conserving time integrator for charged-particle motion developed in Ricketson and Chacón (2020) to include finite Larmor-radius (FLR) effects in the presence of electric-field length-scales comparable to the particle gyro-radius (the gyro-kinetic limit). We introduce two modifications to the earlier scheme. The first is the explicit gyro-averaging of the electric field at the half time-step, along with an analogous modification to the current deposition, which we show preserves total energy conservation in implicit PIC schemes. The number of gyrophase samples is chosen adaptively, ensuring proper averaging for large timesteps and the recovery of full-orbit dynamics in the small time-step limit. The second modification is an alternating large and small time-step strategy that ensures the particle trajectory samples gyrophases evenly. We show that this strategy relaxes the time-step restrictions on the scheme, allowing even larger speed-ups than previously achievable. We demonstrate the new method with several single-particle motion tests in a variety of electromagnetic field configurations featuring gyro-scale variation in the electric field. Finally, the results demonstrate the advertised ability to capture FLR effects accurately even when significantly stepping over the gyration time-scale.
An implicit, conservative electrostatic particle-in-cell algorithm for paraxial magnetic nozzles
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An implicit, conservative and asymptotic-preserving electrostatic particle-in-cell algorithm for arbitrarily magnetized plasmas in uniform magnetic fields
Here, we introduce a new electrostatic particle-in-cell algorithm capable of using large timesteps compared to particle gyro-period under a uniform external magnetic field. The algorithm extends earlier electrostatic fully implicit PIC implementations with a new asymptotic-preserving particle-push scheme that allows timesteps much larger than particle gyroperiods. In the large-timestep limit, the integrator preserves all particle drifts, while recovering the full orbit for small timesteps. The scheme allows for a seamless, efficient treatment of particles with coexisting magnetized and unmagnetized species, and conserves energy and charge exactly without spoiling implicit solver performance. We demonstrate by numerical experiment with several problems of variable species magnetization (diocotron instability, modified two-stream instability, and drift instability) that orders of magnitude wall-clock-time speedups vs. the standard fully implicit electrostatic PIC algorithm are possible without sacrificing solution accuracy.
A deterministic verification strategy for electrostatic particle-in-cell algorithms in arbitrary spatial dimensions using the method of manufactured solutions
As simulations of kinetic plasmas continue to increase in scope and complexity, a rigorous and straightforward method for verifying particle-in-cell (PIC) implementations is necessary to ensure their correctness. Here, in this paper, we present a deterministic method for the rigorous verification of multidimensional, multispecies, electrostatic particle-in-cell codes based on the method of manufactured solutions. Specifically, we prove that rigorous verification is possible through the exclusive examination of errors of grid quantities (i.e., moments and/or fields), allowing for a very light-weight and non-intrusive implementation in existing PIC codes. This is a marked improvement over earlier PIC verification approaches (only demonstrated with one species in 1D-1V), which rely on the comparison of cumulative distribution functions, and are invasive on the code base, introduce additional stochastic noise, are significantly more computationally expensive, and lack rigorous convergence properties. Interestingly, we show that different grid quantities feature different rates of convergence with the number of particles and mesh size, impacting the verification process. These theoretical results are confirmed numerically with a multi-species 2D-2V particle-in-cell code, including the ability of the method to detect order reduction due to an incorrect implementation.
An unsupervised machine-learning checkpoint-restart algorithm using Gaussian mixtures for particle-in-cell simulations
We propose an unsupervised machine-learning checkpoint-restart (CR) algorithm for particle-in-cell (PIC) algorithms using Gaussian mixtures (GM). The algorithm compresses the particle population per spatial cell by constructing a velocity distribution function using GM. Particles are reconstructed at restart time by local resampling of the Gaussians. To guarantee fidelity of the CR process, we ensure the exact preservation of invariants such as charge, momentum, and energy for both compression and reconstruction stages, everywhere on the mesh. We also ensure the preservation of Gauss' law after particle reconstruction by exactly matching the density profile at restart time. As a result, the GM CR algorithm is shown to provide a clean, conservative restart capability while potentially affording orders of magnitude savings in input/output requirements. Here, we demonstrate the algorithm using a recently developed exactly energy- and charge-conserving PIC algorithm using both electrostatic and electromagnetic tests. The tests demonstrate not only a high-fidelity CR capability, but also its potential for enhancing the fidelity of the PIC solution for a given particle resolution.
A fully implicit, scalable, conservative nonlinear relativistic Fokker–Planck 0D-2P solver for runaway electrons
Upon application of a sufficiently strong electric field, electrons break away from thermal equilibrium and approach relativistic speeds. These highly energetic ‘runaway’ electrons (~ MeV) play a significant role in tokamak disruption physics, and therefore their accurate understanding is essential to develop reliable mitigation strategies. As such, we have developed a fully implicit solver for the 0D-2P (i.e., including two momenta coordinates) relativistic nonlinear Fokker–Planck equation (rFP). As in earlier implicit rFP studies (NORSE, CQL3D), electron–ion interactions are modeled using the Lorentz operator, and synchrotron damping using the Abraham–Lorentz–Dirac reaction term. However, our implementation improves on these earlier studies by (1) ensuring exact conservation properties for electron collisions, (2) strictly preserving positivity, and (3) being scalable algorithmically and in parallel. Key to our proposed approach is an efficient multigrid preconditioner for the linearized rFP equation, a multigrid elliptic solver for the Braams–Karney potentials, and a novel adaptive technique to determine the associated boundary values. We verify the accuracy and efficiency of the proposed scheme with numerical results ranging from small electric-field electrical conductivity measurements to the accurate reproduction of runaway tail dynamics when strong electric fields are applied.
A multigroup moment-accelerated deterministic particle solver for 1-D time-dependent thermal radiative transfer problems
We introduce an efficient, robust, Lagrangian (characteristic-based) transport solver for 1-D time-dependent thermal radiative transfer (TRT) applications within the context of a moment-accelerated (High-Order/Low-Order, HOLO) algorithm. This novel transport algorithm inherits the best features of both particle methods (e.g., time accuracy, phase-space adaptivity, positivity) and deterministic, grid-based methods (e.g., no stochastic noise). Particles are adapted by the method of characteristics, with a time-dependent weight that accounts for stiff absorption and reemission process self-consistently. As a result, this approach is able to obtain accurate results while employing large time steps and a moderate number of particles (compared to Implicit Monte Carlo).
Ion species stratification within strong shocks in two-ion plasmas
We report strong collisional shocks in multi-ion plasmas are featured in many environments, with Inertial Confinement Fusion (ICF) experiments being one prominent example. Recent work [Keenan et al., Phys. Rev. E 96, 053203 (2017)] answered in detail a number of outstanding questions concerning the kinetic structure of steady-state, planar plasma shocks, e.g., the shock width scaling by the Mach number, M. However, it did not discuss shock-driven ion-species stratification (e.g., relative concentration modification and temperature separation). These are important effects since many recent ICF experiments have evaded explanation by standard, single-fluid, radiation-hydrodynamic (rad-hydro) numerical simulations, and shock-driven fuel stratification likely contributes to this discrepancy. Employing the state-of-the-art Vlasov-Fokker-Planck code, iFP, along with multi-ion hydro simulations and semi-analytics, we quantify the ion stratification by planar shocks with the arbitrary Mach number and the relative species concentration for two-ion plasmas in terms of ion mass and charge ratios. In particular, for strong shocks, we find that the structure of the ion temperature separation has a nearly universal character across ion mass and charge ratios. Lastly, we find that the shock fronts are enriched with the lighter ion species and the enrichment scales as M 4 for M»1.
Deciphering the kinetic structure of multi-ion plasma shocks
Here, strong collisional shocks in multi-ion plasmas are featured in many high-energy-density environments, including inertial confinement fusion 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 inconsistencies in that regard remain in the literature. In particular, the shock width's dependence on the Mach number has been hotly debated for decades. Using a high-fidelity Vlasov-Fokker-Planck code, iFP, and direct comparisons to multi-ion hydrodynamic simulations and semianalytic predictions, we resolve the structure of steady-state planar shocks in D- 3 He plasmas. Additionally, we derive and confirm with kinetic simulations a quantitative description of the dependence of the shock width on the Mach number and initial ion concentration.
Plasma ion stratification by weak planar shocks
We derive fluid equations for describing steady-state planar shocks of a moderate strength (0 < M - 1 ≲ 1 with M the shock Mach number) propagating through an unmagnetized quasineutral collisional plasma comprising two separate ion species. In addition to the standard fluid shock quantities, such as the total mass density, mass-flow velocity, and electron and average ion temperatures, the equations describe shock stratification in terms of variations in the relative concentrations and temperatures of the two ion species along the shock propagation direction. We have solved these equations analytically for weak shocks (0 < M - 1 << 1), with the results depending on M, ratios of the ion masses and charges, and the upstream mass fraction of one of the ion species. These analytical results are instrumental for gaining understanding in the behavior of weak shocks, and they have been used to verify kinetic simulations of shocks in multi-ion plasmas.
A communication-avoiding implicit–explicit method for a free-surface ocean model
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