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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

An implicit-in-time DPG formulation of the 1D1V Vlasov-Poisson equations

Efficient solution of the Vlasov equation, which can be up to six-dimensional, is key to the simulation of many difficult problems in plasma physics. The discontinuous Petrov-Galerkin (DPG) finite element methodology provides a framework for the development of stable (in the sense of Ladyzhenskaya–Babuška–Brezzi conditions) finite element formulations, with built-in mechanisms for adaptivity. While DPG has been studied extensively in the context of steady-state problems and to a lesser extent with space-time discretizations of transient problems, relatively little attention has been paid to time-marching approaches. In the present work, we study a first application of time-marching DPG to the Vlasov equation, using backward Euler for a Vlasov-Poisson discretization. We demonstrate adaptive mesh refinement for two problems: the two-stream instability problem, and a cold diode problem. Furthermore, we believe the present work is novel both in its application of unstructured adaptive mesh refinement (as opposed to block-structured adaptivity, which has been studied previously) in the context of Vlasov-Poisson, as well as in its application of DPG to the Vlasov-Poisson system. We also discuss extensive additions to the Camellia library in support of both the present formulation as well as extensions to higher dimensions, Maxwell equations, and space-time formulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem

The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costs by performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductions typically on the order of 60 or more and possibly as large as 200. Furthermore, adaptive griding results in more accurate computation of geometric quantities such as x-points associated with the model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Advanced System Thermal Fluids Solver Development for SAM

This work summarizes a feasibility study on testing numerical algorithms that are suitable and efficient for advanced system analysis code development under the mutli-physics framework, MOOSE. The key is the implementation of a high-order one-dimensional staggered-grid finite volume method (SG-FVM), and its direct interaction with the linear/nonlinear solver, PETSc. Leveraging the existing capabilities of the SAM code, significant code coverages were established in the finite volume method code. This in turn allows for a suite of test problems with different problem sizes and levels of complexity to be used to quantify the performance improvement of the finite volume method code. As evidently shown in this study, the implemented SG-FVM demonstrated superior performance improvement against a direct finite element method implementation through MOOSE for the wide range of selected problems. On two computer systems, the speedup was observed to be significant, with at least one order of magnitude of solving time reduction. In addition, for a complex reactor model, transient simulation was performed using the finite volume method code, the results of which agree very well with the reference results from the finite element method code. Overall, this study demonstrates a successful feasibility study on the proposed numerical algorithms and software structure to support advanced system analysis tool development. In this work, short-term priority development and testing items were identified, and long-term code adoption and integration plans were made for the eventual deployment of the finite volume method in the SAM code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

PyAlbany: A Python interface to the C++ multiphysics solver Albany

Albany is a parallel C++ finite element library for solving forward and inverse problems involving partial differential equations (PDEs). In this paper we introduce PyAlbany, a newly developed Python interface to the Albany library. PyAlbany can be used to effectively drive Albany enabling fast and easy analysis and post-processing of applications based on PDEs that are pre-implemented in Albany. PyAlbany relies on the library PyBind11 to bind Python with C++ Albany code. Here we detail the implementation of PyAlbany and showcase its capabilities through a number of examples targeting a heat-diffusion problem. In particular we consider the following: (1) the generation of samples for a Monte Carlo application, (2) a scalability study, (3) a study of parameters on the performance of a linear solver, and finally (4) a tool for performing eigenvalue decompositions of matrix-free operators for a Bayesian inference application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Inertial impedance of coalescence during collision of liquid drops

The fluid dynamics of the collision and coalescence of liquid drops has intrigued scientists and engineers for more than a century owing to its ubiquitousness in nature, e.g. raindrop coalescence, and industrial applications, e.g. breaking of emulsions in the oil and gas industry. The complexity of the underlying dynamics, which includes occurrence of hydrodynamic singularities, has required study of the problem at different scales – macroscopic, mesoscopic and molecular – using stochastic and deterministic methods. In this work, a multi-scale, deterministic method is adopted to simulate the approach, collision, and eventual coalescence of two drops where the drops as well as the ambient fluid are incompressible, Newtonian fluids. The free boundary problem governing the dynamics consists of the Navier–Stokes system and associated initial and boundary conditions that have been augmented to account for the effects of disjoining pressure as the separation between the drops becomes of the order of a few hundred nanometres. This free boundary problem is solved by a Galerkin finite element-based algorithm. The interplay of inertial, viscous, capillary and van der Waals forces on the coalescence dynamics is investigated. It is shown that, in certain situations, because of inertia two drops that are driven together can first bounce before ultimately coalescing. This bounce delays coalescence and can result in the computed value of the film drainage time departing significantly from that predicted from existing scaling theories.

Mechanics↗
DOE OSTI2021

A Fast Solver for the Fractional Helmholtz Equation

The purpose of this paper is to study a Helmholtz problem with a spectral fractional Laplacian, instead of the standard Laplacian. Recently, it has been established that such a fractional Helmholtz problem better captures the underlying behavior in Geophysical Electromagnetics. In this work, we establish the well-posedness and regularity of this problem. We introduce a hybrid spectral-finite element approach to discretize it and show well-posedness of the discrete system. In addition, we derive a priori discretization error estimates. Finally, we introduce an efficient solver that scales aswell as the best possible solver for the classical integer-order Helmholtz equation. We conclude withseveral illustrative examples that confirm our theoretical findings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting

Fully implicit Runge--Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic preconditioning framework for solving the systems of equations that arise from IRK methods applied to linear numerical PDEs (without algebraic constraints). Additionally, this framework also naturally applies to discontinuous Galerkin discretizations in time. Under quite general assumptions on the spatial discretization that yield stable time integration, the preconditioned operator is proven to have condition number bounded by a small, order-one constant, independent of the spatial mesh and time-step size, and with only weak dependence on number of stages/polynomial order; for example, the preconditioned operator for 10th-order Gauss IRK has condition number less than two, independent of the spatial discretization and time step. The new method can be used with arbitrary existing preconditioners for backward Euler-type time-stepping schemes and is amenable to the use of three-term recursion Krylov methods when the underlying spatial discretization is symmetric. The new method is demonstrated to be effective on various high-order finite-difference and finite element discretizations of linear parabolic and hyperbolic problems, demonstrating fast, scalable solution of up to 10th-order accuracy. The new method consistently outperforms existing block preconditioning approaches, and in several cases, the new method can achieve 4th-order accuracy using Gauss integration with roughly half the number of preconditioner applications and wallclock time as required using standard diagonally IRK methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

NRC Multiphysics Analysis Capability Deployment FY2020: Part 3

This report details progress and activities of Idaho National Laboratory (INL) on the Nuclear Regulatory Commission (NRC) project “Development and Modeling Sup- port for Advanced Non-Light Water Reactors.” The tasks completed for this report are: Task2c: Explicit modeling of pebble transient temperature response. In this simulation, the 400 MWth Pebble-Bed Modular Reactor (PBMR) design, PBMR- 400, experiences a 20-second power ramp from 100% to 150% power. This is followed by a similar reduction in the power back to 100%. Several multiscale pebble coupling approaches are tested with one pebble per mesh element in the active core region. The results show good conservation behavior and the stability of the coupling.; Extended scope part 1: An assessment of the computational efficiency of the Discontinuous Finite Element Method (DFEM) heat transfer solver shows good scalability. The DFEM solver is a factor of 4 more expensive in solution time than the Finite Element Method (FEM) solver for heat transfer problems due to the increased number of degrees of freedom. Nonetheless, the DFEM approach provides the user with the flexibility to model gap heat transfer problems.; Extended scope part 2: The GapHeatTransferInterfaceMaterial was improved to give the user increased flexibility with the modeling of heat transfer through gaps with the DFEM solver. A number of gap parameters can now be coupled both through functions and variables.; Extended scope part 3: Demonstration of how the gap width between hexagonal fuel cells can be calculated during a heat-up transient and used in the GapHeatTransferInterface model. A full-domain DFEM model with gap expansion is coupled to a SubApp that models the thermal expansion of the base plate. The results show the expected physical behavior, although have not been fully bench-marked at this point in time.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Characterizing Artificial Viscosity Parameters with Approximate Symmetries

We are often faced with trying to capture the physics of compressible shocks, which are governed by the Euler equations. However, Euler shocks are formally discontinuous at the shock front (translating to a step-function behavior of rel evant flow variables). This poses a practical problem for codes with finite-sized grid elements. As a result, one must make a concession in simulating the be havior of shocks within a discrete framework. In particular, we must blur, or ‘regularize’ Euler shocks so that they may be captured on a finite grid.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Nonlocal and Mixed-Locality Multiscale Finite Element Methods

In many applications the resolution of small-scale heterogeneities remains a significant hurdle to robust and reliable predictive simulations. In particular, while material variability at the mesoscale plays a fundamental role in processes such as material failure, the resolution required to capture mechanisms at this scale is often computationally intractable. Multiscale methods aim to overcome this difficulty through judicious choice of a subscale problem and a robust manner of passing information between scales. One promising approach is the multiscale finite element method, which increases the fidelity of macroscale simulations by solving lower-scale problems that produce enriched multiscale basis functions. Here, in this study, we present the first work toward application of the multiscale finite element method to the nonlocal peridynamic theory of solid mechanics. This is achieved within the context of a discontinuous Galerkin framework that facilitates the description of material discontinuities and does not assume the existence of spatial derivatives. Analysis of the resulting nonlocal multiscale finite element method is achieved using the ambulant Galerkin method, developed here with sufficient generality to allow for application to multiscale finite element methods for both local and nonlocal models that satisfy minimal assumptions. Finally, we conclude with preliminary results on a mixed-locality multiscale finite element method in which a nonlocal model is applied at the fine scale and a local model at the coarse scale.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A Refinement-by-Superposition -Method for (curl)- and (div)-Conforming Discretizations

Here, we present refinement-by-superposition (RBS) hp-refinement infrastructure for computational electromagnetics (CEMs), which permits exponential rates of convergence. In contrast to dominant approaches to hp-refinement for continuous Galerkin methods, which rely on explicit constraint equations, the multilevel strategy presented drastically reduces the implementation complexity. Through the RBS methodology, enforcement of continuity occurs by construction, enabling arbitrary levels of refinement with ease, and without the practical (but not theoretical) limitations of constrained-node refinement. We outline the construction of the RBS hp-method for refinement with H (curl)- and H (div)-conforming finite cells. Numerical simulations for the 2-D finite element method (FEM) solution of the Maxwell eigenvalue problem demonstrate the effectiveness of RBS hp-refinement. As an additional goal of this work, we aim to promote the use of mixed-order (low- and high-order) elements in practical CEM applications.

42 ENGINEERING↗
DOE OSTI2018

Generalized and High-Order Multiscale Finite-Element Methods for Seismic Wave Propagation [Slides]

We have developed a series of multiscale finite-element methods for simulating seismic wave propagation in complex media. The most important feature of multiscale finite-element methods is using medium- and mesh-dependent multiscale basis functions. For different wave equations, or for wave equation modeling in different domains, we design different local spectral/linear problems to compute multiscale basis functions. Multiscale basis functions can accurately capture the fine-scale medium information for coarse-scale modeling problems. Numerical examples have demonstrated the efficiency and accuracy of our multiscale finite-element method framework for wave equation modeling. Future works aim at further improving the efficiency using more levels of information encapsulation, and address more realistic physics problems.

58 GEOSCIENCES↗
DOE OSTI2018

Localized harmonic characteristic basis functions for multiscale finite element methods

We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with discontinuous coefficients. These coefficients represent the conductivity of a composite material. We assume a background with a low conductivity that contains inclusions with different thermal properties. Under this scenario, we design a multiscale finite element method to efficiently approximate solutions. The method is based on an asymptotic expansion of the solution in terms of the ratio between the conductivities. The resulting method constructs (locally) finite element basis functions (one for each inclusion). These bases generate the multiscale finite element space where the approximation of the solution is computed. Numerical experiments show the good performance of the proposed methodology.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Construction of a Code Verification Matrix for Heat Conduction With Finite Element Code Applications

When establishing the pedigree of a simulation tool, code verification is used to ensure that the implemented numerical algorithm is a faithful representation of its underlying mathematical model. During this process, numerical results on various meshes are systematically compared to a reference analytic solution. The selection of analytic solutions can be a laborious process, as it is difficult to establish adequate code confidence without performing redundant work. In this report we address this issue by applying a physics-based process that establishes a set of reference problems. In this process, code simulation options are categorized and systematically tested, which ensures that gaps in testing are easily identified and addressed. The resulting problems are primarily intended for code verification analysis but may also be useful for comparison to other simulation codes, troubleshooting activities, or training exercises. The process is used to select fifteen code verification problems relevant for the one-dimensional steady-state heat conduction equation. These problems are applicable to a wide variety of simulation tools, but, in this work, a demonstration is performed using the finite element-based nuclear fuel performance code BISON. Convergence to the analytic solution at the theoretical rate is quantified for a selection of the problems, which establishes a baseline pedigree for the code. Not only can this standard set of conduction solutions be used for verification of other codes, but also the physics-based process for selecting problems can be utilized to quantify and expand testing for any simulation tool.

42 ENGINEERING↗
DOE OSTI2019

Development of a Novel Accelerator for Neutron Transport Solution Using the Galerkin Spectral Element Methods (Final Report)

This report summarizes the results of a three-year research project sponsored by the U.S. Department of Energy (DOE) Nuclear Energy University Program (NEUP) to develop and implement advanced acceleration schemes for the DOE NEAMS neutronics code PROTEUSSN. The project team included the University of Massachusetts Lowell, The Ohio State University, University of Michigan, and Argonne National Laboratory. The PROTEUS code is a high-fidelity capable deterministic neutron transport code based on unstructured finite element meshes, which solves the steady-state and transient neutron transport problem using the 2nd-order discrete ordinate method (SN2ND), the method of characteristics (MOC), and the advanced nodal transport method (NODAL). The DSA scheme has been implemented in PROTEUS to speed up SN transport calculations. The existing DSA scheme employs a consistent finite element formulation on the same fine mesh structure as the SN solution While the use of consistent discretizations makes the DSA method effective, it does not necessarily make it efficient because the numerical solution of a discretized elliptic diffusion problem itself can be costly, particularly when the problem size becomes large. We developed a new discontinuous Galerkin (DG) discretization of the diffusion equation, called DG-DSA, which can effectively and efficiently accelerate the SN transport iterations. As compared with the previous work, the novelty of our method is that the diffusion equation is solved on a coarse-mesh grid using the DG methods, and the DG diffusion discretization incorporates local hp adaptation, i.e., local adaptation of mesh size and/or polynomial degree, based on local total cross section (or optical thickness). Therefore, the resulting number of degrees of freedom (DOF) of the DG discretization is much less than the conventional consistent DSA discretizations, and thus DG-DSA can achieve significant improvement in computational efficiency. We implemented this scheme in PROTEUS-SN. In addition, we developed a new stabilization scheme named linear prolongation CMFD (lpCMFD). A novel feature of this scheme is that the conventional flat flux ratio–based scaling approach is replaced with a linear interpolation of the scalar flux differences at the coarse-mesh cell edges between the neutron transport and CMFD calculations. Fourier convergence analysis and numerical results show that lpCMFD is unconditionally stable and more effective than other CMFD based on acceleration schemes such as pCMFD, odCMFD. We also developed a new nonlinear diffusion acceleration scheme for solving neutron transport equations. This scheme, called LR-NDA, employs a local refinement approach on the framework of CMFD by solving a local boundary value problem of the scalar flux on the coarse-mesh structure to replace the piecewise constant scalar flux obtained by CMFD. The refined flux is then used to update the scalar flux in the neutron transport source iteration. It has been demonstrated that that LR-NDA is much more effective and stable than CMFD for a wide range of optical thicknesses. LR-NDA is a local adaptive method, which means LR-NDA does not necessarily require local refinement for all the coarse-mesh cells on the problem domain, i.e., it can be used only for relatively optically thick regions where the standard CMFD scheme would encounter the convergence problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

PRISMS-PF: A general framework for phase-field modeling with a matrix-free finite element method

Abstract A new phase-field modeling framework with an emphasis on performance, flexibility, and ease of use is presented. Foremost among the strategies employed to fulfill these objectives are the use of a matrix-free finite element method and a modular, application-centric code structure. This approach is implemented in the new open-source PRISMS-PF framework. Its performance is enabled by the combination of a matrix-free variant of the finite element method with adaptive mesh refinement, explicit time integration, and multilevel parallelism. Benchmark testing with a particle growth problem shows PRISMS-PF with adaptive mesh refinement and higher-order elements to be up to 12 times faster than a finite difference code employing a second-order-accurate spatial discretization and first-order-accurate explicit time integration. Furthermore, for a two-dimensional solidification benchmark problem, the performance of PRISMS-PF meets or exceeds that of phase-field frameworks that focus on implicit/semi-implicit time stepping, even though the benchmark problem’s small computational size reduces the scalability advantage of explicit time-integration schemes. PRISMS-PF supports an arbitrary number of coupled governing equations. The code structure simplifies the modification of these governing equations by separating their definition from the implementation of the numerical methods used to solve them. As part of its modular design, the framework includes functionality for nucleation and polycrystalline systems available in any application to further broaden the phenomena that can be used to study. The versatility of this approach is demonstrated with examples from several common types of phase-field simulations, including coarsening subsequent to spinodal decomposition, solidification, precipitation, grain growth, and corrosion.

36 MATERIALS SCIENCE↗
DOE OSTI2018

A gradient-based optimization approach for the detection of partially connected surfaces using vibration tests

The integrity of engineering structures is often compromised by embedded surfaces that result from incomplete bonding during the manufacturing process, or initiation of damage from fatigue or impact processes. Examples include delaminations in composite materials, incomplete weld bonds when joining two components, and internal crack planes that may form when a structure is damaged. In many cases the areas of the structure in question may not be easily accessible, thus precluding the direct assessment of structural integrity. In this paper, we present a gradient-based, partial differential equation (PDE)-constrained optimization approach for solving the inverse problem of interface detection in the context of steady-state dynamics. An objective function is defined that represents the difference between the model predictions of structural response at a set of spatial locations, and the experimentally measured responses. One of the contributions of our work is a novel representation of the design variables using a density field that takes values in the range [0, 1] and raised to an integer exponent that promotes solutions to be near the extrema of the range. The density field is combined with the penalty method for enforcing a zero gap condition and realizing partially bonded surfaces. Furthermore the use of the penalty method with a density field representation leads to objective functions that are continuously differentiable with respect to the unknown parameters, enabling the use of efficient gradient-based optimization algorithms. Numerical examples of delaminated plates are presented to demonstrate the feasibility of the approach.

42 ENGINEERING↗
DOE OSTI2021

Effects of finite element discretization and model simplification on calculations of ductile failure initiation

The finite element method is a scheme to discretize the infinite number of degrees of freedom in continuum-level problems down to a finite number of degrees of freedom. This discretization is done in conjunction with methods that also reduce the field differential equations to sets of algebraic ones that can be solved by arithmetical operations. Therefore, solutions attained by finite element models are approximations to the exact solutions of the field equations.

97 MATHEMATICS AND COMPUTING↗