Parallelization in time of numerical simulations of fully-developed plasma turbulence using the parareal algorithm

16 pages, 12 figures.It is shown that numerical simulations of fully-developed plasma turbulence can be successfully parallelized in time using the parareal algorithm. The result is far from trivial, and even unexpected, since the exponential divergence of Lagrangian trajectories as well as the extreme sensitivity to initial conditions characteristic of turbulence set these type of simulations apart from the much simpler systems to which the parareal algorithm has been applied to this day. It is also shown that the parallel gain obtainable with this method is very promising (close to an order of magnitude for the cases and implementations described), even when it scales with the number of processors quite differently to what is typical for spatial parallelization.Part of the research was carried out at the University of Alaska Fairbanks, funded by the DOE Office of Science Grant No. DE-FG02-04ER54741. Research was also carried out in part at Oak Ridge National Laboratory, managed by UT-Battelle LLC, for US DOE under Contract No. DE-AC05–00OR22725, and funded via the Seed Money Initiative Program.Publicad

Investigation of the interaction between competing types of nondiffusive transport in drift wave turbulence

Radial transport in turbulence dominated tokamak plasmas has been observed to deviate from classical diffusion in certain regimes relevant for magnetic confinement fusion. These situations at least include near-marginal turbulence, where radial transport becomes superdiffusive and mediated by elongated radial structures (or avalanches) and transport across radially sheared poloidal flows, where radial subdiffusion often ensues. In this paper, the interaction between very different physical ingredients responsible for these two types of nondiffusive dynamics (namely, turbulent profile relaxation close to a local threshold and the interaction with radially sheared zonal flows) is studied in detail in the context of a simple two-dimensional electrostatic plasma fluid turbulence model based on the dissipative trapped electron mode. It is shown that, depending on the relative relevance of each of these ingredients, which can be tuned in various ways, a variety of nondiffusive radial transport behaviors can be found in the system. The results also illustrate the fact that the classical diffusion paradigm is often insufficient to describe turbulent transport in systems with self-generated flows and turbulent profile relaxations. Published by AIP Publishing.This work was supported by U.S. DOE under Contract No. DE-FG02-04ER54741 with the University of Alaska Fairbanks and in part by a grant of HPC resources from the Arctic Region Supercomputing Center at the University of Alaska Fairbanks. This research was also sponsored in part by DGICT (Direccion General de Investigaciones Cientıficas y Tecnologicas) of Spain under Project No. ENE2015-68265

Transport dynamics of self-consistent, near-marginal drift-wave turbulence. II. Characterization of transport by means of passive scalars

From theoretical and modeling points of view, following Lagrangian trajectories is the most straightforward way to characterize the transport dynamics. In real plasmas, following Lagrangian trajectories is difficult or impossible. Using a blob of passive scalar (a tracer blob) allows a quasi-Lagrangian view of the dynamics. Using a simple two-dimensional electrostatic plasma turbulence model, this work demonstrates that the evolution of the tracers and the passive scalar field is equivalent between these two fluid transport viewpoints. When both the tracers and the passive scalar evolve in tandem and closely resemble stable distributions, namely, Gaussian distributions, the underlying turbulent transport character can be recovered from the temporal scaling of the second moments of both. This local transport approach corroborates the use of passive scalar as a turbulent transport measurement. The correspondence between the local transport character and the underlying transport is quantified for different transport regimes ranging from subdiffusive to superdiffusive. This correspondence is limited to the initial time periods of the spread of both the tracers and the passive scalar in the given transport regimes.This work was supported by U.S. DOE Contract No. DE-FG02-04ER54741 with the University of Alaska Fairbanks and in part by a grant of HPC resources from the Arctic Region Supercomputing Center at the University of Alaska Fairbanks. This research was also sponsored in part by DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project No. ENE2015-68265

Optimized implementation of power dispatch in the OPA model and its implications for dispatch sensitivity for the WECC power network

The social and economic costs of large blackouts in power transmission networks make it critical to properly understand their dynamics. The OPA model was developed with this objective in mind and has previously been applied to power grids of small and medium size, some of them properly modeling realistic cases such as the simplified WECC network, covering the Western region of the US. The bulk of the OPA model's computational cost comes from the repeated solution of a linear programming problem using the Simplex method which is difficult to parallelize. In this paper we introduce important improvements to the modeling part of the linear problem, accelerating the previous implementation by a factor of up to 200, depending on the network. These improvements make it possible, from a practical point of view, to simulate the largest, most detailed, WECC network consisting of 19,402 nodes, reducing the wall-clock time of the simulation from two years to only 10 days. The first simulations show an interesting result: the detailed 19,402 nodes network displays a reduced sensitivity of the dynamics to the dispatch, when compared to the previously used simplified WECC models containing only 1553 and 2504 nodes.This research was sponsored by Ministerio de Economía y Competitividad of Spain under Projects No. ENE2012-31753, ENE2012- 33219, ENE2015-68265-P and ENE2015-68265-P. Simulations have been run in the supercomputer cluster Uranus located at Universidad Carlos III de Madrid (Spain), funded by the Spanish Government via the national projects UNC313-4E-2361, ENE2012-33219 and ENE2012- 31753

Tracer particle transport dynamics in the diffusive sandpile cellular automaton

The confinement properties of the diffusive running sandpile are characterized by tracking the motion of a population of marked grains of sand. It is found that, as the relative strength of the avalanching to the diffusive transport channel is varied, a point is reached at which the particle global confinement time and the probability density functions of the jump-sizes and waiting-times of the tracked grains experience a sudden change, thus revealing a dynamical transition, that is consistent with previous studies (Newman DE et al., Phys Rev Lett 2002;88(20):204304). Across this transition, the sandpile moves from a regime characterized by self-similarity and memory, where avalanches of all possible sizes dominate transport across the system, to another regime where transport is taken over by near system-size, quasi-periodic avalanches. Values for the fractional transport exponents that quantify effective transport across the sandpile prior to the transition are also obtained.This research has been sponsored in part by Ministerio de Economía y Competitividad of Spain under Projects No. ENE2015- 68265-P and No. ENE2015-66444-R. Research also supported in part by DOE-OFES Grant No. DE-FG02-04ER5741 at University of Alaska. Sandpile simulations have been run in Uranus, a supercomputer cluster at Universidad Carlos III de Madrid (Spain) that has been funded by the Spanish Government via the national projects UNC313-4E-2361, ENE2009-12213-C03-03, ENE2012-33219 and ENE2012-31753

Recurrence quantification analysis of simulations of near-marginal dissipative-trapped-electron-mode turbulence

Recurrence quantification analysis (RQA) is a powerful tool to study dynamical systems and to help us understand and characterize the underlying physics when a transition occurs. The idea is based on the fact that, given sufficiently long time lapses, every dynamical system returns to states arbitrarily close to those it had in the past. This fundamental property of dynamical systems is called recurrence. In this work, we analyze, using the RQA technique, the recurrence properties of time series obtained from a series of numerical simulations of a dissipative-trapped-electron-mode (DTEM) turbulence model in near-marginal conditions where a transition in the nature of turbulent transport was observed as a subdominant diffusive channel strength is increased from zero [J. A. Mier et al., Phys. Plasmas 15, 112301 (2008)]. The results of the RQA analysis clearly show that the degree of determinism and complexity of the dynamics closely follows the degree of non-diffusiveness in the observed transportThis research was sponsored by DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project No. ENE2009-12213-C03-03=FTN. Research supported in part by DOE Office of Science Grant No. DE-FG02-04ER5741 at University of Alaska

Implementation of 2D Domain Decomposition in the UCAN Gyrokinetic Particle-in-Cell Code and Resulting Performance of UCAN2

The massively parallel, nonlinear, three-dimensional (3D), toroidal, electrostatic, gyrokinetic, particle-in-cell (PIC), Cartesian geometry UCAN code, with particle ions and adiabatic electrons, has been successfully exercised to identify non-diffusive transport characteristics in present day tokamak discharges. The limitation in applying UCAN to larger scale discharges is the 1D domain decomposition in the toroidal (or z-) direction for massively parallel implementation using MPI which has restricted the calculations to a few hundred ion Larmor radii or gyroradii per plasma minor radius. To exceed these sizes, we have implemented 2D domain decomposition in UCAN with the addition of the y-direction to the processor mix. This has been facilitated by use of relevant components in the P2LIB library of field and particle management routines developed for UCLA's UPIC Framework of conventional PIC codes. The gyro-averaging specific to gyrokinetic codes is simplified by the use of replicated arrays for efficient charge accumulation and force deposition. The 2D domain-decomposed UCAN2 code reproduces the original 1D domain nonlinear results within round-off. Benchmarks of UCAN2 on the Cray XC30 Edison at NERSC demonstrate ideal scaling when problem size is increased along with processor number up to the largest power of 2 available, namely 131,072 processors. These particle weak scaling benchmarks also indicate that the 1 nanosecond per particle per time step and 1 TFlops barriers are easily broken by UCAN2 with 1 billion particles or more and 2000 or more processors.This work was supported in part in the USA by Grant No. DE-FG02-04ER54741 to the University of Alaska, Fairbanks, AK, from the Office of Fusion Energy Sciences, Office of Science, United States Department of Energy. It was also supported in part at Universidad Carlos III, Madrid, Spain, by Spanish National Project No. ENE2009-12213-C03-03. This research used resources of the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. It also took advantage of resources at the Barcelona Supercomputing Center (BSC), Centro Nacional de Supercomputación, Barcelona, Spain. One of us (Leboeuf) would particularly like to thank David Vicente from BSC and Zhengji Zhao from NERSC for their help in the porting, debugging, and optimization of UCAN2 on the mainframes at their respective centers

Characterization of nondiffusive transport in plasma turbulence via a novel Lagrangian method

4 pages, 3 figures.-- PACS nrs.: 52.35.Ra, 05.40.Fb, 47.27.−i, 52.65.Kj.A novel method to probe and characterize the nature of the transport of passive scalars carried out by a turbulent flow is introduced. It requires the determination of two exponents which encapsulate the statistical and correlation properties of the component of interest of the Lagrangian velocities of the flow. Numerical simulations of a magnetically confined, near-critical turbulent plasma, known to exhibit superdiffusive radial transport, are used to illustrate the method. It is shown that the method can easily detect the change in the dynamics of the radial transport that takes place after adding to the simulations a (subdominant) diffusive channel of tunable strength.Research supported by Spanish DGES Grant No. ENE2006-15244-C03-01/FTN and DOE Office of Science Grant No. DE-FG02-04ER54741 at University of Alaska. ORNL researchers sponsored by U.S. DOE under Contract No. DE-AC05-00OR22725.Publicad

Nature of Transport across Sheared Zonal Flows in Electrostatic Ion-Temperature-Gradient Gyrokinetic Plasma Turbulence

4 pages, 4 figures.-- PACS nrs.: 52.35.Ra, 05.40.Fb, 52.55.Fa, 52.65.Tt.It is shown that the usual picture for the suppression of turbulent transport across a stable sheared flow based on a reduction of diffusive transport coefficients is, by itself, incomplete. By means of toroidal gyrokinetic simulations of electrostatic, collisionless ion-temperature-gradient turbulence, it is found that the nature of the transport is altered fundamentally, changing from diffusive to anticorrelated and subdiffusive. Additionally, whenever the flows are self-consistently driven by turbulence, the transport gains an additional non-Gaussian character. These results suggest that a description of transport across sheared flows using effective diffusivities is oversimplified.Research carried out at ORNL, managed by UT-Battelle LLC, for US DOE under Contract No. DE-AC05-00OR22725. Research funded by DOE Office of Science Grants No. DE-FG02-04ER54741 at University of Alaska and No. DE-FG02-04ER54740 at UCLA.Publicad

Fourier signature of filamentary vorticity structures in two-dimensional turbulence

It is shown that coherent regions of isotropic two-dimensional (2D) turbulence can be clearly identified in the phase part of the Fourier spectrum. Certain spectral phase events are particularly prominent, and are much stronger in the range of wave numbers corresponding to the dissipation range. It is shown that these events are associated with spatially localized filamentary structures in the 2D vorticity field that historically have been related to the intermittency of dissipation. The identified phase signature provides a particularly transparent diagnostic of the temporal evolution of the coherent coupling of disparate scales in anisostropic intermittent dissipative events. These results open the possibility of using the phase of the Fourier transform as a new turbulence diagnostic that identifies and quantitatively characterizes details pertaining to dissipative events.Research supported in part by the Spanish national projects No. ENE2009-12213-C03-03, ENE2012-33219, UNC313-4E-2361 and ENE2012-31753 and the US DOE Office of Science Grants No. DE-FG02-04ER54741 and DE-FG02-89ER53291. Simulations run at the Uranus supercomputer cluster at Universidad Carlos III de Madrid