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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Optimizing multigrid reduction-in-time and Parareal coarse-grid operators for linear advection

Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent partial differential equations (PDEs) in modern high-performance computing environments. While these techniques have been very successful for parabolic equations, it has often been observed that their performance suffers dramatically when applied to advection-dominated problems or purely hyperbolic PDEs using standard rediscretization approaches on coarse grids. In this paper, we apply MGRIT or Parareal to the constant-coefficient linear advection equation, appealing to existing convergence theory to provide insight into the typically nonscalable or even divergent behavior of these solvers for this problem. To overcome these failings, we replace rediscretization on coarse grids with improved coarse-grid operators that are computed by applying optimization techniques to approximately minimize error estimates from the convergence theory. Therefore, one of our main findings is that, in order to obtain fast convergence as for parabolic problems, coarse-grid operators should take into account the behavior of the hyperbolic problem by tracking the characteristic curves. Our approach is tested for schemes of various orders using explicit or implicit Runge–Kutta methods combined with upwind-finite-difference spatial discretizations. In all cases, we obtain scalable convergence in just a handful of iterations, with parallel tests also showing significant speed-ups over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials

Efficient simulation of many-body quantum systems is central to advances in physics, chemistry, and quantum computing, with a key question being whether the simulation cost scales polynomially with the system size. Here, in this work, we analyze many-body quantum systems with Coulomb interactions, which are fundamental to electronic and molecular systems. We prove that Trotterization for such unbounded Hamiltonians achieves a 1/4-order convergence rate, with explicit polynomial dependence on the number of particles. The result holds for all initial wavefunctions in the domain of the Hamiltonian, and the 1/4-order convergence rate is optimal, as previous work has numerically demonstrated that it can be saturated by a specific initial ground state. The main challenges arise from the many-body structure and the singular nature of the Coulomb potential. Our proof strategy differs from prior state-of-the-art Trotter analyses, addressing both difficulties in a unified framework. Our analysis treats the Coulomb potential as an unbounded operator without modification or regularization, and does not rely on spatial discretization, making it compatible with both first- and second-quantized circuit constructions.

Fang, Di [Duke Univ., Durham, NC (United States)]↗
DOE OSTI2020

Nonoverlapping Localized Exponential Time Differencing Methods for Diffusion Problems

In this paper, we propose nonoverlapping localized exponential time differencing (ETD) methods for diffusion problems. The model time-dependent diffusion equation is first reformulated on subdomains based on the nonoverlapping domain decomposition, in which Neumann boundary conditions are imposed on the interfaces for the subdomain problems and Dirichlet type conditions are enforced to form a space-time interface problem. After spatial discretization by standard central finite differences and temporal integration with the first or second order ETD methods, the fully discrete interface problem is obtained. Such an interface problem is then solved iteratively either at each time step or over the whole time interval: the former involves the solution of stationary problems in each subdomain at each iteration while the latter involves the solution of time-dependent subdomain problems at each iteration. For both approaches, we prove that localized ETD solutions conserve mass exactly and converge in time to the exact space semidiscrete solution. Numerical experiments in two dimensions are also presented to illustrate the performance of the proposed methods.

Mass conservation↗
DOE OSTI2024

Griffin: A MOOSE-based reactor physics application for multiphysics simulation of advanced nuclear reactors

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor physics application for multiphysics simulations of advanced reactor designs jointly developed by Idaho National Laboratory and Argonne National Laboratory. This paper summarizes the motivation, significance, architecture, design, and features of Griffin. Griffin offers flexible and extensible features to address the challenges associated with advanced reactor designs. These features range from fundamental particle transport to specific reactor physics tasks. The features cover a wide range including on-the-fly and traditional two-step cross-section generation methods, steady-state and transient transport solvers suitable for both heterogeneous and homogeneous models, high-fidelity depletion where thousands of isotopes can be tracked and low-fidelity depletion characterized by burnup, etc. The most fundamental aspect that sets Griffin apart from other reactor analysis codes is that it is developed based on the MOOSE framework. A modular development approach is strongly enforced, with multiphysics being an essential element considered since the beginning of Griffin’s development. Griffin links various MOOSE physics modules and couples to other MOOSE-based applications and non-MOOSE-based applications for multiphyiscs simulations. Griffin includes three modules: ISOXML for preparing and managing multigroup cross sections, radiation transport for solving the neutron transport equation, and reactor analysis for user-oriented reactor physics analysis functionalities. Griffin uses various finite element methods for spatial discretization, multigroup approximation for energy discretization and discrete ordinates method, spherical harmonics expansion method, and diffusion approximation for streaming direction discretization to solve the neutron transport equation. Griffin’s flexibility is evidenced through Griffin’s various applications to fast reactor, high-temperature reactor, pebble bed reactor, molten salt reactor, and microreactor designs. Griffin development follows the software quality assurance procedure for MOOSE-based applications and with software requirements consistent with the ASME NQA-1 standard. Griffin has been adopted into the reactor analysis system for the U.S. NRC and is in use at U.S. companies, universities and national laboratories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods

We construct a family of embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods of order 2 ≤ p ≤ 4 to be used to obtain numerical solution of spatially discretized hyperbolic PDEs. In this construction, the goals include non-defective property, large stability region, and small error values as defined in Dekker and Verwer (1984) and Kennedy et al. (2000). The new family of embedded pairs offer the ability for strong stability preserving (SSP) methods to adapt by varying the step-size. Through several numerical experiments, we assess the overall effectiveness in terms of work versus precision while also taking into consideration accuracy and stability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

An investigation of the multi-mode Richtmyer-Meshkov instability at a gas/HE interface using Pagosa

Here, in this work, we present a hydrocode Pagosa and explore the Richtmyer-Meshkov Instability (RMI) at an air/high explosive (HE) interface for the first time that is important but has not received much attention yet in the high explosive safety field. Thus, the presented Pagosa can be expected to predict the whole deflagration-to-detonation transition (DDT) process in future. In Pagosa, spatial discretization is implemented on cubic staggered grids by computing different variables at the vertex and the cell center, respectively, a special operator-splitting technique is employed to reduce the computational cost, and an artificial viscosity is added to handle the discontinuous shock waves in our simulations. To quantitatively evaluate the capability of Pagosa to solve these kinds of instabilities, the single mode Rayleigh-Taylor instability (RTI) and the multimode RMI at an air/SF 6 interface are first performed, respectively. The Pagosa results are compared with the related numerical solutions in the existing references and the experimental result. Moreover, a theoretical derivation of growth of RTI is also provided based on our numerical method. Subsequently, we explore the multi-mode RMI at an air/HE interface as well as the effects of several factors using Pagosa. Numerical results show that Pagosa is a powerful toolset to generate the right structures and the amplitude of RTI and RMI at an air/SF 6 interface. The solid HE can be penetrated by a strong shock wave and forms RMI deformations. The RMI at an air/HE interface behaves very different than at an air/SF 6 interface, periodic, decreased oscillation is observed due to material character, and is very sensitive to the initial simulation settings, that is, a tiny change in physical quantities will lead to a remarkable RMI structure, which is also observed in a shock bubble interaction. The findings in this work are significant, and will present a new insight for the high explosive field.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A coupled multipoint stress–multipoint flux mixed finite element method for the Biot system of poroelasticity

In this work, we present a mixed finite element method for a five-field formulation of the Biot system of poroelasticity that reduces to a cell-centered pressure–displacement system on simplicial and quadrilateral grids. A mixed stress–displacement–rotation formulation for elasticity with weak stress symmetry is coupled with a mixed velocity–pressure Darcy formulation. The spatial discretization is based on combining the multipoint stress mixed finite element (MSMFE) method for elasticity and the multipoint flux mixed finite element (MFMFE) method for Darcy flow. It uses the lowest order Brezzi–Douglas–Marini mixed finite element spaces for the poroelastic stress and Darcy velocity, piecewise constant displacement and pressure, and continuous piecewise linear or bilinear rotation. A vertex quadrature rule is applied to the velocity, stress, and stress–rotation bilinear forms, which block-diagonalizes the corresponding matrices and allows for local velocity, stress, and rotation elimination. This leads to a cell-centered positive-definite system for pressure and displacement at each time step. We perform error analysis for the semidiscrete and fully discrete formulations, establishing first order convergence for all variables in their natural norms. The numerical tests confirm the theoretical convergence rates and illustrate the locking-free property of the method.

42 ENGINEERING↗
DOE OSTI2021

A scalable exponential-DG approach for nonlinear conservation laws: With application to Burger and Euler equations

In this work, we propose an Exponential DG framework for partial differential equations. We decompose 7 governing equations into linear and nonlinear parts to which we apply the discontinuous Galerkin 8 (DG) spatial discretization. In particular, we construct the linear part using Jacobian that effectively 9 capture stiff characteristics in the system. The former is integrated analytically, whereas the latter 10 is approximated. This approach i) is stable with a large Courant number (Cr > 1); ii) supports 11 high-order solutions both in time and space; iii) is computationally favorable compared to IMEX 12 DG methods with no preconditioner; iv) becomes comparable to explicit RKDG methods on uniform 13 mesh and beneficial on non-uniform grid for Euler equations; v) is scalable in a modern massively 14 parallel computing architecture due to its explicit nature of exponential time integrators and com15 pact communication stencil of DG method. Numerical results demonstrate the performance of our 16 proposed methods through various examples. We also discuss the stability and convergence analysis 17 for our exponential DG scheme in the context of Burgers equation.

42 ENGINEERING↗
DOE OSTI2022

Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods

Here, a high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial discretization, which enables boundary and interface conditions to be enforced with high-order accuracy on curved embedded geometries. High-order accuracy is achieved via high-order quadrature rules for implicitly-defined domains and boundaries, whilst a cell-merging strategy addresses the presence of small cut cells. The framework is used to discretize the governing equations of elastodynamics, written using a first-order hyperbolic momentum-strain formulation, and an exact Riemann solver is employed to compute the numerical flux at the interface between dissimilar materials with general anisotropic properties. The space-discretized equations are then advanced in time using explicit high-order Runge–Kutta algorithms. Several two- and three-dimensional numerical tests including dynamic adaptive mesh refinement are presented to demonstrate the high-order accuracy and the capability of the method in the elastodynamic analysis of single- and bi-phases solids containing complex geometries.

42 ENGINEERING↗
DOE OSTI2023

Conditional Karhunen–Loève regression model with Basis Adaptation for high-dimensional problems: Uncertainty quantification and inverse modeling

Here, we propose a methodology for improving the accuracy of surrogate models of the observable response of physical systems as a function of the systems’ spatially heterogeneous parameter fields, with applications to uncertainty quantification and parameter estimation in high-dimensional problems. Practitioners often formulate finite-dimensional representations of spatially heterogeneous parameter fields using truncated unconditional Karhunen–Loève expansions (KLEs) for a certain choice of unconditional covariance kernel and construct surrogate models of the observable response with respect to the KLE coefficients. When direct measurements of the parameter fields are available, we propose improving the accuracy of these surrogate models by representing the parameter fields via conditional Karhunen-Loève expansions (CKLEs). CKLEs are constructed by conditioning the covariance kernel of the unconditional expansion on the direct measurements of the parameter field via Gaussian process regression, and then truncating the corresponding KLE. We apply the proposed methodology to constructing surrogate models via the Basis Adaptation (BA) method of the stationary hydraulic head response, measured at spatially discrete observation locations, of a groundwater flow model of the Hanford Site, as a function of the 1000-dimensional representation of the model’s log-transmissivity field. We find that BA surrogate models of the hydraulic head based on CKLEs are more accurate than BA surrogate models based on unconditional expansions for forward uncertainty quantification tasks. Furthermore, we find that inverse estimates of the hydraulic transmissivity field computed using CKLE-based BA surrogate models are more accurate than those computed using unconditional BA surrogate models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

HTR solver: An open-source exascale-oriented task-based multi-GPU high-order code for hypersonic aerothermodynamics

In this study, the open-source Hypersonics Task-based Research (HTR) solver for hypersonic aerothermodynamics is described. The physical formulation of the code includes thermochemical effects induced by high temperatures (vibrational excitation and chemical dissociation). The HTR solver uses high-order TENO-based spatial discretization on structured grids and efficient time integrators for stiff systems, is highly scalable in GPU-based supercomputers as a result of its implementation in the Regent/Legion stack, and is designed for direct numerical simulations of canonical hypersonic flows at high Reynolds numbers. Additionally, the performance of the HTR solver is tested with benchmark cases including inviscid vortex advection, low- and high-speed laminar boundary layers, inviscid one-dimensional compressible flows in shock tubes, supersonic turbulent channel flows, and hypersonic transitional boundary layers of both calorically perfect gases and dissociating air.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Toward more mechanistic representations of biogeochemical processes in river networks: Implementation and demonstration of a multiscale model

A recently introduced multiscale model for representing the effects of small-scale hyporheic-zone biogeochemical processes is extended from the reach scale to river network scales. The model uses advection-dispersion-reaction equations for the channel network and one-dimensional advection-reaction subgrid models for the hyporheic zone. We summarize implementation in the integrated surface/subsurface hydrology modeling system Amanzi-ATS. The extension uses topologically defined meshes to represent stream/river networks and associates a hyporheic subgrid model with each channel grid cell. Biogeochemical reaction modeling capability residing in community software is accessed through an application programming interface. The implementation is verified against independent numerical solutions on a single reach. Mesh convergence studies show that commonly used semi-distributed representations can introduce significant spatial discretization error. Denitrification of farm runoff in a subbasin of the Portage River Basin in Ohio, USA is used to demonstrate the general-purpose reactive transport capability.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

A Full-Induction Magnetohydrodynamics Solver for Liquid Metal Fusion Blankets in Vertex-CFD

Multiphysics modeling of liquid metal fusion blankets, which produce tritium and convert energy of neutrons created via fusion reactions into heat, is crucial for predicting performance, ensuring structural integrity, and optimizing energy production. While traditional blanket modeling of liquid metal flows during normal steady operating conditions commonly employs the inductionless approximation of the magnetohydrodynamics (MHD) equations, transient scenarios, when the plasma-confining magnetic field varies on millisecond time scales, require a full-induction MHD approach that dynamically evolves the magnetic field via the time-dependent induction equation. This paper presents the formulation, implementation, and initial verification of a full-induction MHD solver integrated within the open-source Vertex-CFD framework, which aims to achieve tight multiphysics coupling, a flexible software design enabling easy extension and addition of physics models, and performance portability across computing platforms. The solver utilizes finite element spatial discretization, implicit Runge–Kutta time integration, and an inexact Newton method to solve the resulting discrete nonlinear system, leveraging Trilinos packages for efficient computation. Verification against selected benchmark problems demonstrates accuracy and robustness of the solver. Furthermore, when the solver is applied to an idealized blanket model in 2.5D and full 3D, results obtained with Vertex-CFD are in good agreement with recently published quasi-2D simulations. These findings establish a computational foundation for future simulations of transient MHD phenomena in liquid metal blankets with Vertex-CFD, and open avenues for future extensions and performance optimizations.

Endeve, Eirik [ORNL] (ORCID:0000000312519507)↗
DOE OSTI2021

Tusas: A fully implicit parallel approach for coupled phase-field equations

In this study, we develop a fully-coupled, fully-implicit approach for phase-field modeling of solidification in metals and alloys. Predictive simulation of solidification in pure metals and metal alloys remains a significant challenge in the field of materials science, as microstructure formation during the solidification process plays a critical role in the properties and performance of the solid material. Our simulation approach consists of a finite element spatial discretization of the fully-coupled nonlinear system of partial differential equations at the microscale, which is treated implicitly in time with a preconditioned Jacobian-free Newton-Krylov method. The approach is algorithmically scalable as well as efficient due to an effective preconditioning strategy based on algebraic multigrid and block factorization. We implement this approach in the open-source Tusas framework, which is a general, flexible tool developed in C++ for solving coupled systems of nonlinear partial differential equations. The performance of our approach is analyzed in terms of algorithmic scalability and efficiency, while the computational performance of Tusas is presented in terms of parallel scalability and efficiency on emerging heterogeneous architectures. We demonstrate that modern algorithms, discretizations, and computational science, and heterogeneous hardware provide a robust route for predictive phase-field simulation of microstructure evolution during additive manufacturing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Sylvester-preconditioned adaptive-rank implicit time integrators for advection-diffusion equations with variable coefficients

Here, we consider the adaptive-rank integration of multi-dimensional time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with high-order diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with a projection-based adaptive-rank algorithm structured around two key strategies: (i) constructing dimension-wise subspaces using a novel atypical extended Krylov strategy, and (ii) efficiently solving the basis coefficient matrix with a preconditioned GMRES solver. The low-rank decomposition is performed in 2D using SVD and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format. For d-dimensional problems (here, d = 2 or 3), the computational complexity and memory storage of the approach are found numerically to scale as and $\mathscr{O}(Nr^2) + \mathscr{O} (r^{d+1})$ and $\mathscr{O}(Nr) + \mathscr{O} (r^{d})$, respectively, with the one-dimensional resolution and the maximal rank during the Krylov iteration (which we find to be largely independent of on our numerical examples). We present numerical examples that illustrate the advertised properties of the algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A high accuracy/resolution spectral element/Fourier–Galerkin method for the simulation of shoaling non-linear internal waves and turbulence in long domains with variable bathymetry

A high-order hybrid continuous-Galerkin numerical method, designed for the simulation of non-linear, non -hydrostatic internal waves and turbulence in long computational domains with complex bathymetry, is presented. The spatial discretization in the non-periodic wave-propagating directions, utilizes the nodal spectral element method. Such a high-order element-based discretization allows the highly accurate representation of complex domain geometry along with the flexibility of concentrating resolution in areas of interest. Under the assumption of the normal-to-isobath propagation of non-linear internal waves, a third periodic direction is incorporated via a Fourier-Galerkin discretization. The distinct non-hydrostatic nature of non-linear internal waves and, any instabilities and turbulence therein, necessitates the numerically challenging solution of the pressure Poisson problem. A defining feature of this work is the application of a domain decomposition approach, combined with block-Jacobi/deflation-based preconditioning to the pressure Poisson problem. Such a combined approach is particularly suitable for the long high aspect-ratio complex domains of interest and enables the efficient high-accuracy reproduction of the non-hydrostatic dynamics of non-linear internal waves. Implementation details are also described in the context of the stability of the solver and its parallelization strategy. A series of benchmarks of increasing complexity demonstrate the robustness of the flow solver. The benchmarks culminate with the three-dimensional simulation of a convectively breaking mode-one non-linear internal wave over a realistic South-China-Sea bathymetric transect and background current/stratification profiles.

Deflation↗
DOE OSTI2020

Strategies for simultaneous strengthening and toughening via nanoscopic intracrystalline defects in a biogenic ceramic

While many organisms synthesize robust skeletal composites consisting of spatially discrete organic and mineral (ceramic) phases, the intrinsic mechanical properties of the mineral phases are poorly understood. Using the shell of the marine bivalve Atrina rigida as a model system, and through a combination of multiscale structural and mechanical characterization in conjunction with theoretical and computational modeling, we uncover the underlying mechanical roles of a ubiquitous structural motif in biogenic calcite, their nanoscopic intracrystalline defects. These nanoscopic defects not only suppress the soft yielding of pure calcite through the classical precipitation strengthening mechanism, but also enhance energy dissipation through controlled nano- and micro-fracture, where the defects’ size, geometry, orientation, and distribution facilitate and guide crack initialization and propagation. These nano- and micro-scale cracks are further confined by larger scale intercrystalline organic interfaces, enabling further improved damage tolerance.

36 MATERIALS SCIENCE↗
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↗