Peter McCorquodale

Application of adaptive mesh refinement to particle-in-cell simulations of plasmas and beams

Plasma simulations are often rendered challenging by the disparity of scales in time and in space which must be resolved. When these disparities are in distinctive zones of the simulation domain, a method which has proven to be effective in other areas (e.g. fluid dynamics simulations) is the mesh refinement technique. We briefly discuss the challenges posed by coupling this technique with plasma Particle-In-Cell simulations, and present examples of application in Heavy Ion Fusion and related fields which illustrate the effectiveness of the approach. We also report on the status of a collaboration under way at Lawrence Berkeley National Laboratory between the Applied Numerical Algorithms Group (ANAG) and the Heavy Ion Fusion group to upgrade ANAGs mesh refinement library Chombo to include the tools needed by Particle-In-Cell simulation codes.

Implementations of mesh refinement schemes for Particle-In-Cell plasma simulations

Plasma simulations are often rendered challenging by the disparity of scales in time and in space which must be resolved. When these disparities are in distinctive zones of the simulation region, a method which has proven to be effective in other areas (e.g. fluid dynamics simulations) is the mesh refinement technique. We briefly discuss the challenges posed by coupling this technique with plasma Particle-In-Cell simulations and present two implementations in more detail, with examples.

Simulation of neoclassical transport with the continuum gyrokinetic code COGENT

The development of the continuum gyrokinetic code COGENT for edge plasma simulations is reported. The present version of the code models a nonlinear axisymmetric 4D (R, v∥, μ) gyrokinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. Here, R is the particle gyrocenter coordinate in the poloidal plane, and v∥ and μ are the guiding center velocity parallel to the magnetic field and the magnetic moment, respectively. The COGENT code utilizes a fourth-order finite-volume (conservative) discretization combined with arbitrary mapped multiblock grid technology (nearly field-aligned on blocks) to handle the complexity of tokamak divertor geometry with high accuracy. Topics presented are the implementation of increasingly detailed model collision operators, and the results of neoclassical transport simulations including the effects of a strong radial electric field characteristic of a tokamak pedestal under H-mode conditions.

High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

We present an approach to solving hyperbolic conservation laws by finite-volume methods on mapped multiblock grids, extending the approach of Colella, Dorr, Hittinger, and Martin (2011) 10 for grids with a single mapping. We consider mapped multiblock domains for mappings that are conforming at inter-block boundaries. By using a smooth continuation of the mapping into ghost cells surrounding a block, we reduce the inter-block communication problem to finding an accurate, robust interpolation into these ghost cells from neighboring blocks. We demonstrate fourth-order accuracy for the advection equation for multiblock coordinate systems in two and three dimensions.

High-order finite-volume adaptive methods on locally rectangular grids

We are developing a new class of finite-volume methods on locally-refined and mapped grids, which are at least fourth-order accurate in regions where the solution is smooth. This paper discusses the implementation of such methods for time-dependent problems on both Cartesian and mapped grids with adaptive mesh refinement. We show 2D results with the Berger-Colella shock-ramp problem in Cartesian coordinates, and fourth-order accuracy of the solution of a Gaussian pulse problem in a polytropic gas in mapped coordinates.

A scalable parallel Poisson solver in three dimensions with infinite-domain boundary conditions

The authors presented an elliptic free space solver that offers vastly improved performance over a previous variant of the algorithm. Processors of an IBM SP system were currently scaled up to 1024, and it is planned to port the solver to Blue Gene/L. The solver employs a method of local corrections that avoids the need for costly communication, while retaining parallel scalability of the method. Communication costs are generally small: 25 percent of the total running time or less for runs on up to 512 processors and 37 percent of the total time on 1024 processors. The numerical overheads incurred are independent of the number of processors for a wide range of problem sizes. The solver currently handles infinite-domain (free space) boundary conditions, but may be reformulated to accommodate other kinds of boundary conditions as well.

Analyzing the Adaptive Mesh Refinement (AMR) Characteristics of a High-Order 2D Cubed-Sphere Shallow-Water Model

AbstractAdaptive mesh refinement (AMR) is a technique that has been featured only sporadically in atmospheric science literature. This paper aims to demonstrate the utility of AMR for simulating atmospheric flows. Several test cases are implemented in a 2D shallow-water model on the sphere using the Chombo-AMR dynamical core. This high-order finite-volume model implements adaptive refinement in both space and time on a cubed-sphere grid using a mapped-multiblock mesh technique. The tests consist of the passive advection of a tracer around moving vortices, a steady-state geostrophic flow, an unsteady solid-body rotation, a gravity wave impinging on a mountain, and the interaction of binary vortices. Both static and dynamic refinements are analyzed to determine the strengths and weaknesses of AMR in both complex flows with small-scale features and large-scale smooth flows. The different test cases required different AMR criteria, such as vorticity or height-gradient based thresholds, in order to achieve the...

SciDAC advances and applications in computational beam dynamics

SciDAC has had a major impact on computational beam dynamics and the design of particle accelerators. Particle accelerators -- which account for half of the facilities in the DOE Office of Science Facilities for the Future of Science 20 Year Outlook -- are crucial for US scientific, industrial, and economic competitiveness. Thanks to SciDAC, accelerator design calculations that were once thought impossible are now carried routinely, and new challenging and important calculations are within reach. SciDAC accelerator modeling codes are being used to get the most science out of existing facilities, to produce optimal designs for future facilities, and to explore advanced accelerator concepts that may hold the key to qualitatively new ways of accelerating charged particle beams. In this poster we present highlights from the SciDAC Accelerator Science and Technology (AST) project Beam Dynamics focus area in regard to algorithm development, software development, and applications.

Quantitative Performance Assessment of Proxy Apps and Parents

David Richards, Omar Aaziz, Jeanine Cook, Hal Finkel, Brian Homerding, Peter McCorquodale, Tiffany Mintz, Shirley Moore, Vinay Ramakrishnaiah, Courtenay Vaughan, and Greg Watson Lawrence Livermore National Laboratory, Livermore, CA Sandia National Laboratories, Albuquerque, NM Argonne National Laboratory, Chicago, IL Lawrence Berkeley National Laboratory, Berkeley, CA Oak Ridge National Laboratory, Oak Ridge, TN Los Alamos National Laboratory, Los Alamos, NM