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761 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

An Adaptive Newton-Based Free-Boundary Grad–Shafranov Solver

Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for the poloidal magnetic flux, commonly known as the Grad–Shafranov equation. It is challenging to develop a scalable and accurate free-boundary Grad–Shafranov solver, since it is a fully nonlinear optimization problem that simultaneously solves for the magnetic field coil current outside the plasma to control the plasma shape. In this work, we develop a Newton-based free-boundary Grad–Shafranov solver using adaptive finite elements and preconditioning strategies. The free-boundary interaction leads to the evaluation of a domain-dependent nonlinear form of which its contribution to the Jacobian matrix is achieved through shape calculus. The optimization problem aims to minimize the distance between the plasma boundary and specified control points while satisfying two nontrivial constraints, which correspond to the nonlinear finite element discretization of the Grad–Shafranov equation and a constraint on the total plasma current involving a nonlocal coupling term. The linear system is solved by a block factorization, and AMG is called for subblock elliptic operators. The unique contributions of this work include the treatment of a global constraint, preconditioning strategies, nonlocal reformulation, and the implementation of adaptive finite elements. Furthermore, it is found that the resulting Newton solver is robust, successfully reducing the nonlinear residual to 1e-6 and lower in a small handful of iterations while addressing the challenging case to find a Taylor state equilibrium where conventional Picard-based solvers fail to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

CEED-MS8:Initial Integration of CEED Software in ECP Applications

Key components of CEED software development involve fast finite element operator storage and evaluation, architecture optimizations, performant algorithms for all orders, global kernels for finite element operators, efficient use of the memory sub-system, optimal data locality and motion, enhanced scalability and parallelism, and fast tensor contractions. As ultimate goals of the project, CEED is exploring and identifying the best algorithms for the full range of discretizations and applying algorithmic and software development to support ECP applications’ needs. In this milestone we report on the initial integration of CEED software in the selected first-wave ECP/CEED apps and the continued exploration of other ECP applications as second-wave (milestone CEED-MS23) and third-wave (milestone CEED-MS35) ECP/CEED application candidates. An extensive evaluation of various approaches for GPU acceleration of the CEED computational motives is also a major focus of the report, both in the settings of CEED’s Nekbone and Laghos miniapps, as well as versions of CEED’s bake-off problems (introduced in milestone CEED-MS6). The first-wave ECP applications targeted for coupling with CEED software include the ExaSMR and MARBL applications. We also report on near-term collaboration with the seed-funded Urban Systems project, as well as engagements with ACME, ExaAM, GEOS and the Application Assessment and Proxy App projects. The ExaSMR project involves coupled thermal-hydraulics/neutronics, with the latter based on Monte Carlo methods and the former based on high-order discretizations of the Navier-Stokes and energy equations for accurate simulation of turbulent transport. The project requires fast and efficient turbulence simulation capabilities that will scale to exascale platforms. Work within CEED will ensure that all aspects of the Nek5000 workflow scale to the target problem space, which involves > 10 10 degrees of freedom in typical production runs. CEED’s goal is to provide implementations that perform with maximum attainable efficiency and deliver low turn-around times. A deliverable for this milestone is beta-release of the GPU-based variant of Nek5000. MARBL is targeting high-energy-density physics problems, including single fluid multi-material hydrodynamics and radiation/magnetic diffusion simulation, with applications in inertial confined fusion, pulsed power experiments, and equation of state/material strength analysis. The code uses high-order methods based arbitrary Lagrangian-Eulerian, direct Eulerian, and unstructured adaptive mesh refinement. A deliverable for this milestone is collaboration with MARBL for improved performance based on partially-assembled operators. The Urban exascale project is planning to couple real-time data with high performance simulations to study particulate transport in cities. Nek5000 will be used for large eddy and RANS (Reynolds-averaged Navier-Stokes) simulations of turbulent transport in these domains. Areas where the CEED team is aiding the Urban Canyon group include creating high-order meshes for urban geometries and developing boundary conditions appropriate for simulations close to real-life urban conditions. The software artifacts delivered as part of this milestone include GPU-enabled versions of the Nekbone and Laghos miniapps, which are provided through the CEED website, http://ceed.exascaleproject.org and the CEED GitHub organization, http://github.com/ceed. In addition to details and results from the above R&D efforts, in this document we are also reporting on other project-wide activities performed in Q4 of FY17, including: the CEED first annual meeting and participation of CEED researchers in a variety of outreach activities.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1999

Field Encapsulation Library The FEL 2.2 User Guide

This document describes version 2.2 of the Field Encapsulation Library (FEL), a library of mesh and field classes. FEL is a library for programmers - it is a "building block" enabling the rapid development of applications by a user. Since FEL is a library intended for code development, it is essential that enough technical detail be provided so that one can make full use of the code. Providing such detail requires some assumptions with respect to the reader's familiarity with the library implementation language, C++, particularly C++ with templates. We have done our best to make the explanations accessible to those who may not be completely C++ literate. Nevertheless, familiarity with the language will certainly help one's understanding of how and why things work the way they do. One consolation is that the level of understanding essential for using the library is significantly less than the level that one should have in order to modify or extend the library. One more remark on C++ templates: Templates have been a source of both joy and frustration for us. The frustration stems from the lack of mature or complete implementations that one has to work with. Template problems rear their ugly head particularly when porting. When porting C code, successfully compiling to a set of object files typically means that one is almost done. With templated C++ and the current state of the compilers and linkers, generating the object files is often only the beginning of the fun. On the other hand, templates are quite powerful. Used judiciously, templates enable more succinct designs and more efficient code. Templates also help with code maintenance. Designers can avoid creating objects that are the same in many respects, but not exactly the same. For example, FEL fields are templated by node type, thus the code for scalar fields and vector fields is shared. Furthermore, node type templating allows the library user to instantiate fields with data types not provided by the FEL authors. This type of flexibility would be difficult to offer without the support of the language. For users who may be having template-related problems, we offer the consolation that support for C++ templates is destined to improve with time. Efforts such as the Standard Template Library (STL) will inevitably drive vendors to provide more thorough, optimized tools for template code development. Furthermore, the benefits will become harder to resist for those who currently subscribe to the least-common-denominator "code it all in C" strategy. May FEL bring you both increased productivity and aesthetic satisfaction.

Moran, Patrick J.↗
DOE OSTI2017

Initial CEED API (CEED-MS10)

Key components of CEED software development involve fast finite element operator storage and evaluation, architecture optimizations, performant algorithms for all orders, global kernels for finite element operators, efficient use of the memory sub-system, optimal data locality and motion, enhanced scalability and parallelism, and fast tensor contractions. As ultimate goals of the project, CEED is exploring and identifying the best algorithms for the full range of discretizations and applying algorithmic and software development to support ECP applications’ needs. In this milestone, we initiated the development and implementation of a common CEED API consisting of two main components: low-level and high-level APIs. We accomplished the goal of having the low-level component ready for the release of CEED v1.0 in the next quarter, see CEED-MS13. In this report we also provide a highlight from CEED’s integration with the MARBL app and the corresponding Laghos miniapp. A main theme in this work has been the systematic transition of advanced algorithms, developed and tested in Laghos, to the large-scale multi-physics settings of the MARBL code. The low-level CEED API provides a set of FE kernels and components for writing new low-level kernels. Examples include: vector and sparse linear algebra, element matrix assembly over a batch of elements, partial assembly and action for efficient high-order operators like mass, diffusion, advection, etc. The main goal of the low-level API is to establish the basis for the high-level API. Also, identifying such low-level kernels and providing a reference implementation for them serves as the basis for collaboration with vendors and STs. Another goal for the low-level API is to make it easy for applications with their own discretization infrastructure, who do not want to switch directly to using the high-level CEED API, to still evaluate and use the core operations provided by the low-level API. One of the challenges with high-order methods is that a global sparse matrix is no longer a good representation of a high-order linear operator, both with respect to the FLOPs needed for its evaluation, as well as the memory transfer needed for a matvec. Thus, another important question we tried to address while developing the low-level API is: is it possible to abstract out in a natural and efficient way the different implementations and data structures that arise when dealing with various computational device types: CPUs, GPUs, etc. Fully answering this question is beyond the scope of this particular milestone, since that requires longer time as we develop and expand the devices we support. The future high-level API will be the frontend provided by CEED consisting of high-level abstractions such as meshes, finite element spaces and solutions, bilinear forms, solvers, etc. At this high-level, an important aspect of the API will be to provide a uniform abstraction layer for writing code in a portable manner. To achieve that, we plan to utilize the MPI programming model combined with a device abstraction layer (DAL) for finite element computations that we will develop. The DAL will serve as the bridge between the low- and the high-level APIs, allowing a variety of programming models to be used for the low-level kernel implementations. The software artifacts delivered as part of this milestone include an initial CEED API software implementation (libCEED) provided through the CEED website, http://ceed.exascaleproject.org and the CEED GitHub organization, http://github.com/ceed. In addition to details and results from the above R&D efforts, in this document we are also reporting on other project-wide activities performed in Q1 of FY18, including: the Nek5000 v17.0 MFEM v3.3.2 and PETSc v3.8 releases, collaborations with ECP/ST and SciDAC projects, the inaugural Nek5000 hackathon and various outreach activities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Breakup dynamics in a pressure-swirl injector for urea-water solution applications: A computational study

The co-optimization of in-cylinder combustion and after-treatment technology has become a major aspect in engine design and development, with the goal of meeting the increasingly restrictive emission regulations in the transportation industry. Selective Catalytic Reduction is a robust technology to control the emission of NO x , and the injection of urea in water solution is the exhaust tailpipe is a key aspect of its operation. The proposed work uses high-fidelity Computational Fluid Dynamics to characterize the atomization dynamics of the liquid jet in relevant cross-flow conditions. The study focuses on a commercial low-pressure (9 bar) pressure-swirl injector which is characterized in its internal geometry through high-resolution X-ray micro-computational tomography. The internal two-phase flow has been modeled according to the volume-of-fluid approach in a large eddy simulation framework and validated against near-nozzle X-ray radiography measurement. Moreover, characterizing the breakup dynamics for the swirling hollow cone formation, and assessing the influence of the cross-flow in the breakup dynamics was completed. The results have been reported proposing Re-Oh maps and probability density functions of the spray kinematics. Higher cross-flow momentum generates an increase in the jet intact length and a reduction of the liquid droplet diameters. The axial momentum of the jet is affected by the cross-flow already in the near-nozzle region, determining a relevant deviation of the spray velocities. In conclusion, this work aims to inform the initialization of Eulerian-Lagrangian spray models through the assignment of droplet kinematics and static one-way coupling between volume-of-fluid results and Lagrangian spray parcels, to be used for system-size domain simulations.

33 ADVANCED PROPULSION SYSTEMS↗