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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Snap-Through Buckling Pressure Prediction of Spherical Caps: A Comparison of Analytical, Implicit, and Explicit Methods

Snap-through buckling is a nonlinear and dynamic instability that occurs in curved shell structures such as domes, pressure vessels, and aerospace panels. Unlike classical linear buckling, it involves a sudden transition between equilibrium states caused by geometric nonlinearity and rapid strain-to-kinetic energy conversion (Timoshenko & Gere, 1961; Budiansky & Roth, 1962). This study investigates the snap-through behavior of thin spherical caps using both implicit and explicit solvers in ANSYS Workbench. While implicit analysis accurately captures quasi-static response, it struggles with convergence near instability. In contrast, explicit LS-DYNA simulation naturally handles the nonlinear dynamic event with minimal tuning and computational cost.

42 ENGINEERING↗
DOE OSTI2024

A Fast Algebraic Multigrid Solver and Accurate Discretization for Highly Anisotropic Heat Flux I: Open Field Lines

We present a novel solver technique for the anisotropic heat flux equation, aimed at the high level of anisotropy seen in magnetic confinement fusion plasmas. Such problems pose two major challenges: (i) discretization accuracy and (ii) efficient implicit linear solvers. We simultaneously address each of these challenges by constructing a new finite element discretization with excellent accuracy properties, tailored to a novel solver approach based on algebraic multigrid (AMG) methods designed for advective operators. We pose the problem in a mixed formulation, introducing the directional temperature gradient as an auxiliary variable. The temperature and auxiliary fields are discretized in a scalar discontinuous Galerkin space with upwinding principles used for discretizations of advection. We demonstrate the proposed discretization’s superior accuracy over other discretizations of anisotropic heat flux, achieving error 1000x smaller for anisotropy ratio of 10 9 , for closed field lines. The block matrix system is reordered and solved in an approach where the two advection operators are inverted using AMG solvers based on approximate ideal restriction, which is particularly efficient for upwind discontinuous Galerkin discretizations of advection. To ensure that the advection operators are nonsingular, in this paper we restrict ourselves to considering open (acyclic) magnetic field lines for the linear solvers. We demonstrate fast convergence of the proposed iterative solver in highly anisotropic regimes where other diffusion-based AMG methods fail.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Evaluation of the accuracy of an offline seasonally-varying matrix transport model for simulating ideal age

Newton-Krylov solvers for ocean tracers have the potential to greatly decrease the computational costs of spinning up deep-ocean tracers, which can take several thousand model years to reach equilibrium with surface processes. One version of the algorithm uses offline tracer transport matrices to simulate an annual cycle of tracer concentrations and applies Newton’s method to find concentrations that are periodic in time. Here we present the impact of time-averaging the transport matrices on the equilibrium values of an ideal-age tracer. We compared annually-averaged, monthly-averaged, and 5-day-averaged transport matrices to an online simulation using the ocean component of the Community Earth System Model (CESM) with a nominal horizontal resolution of 1° × 1° and 60 vertical levels. We found that increasing the time resolution of the offline transport model reduced a low age bias from 12% for the annually-averaged transport matrices, to 4% for the monthly-averaged transport matrices, and to less than 2% for the transport matrices constructed from 5-day averages. The largest differences were in areas with strong seasonal changes in the circulation, such as the Northern Indian Ocean. As a result, for many applications the relatively small bias obtained using the offline model makes the offline approach attractive because it uses significantly less computer resources and is simpler to set up and run.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

A second-order semi-implicit δf method for hybrid simulation

A second-order accurate semi-implicit Lorentz force ions, fluid electrons δf hybrid model has been developed using a “current closure” scheme. The model assumes quasi-neutrality and is fully electromagnetic. The implicit field solver improves numerical accuracy by separating the equilibrium terms in the presence of small perturbations. The equilibrium part of the generalized Ohm’s law is solved by direct matrix inversion along the direction of gradients for every Fourier mode in the other two directions, while the nonlinear part is solved iteratively. The simulation has been benchmarked on Alfvén waves, ion sound waves and whistler waves against analytical dispersion relation in a slab. In particular, the first-order and second-order schemes are compared by studying the numerical damping of whistler waves. The full evolution of the resistive tearing mode using the Harris sheet equilibrium is also investigated. The linear growth rate and mode structure are compared with the resistive MHD theory. Important tearing mode nonlinear phenomena such as the Rutherford regime and saturation are demonstrated. We also presented systematic study of Rutherford growth rates and saturation island width, which is consistent with previous MHD studies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach

Here, a hybrid, design-order sliding mesh algorithm, which uses a control volume finite element method (CVFEM), in conjunction with a discontinuous Galerkin (DG) approach at non-conformal interfaces, is outlined in the context of a low-Mach fluid dynamics equation set. This novel hybrid DG approach is also demonstrated to be compatible with a classic edge-based vertex centered (EBVC) scheme. For the CVFEM, element polynomial, P , promotion is used to extend the low-order P = 1 CVFEM method to higher-order, i.e., P = 2. An equal-order low-Mach pressure-stabilized methodology, with emphasis on the non-conformal interface boundary condition, is presented. A fully implicit matrix solver approach that accounts for the full stencil connectivity across the non-conformal interface is employed. A complete suite of formal verification studies using the method of manufactured solutions (MMS) is performed to verify the order of accuracy of the underlying methodology. The chosen suite of analytical verification cases range from a simple steady diffusion system to a traveling viscous vortex across mixed-order non-conformal interfaces. Results from all verification studies demonstrate either second- or third-order spatial accuracy and, for transient solutions, second-order temporal accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Physics constrained learning for data-driven inverse modeling from sparse observations

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that measures the discrepancy between predictions and observations in some chosen norm. This loss function often includes the PDE constraints as a penalty term when only sparse observations are available. As a result, the PDE is only satisfied approximately by the solution. However, the penalty term typically slows down the convergence of the optimizer for stiff problems. We present a new approach that trains the embedded DNNs while numerically satisfying the PDE constraints. We develop an algorithm that enables differentiating both explicit and implicit numerical solvers in reverse-mode automatic differentiation. This allows the gradients of the DNNs and the PDE solvers to be computed in a unified framework. We demonstrate that our approach enjoys faster convergence and better stability in relatively stiff problems compared to the penalty method. Furthermore, our approach allows for the potential to solve and accelerate a wide range of data-driven inverse modeling, where the physical constraints are described by PDEs and need to be satisfied accurately.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Kinetic particle simulation of discharge and wall erosion of a Hall thruster

The primary lifetime limiting factor of Hall thrusters is the wall erosion caused by the ion induced sputtering, which is predominated by dielectric wall sheath and pre-sheath. However, so far only fluid or hybrid simulation models were applied to wall erosion and lifetime studies in which this non-quasi-neutral and non-equilibrium area cannot be treated directly. Thus, in this study, a 2D fully kinetic particle-in-cell model was presented for Hall thruster discharge and lifetime simulation. Because the fully kinetic lifetime simulation was yet to be achieved so far due to the high computational cost, the semi-implicit field solver and the technique of mass ratio manipulation was employed to accelerate the computation. However, other artificial manipulations like permittivity or geometry scaling were not used in order to avoid unrecoverable change of physics. Additionally, a new physics recovering model for the mass ratio was presented for better preservation of electron mobility at the weakly magnetically confined plasma region. The validity of the presented model was examined by various parametric studies, and the thrust performance and wall erosion rate of a laboratory model magnetic layer type Hall thruster was modeled for different operation conditions. The simulation results successfully reproduced the measurement results with typically less than 10% discrepancy without tuning any numerical parameters. It is also shown that the computational cost was reduced to the level that the Hall thruster fully kinetic lifetime simulation is feasible.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

photon-plasma: A modern high-order particle-in-cell code

We present the photon-plasma code, a modern high order charge conserving particle-in-cell code for simulating relativistic plasmas. The code is using a high order implicit field solver and a novel high order charge conserving interpolation scheme for particle-to-cell interpolation and charge deposition. It includes powerful diagnostics tools with on-the-fly particle tracking, synthetic spectra integration, 2D volume slicing, and a new method to correctly account for radiative cooling in the simulations. A robust technique for imposing (time-dependent) particle and field fluxes on the boundaries is also presented. Using a hybrid OpenMP and MPI approach, the code scales efficiently from 8 to more than 250.000 cores with almost linear weak scaling on a range of architectures. The code is tested with the classical benchmarks particle heating, cold beam instability, and two-stream instability. We also present particle-in-cell simulations of the Kelvin-Helmholtz instability, and new results on radiative collisionless shocks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Numerical simulations of optically thick accretion onto a black hole. II. Rotating flow

In this paper, we report on recent upgrades to our general relativistic radiation magnetohydrodynamics code, Cosmos++, including the development of a new primitive inversion scheme and a hybrid implicit-explicit solver with a more general M {sub 1} closure relation for the radiation equations. The new hybrid solver helps stabilize the treatment of the radiation source terms, while the new closure allows for a much broader range of optical depths to be considered. These changes allow us to expand by orders of magnitude the range of temperatures, opacities, and mass accretion rates, and move a step closer toward our goal of performing global simulations of radiation-pressure-dominated black hole accretion disks. In this work, we test and validate the new method against an array of problems. We also demonstrate its ability to handle super-Eddington, quasi-spherical accretion. Even with just a single proof-of-principle simulation, we already see tantalizing hints of the interesting phenomenology associated with the coupling of radiation and gas in super-Eddington accretion flows.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

PVRD-FASP: A Unified Solver for Modeling Carrier and Defect Transport in Photovoltaic Devices

In our paper, we present a simulator for modeling transport of charge carriers and electrically active defect centers in solar cells by treating them on an equal footing, which allows us to address metastability and reliability issues. The exact nonlinear differential equations set solved by our solver is presented. The formulation of such differential equations, namely the continuity equations, drift-diffusion equation, and Poisson equation, for studying charge and defect transport is explained. The parameters needed for forming the differential equations are taken from first principle calculations. The solver is verified with test cases built on PN heterojunctions, Cu diffusion in single crystal CdTe and comparing Silvaco simulations with our numerical results.

14 SOLAR ENERGY↗
DOE OSTI2017

Level set methods for detonation shock dynamics using high-order finite elements

Level set methods are a popular approach to modeling evolving interfaces. We present a level set ad- vection solver in two and three dimensions using the discontinuous Galerkin method with high-order nite elements. During evolution, the level set function is reinitialized to a signed distance function to maintain ac- curacy. Our approach leads to stable front propagation and convergence on high-order, curved, unstructured meshes. The ability of the solver to implicitly track moving fronts lends itself to a number of applications; in particular, we highlight applications to high-explosive (HE) burn and detonation shock dynamics (DSD). We provide results for two- and three-dimensional benchmark problems as well as applications to DSD.

finite element methods↗
DOE OSTI2017

Aeroelastic oscillations of a cantilever with structural nonlinearities: theory and numerical simulation.

Our study details the derivation of the nonlinear equations of motion for the axial, biaxial bending and torsional vibrations of an aeroelastic cantilever undergoing rigid body (pitch) rotation at the base. The primary attenstion is focussed on the geometric nonlinearities of the system, whereby the aeroelastic load is modeled by the theory of linear quasisteady aerodynamics. This modelling effort is intended to mimic the wind-tunnel experimental setup at the Royal Military College of Canada. While the derivation closely follows the work of Hodges and Dowell [1] for rotor blades, this aeroelastic system contains new inertial terms which stem from the fundamentally different kinematics than those exhibited by helicopter or wind turbine blades. Using the Hamilton’s principle, a set of coupled nonlinear partial differential equations (PDEs) and an ordinary differential equation (ODE) are derived which describes the coupled axial-bending-bending-torsion-pitch motion of the aeroelastic cantilever with the pitch rotation. The finite dimensional approximation of the coupled system of PDEs are obtained using the Galerkin projection, leading to a coupled system of ODEs. Subsequently, these nonlinear ODEs are solved numerically using the built-in MATLAB implicit ODE solver and the associated numerical results are compared with those obtained using Houbolt’s method. It is demonstrated that the system undergoes coalescence flutter, leading to a limit cycle oscillation (LCO) due to coupling between the rigid body pitching mode and teh flexible mode arising from the flapwise bending motion.

42 ENGINEERING↗
DOE OSTI2018

High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit–explicit Runge–Kutta schemes

This work introduces a general framework for constructing high-order, linearly stable, partitioned solvers for multiphysics problems from a monolithic implicit–explicit Runge–Kutta (IMEX-RK) discretization of the semi-discrete equations. The generic multiphysics problem is modeled as a system of n systems of partial differential equations where the i th subsystem is coupled to the other subsystems through a coupling term that can depend on the state of all the other subsystems. This coupled system of partial differential equations reduces to a coupled system of ordinary differential equations via the method of lines where an appropriate spatial discretization is applied to each subsystem. The coupled system of ordinary differential equations is taken as a monolithic system and discretized using an IMEX-RK discretization with a specific implicit–explicit decomposition that introduces the concept of a predictor for the coupling term. We propose four coupling predictors that enable the monolithic system to be solved in a partitioned manner, i.e., subsystem-by-subsystem, and preserve the IMEX-RK structure and therefore the design order of accuracy of the monolithic scheme. The four partitioned solvers that result from these predictors are high-order accurate, allow for maximum re-use of existing single-physics software, and two of the four solvers allow the subsystems to be solved in parallel at a given stage and time step. We also analyze the stability of a coupled, linear model problem with a specific coupling structure and show that one of the partitioned solvers achieves unconditional linear stability for this problem, while the others are unconditionally stable only for certain values of the coupling strength. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems including a simple linear system of ODEs, advection–diffusion–reaction systems, fluid–structure interaction problems, and particle-laden flows, where we verify the design order of the IMEX schemes and study various stability properties.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Implicit, manifold-preserving numerical representations and solvers for multiscale kinetic simulations of plasmas

Presentation Conclusions: We have derived manifold-preserving algorithms for kinetic plasma simulation; Collisionless (PIC): we have solved the 40-year-old algorithmic challenge of developing accurate implicit PIC algorithms; Collisional (VFP): we have demonstrated a truly multiscale algorithm that has enabled routine simulation of ICF spherical capsule implosions with a few hundred cores for a couple of days.; In both cases: Strict conservation properties have been shown to be critical for long-term accuracy.; Significant algorithmic acceleration has been achieved by using nested asymptotic models.; We have seen similar benefits in other applications

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

A High-Order Low-Order Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer

In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S 2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used to compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.

97 MATHEMATICS AND COMPUTING↗