Results for “solve time” — Page 82

NASA NTRS1973

Numerical solution of viscous reacting blunt body flows of a multicomponent mixture.

Hypersonic flow of a chemically nonequilibrium multicomponent mixture past an axisymmetric blunt body is considered on the basis of the exact Navier-Stokes and chemical rate equations. The flowfield, characterized by a sharp shock and a boundary layer, is solved numerically in the region between the shock and the body. The governing equations are first formulated in generalized orthogonal coordinates, and then recast in computational coordinates in which both the shock and the body are two straight lines and one coordinate is stretched to allow higher space resolution near the body. The thermodynamic and transport properties are obtained from the most rigorous theories and reliable data for each component and for the mixture itself. A time-marching second-order finite-difference method is used to solve the equations.

Li, C. P.↗

DOE OSTI2019

A space-time adaptive finite element method with exponential time integrator for the phase field model of pitting corrosion

In this paper we propose a space-time adaptive finite element method for the phase field model of pitting corrosion, which is a parabolic partial differential equation system consisting of a phase variable and a concentration variable. A major challenge in solving this phase field model is that the problem is very stiff, which makes the time step size extremely small for standard temporal discretizations. Another difficulty is that a high spatial resolution is required to capture the steep gradients within the diffused interface, which results in very large number of degrees of freedom for uniform meshes. To overcome the stiffness of this model, we combine the Rosenbrock–Euler exponential integrator with Crank–Nicolson scheme for the temporal discretization. Moreover, by exploiting the fact that the speed of the corroding interface decreases with time, we derive an adaptive time stepping formula. For the spatial approximation, we propose a simple and efficient strategy to generate adaptive meshes that reduces the computational cost significantly. Thus, the proposed method utilizes local adaptivity and mesh refinement for efficient simulation of the corrosive dissolution over long times in heterogeneous media with complex microstructures. We also present an extensive set of numerical experiments in both two and three dimensional spaces to demonstrate efficiency and robustness of the proposed method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1991

Comparison of advanced reduced-basis methods for transient structural analysis

Two advanced reduced-basis methods for linear, transient structural analysis, the force-derivative method and the Lanczos method, are compared to two widely-used modal methods, the mode-displacement method and the mode-acceleration method. Comparisons are made for two linear example problems: a proportionally-damped cantilevered beam subject to a discrete tip load which varies linearly with time, and a discretely-damped multispan beam subject to a uniformly distributed load which varies as a quintic function of time. Results from the methods are compared in terms of the number of basis vectors required to obtain a desired level of accuracy and the associated computational times. The results are problem dependent, and it is shown that for the cantilevered beam problem, the mode-acceleration and force-derivative methods are the most efficient in terms of the number of basis vectors and computational time. The force-derivative method is shown to be the most effective method for solving the multispan beam problem with closely-spaced frequencies. In general, the force-derivative method is shown to produce an accurate solution using very few basis vectors and to require less computational time as compared to the other methods studied.

Mcgowan, David M.↗

NASA NTRS1992

Thermal mathematical modeling of a multicell common pressure vessel nickel-hydrogen battery

A two-dimensional and time-dependent thermal model of a multicell common pressure vessel (CPV) nickel-hydrogen battery was developed. A finite element solver called PDE/Protran was used to solve this model. The model was used to investigate the effects of various design parameters on the temperature profile within the cell. The results were used to help find a design that will yield an acceptable temperature gradient inside a multicell CPV nickel-hydrogen battery. Steady-state and unsteady-state cases with a constant heat generation rate and a time-dependent heat generation rate were solved.

Kim, Junbom↗

DOE OSTI2024

A novel conditional generative model for efficient ensemble forecasts of state variables in large-scale geological carbon storage

Integrating monitoring data to efficiently update reservoir pressure and CO 2 plume distribution forecasts presents a significant challenge in geological carbon storage (GCS) applications. Inverse modeling techniques are commonly used to fuse observational data and refine reservoir model parameters, thereby improving state variable forecasts. However, these techniques often rely on linear or Gaussian assumptions, which can limit their effectiveness in accurately predicting state variables. Moreover, simulating large-scale three-dimensional (3D) GCS problems is computationally expensive, making iterative runs in inverse problems prohibitive. To address these challenges, we propose a conditional generative model utilizing the score-based diffusion method for real-time 3D pressure and saturation field distribution predictions. Our approach involves solving the score function with a mini-batch-based Monte Carlo estimator to generate labeled data. This data is subsequently employed to train a fully connected neural network, enabling it to learn the conditional sample generator within a supervised learning framework. This method enables the rapid generation of a large ensemble of predictions, facilitating comprehensive uncertainty quantification of state variables. Here we applied our method to forecast the dynamic 3D distributions of pressure and saturation fields over a 30-year injection period. The statistical assessment with low root mean square error (RMSE) values demonstrates that our method can accurately predict the spatiotemporal distributions of both pressure and saturation fields. Moreover, the developed conditional generative model shows high computational efficiency by generating 100 ensemble forecasts of 3D state variables in less than 10 min. The consistency between ensemble averages and ground truth values further illustrates the model’s capability to capture state variable dynamics during the CO 2 plume injection process. Notably, the ground truth values fall within the ensemble forecasts, indicating that our uncertainty quantification effectively captures variability and potential noise in the observations. Thus, the developed conditional generative model proves to be a more efficient, accurate, and practical tool for GCS applications, facilitating timely risk analysis and informed decision-making.

58 GEOSCIENCES↗

DOE OSTI2020

Surrogate Model Development of Spent Fuel Degradation for Repository Performance Assessment

In model simulations of deep geologic repositories, UO 2 fuel matrix degradation typically begins as soon as the waste package breaches and groundwater contacts the fuel surface. The initial degradation rate depends on the timing of these events, burnup of the fuel, temperature, and concentrations of dissolved reactants. Estimating the initial rate of degradation is fairly straightforward, but as UO 2 corrosion products precipitate on the fuel surface and the movement of dissolved species between the fuel surface and environment is impeded by the precipitated solids, the rate is more difficult to quantify. At that point, calculating the degradation rate becomes a reactive-transport problem in which a large number of equations must be solved by iteration for a large number of grid cells at each time step. The consequence is that repository simulations, which are already expensive, become much more expensive, especially when hundreds or thousands of waste packages breach. The Fuel Matrix Degradation (FMD) model is the process model of the Spent Fuel and Waste Science and Technology (SFWST) campaign of the US Department of Energy (DOE). It calculates spent fuel degradation rates as a function of radiolysis, redox reactions, electrochemical reactions, alteration layer growth, and diffusion of reactants through the alteration layer. Like other similar fuel degradation process models, it is a complicated model requiring a large number of calculations and iterations at each time step.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1985

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

Gibson, J. S.↗

NASA NTRS1987

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

Gibson, J. S.↗

NASA NTRS2012

LEGION: Lightweight Expandable Group of Independently Operating Nodes

LEGION is a lightweight C-language software library that enables distributed asynchronous data processing with a loosely coupled set of compute nodes. Loosely coupled means that a node can offer itself in service to a larger task at any time and can withdraw itself from service at any time, provided it is not actively engaged in an assignment. The main program, i.e., the one attempting to solve the larger task, does not need to know up front which nodes will be available, how many nodes will be available, or at what times the nodes will be available, which is normally the case in a "volunteer computing" framework. The LEGION software accomplishes its goals by providing message-based, inter-process communication similar to MPI (message passing interface), but without the tight coupling requirements. The software is lightweight and easy to install as it is written in standard C with no exotic library dependencies. LEGION has been demonstrated in a challenging planetary science application in which a machine learning system is used in closed-loop fashion to efficiently explore the input parameter space of a complex numerical simulation. The machine learning system decides which jobs to run through the simulator; then, through LEGION calls, the system farms those jobs out to a collection of compute nodes, retrieves the job results as they become available, and updates a predictive model of how the simulator maps inputs to outputs. The machine learning system decides which new set of jobs would be most informative to run given the results so far; this basic loop is repeated until sufficient insight into the physical system modeled by the simulator is obtained.

Burl, Michael C.↗

NASA NTRS1999

Evolution of Plasmaspheric Refilling: A Comparison of Measurements with an Interhemispheric Plasmasphere Model

The evolution of plasmasphere is closely coupled to processes governing flux tube refilling and transport. In this study we follow this evolution through a series of sequential ion observations made by RIMS on the DE 1 satellite and with the intervening time intervals filled by simulations made with the FLIP model. The FLIP model solves the continuity and momentum equations for the major ion species as well as the energy equations for ions and electrons along entire flux tubes rom 100 k altitude in both hemispheres. Convection has recently been included, driven a dawn-dusk electric field model. Since the observations are necessarily restricted to two local time passes through the plasmasphere per orbit, the FLIP code will follow the observed flux tubes as they corotate and convect through the other local times. The period of DE 1 is such that nearly the same flux tubes are observed every second day or every sixth orbit. The composite of observations and simulations allows assessment of the degree to which the degree to which the FLIP simulations accurately describe the processes which govern flux tube refilling over the two-day period between observations of the same flux tubes.

Comfort, Richard H.↗

DOE OSTI2024

Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. Here, to address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parameterized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.

Neural operator↗

NASA NTRS1981

Data enhancement and analysis through mathematical deconvolution of signals from scientific measuring instruments

Mathematical deconvolution of digitized analog signals from scientific measuring instruments is shown to be a means of extracting important information which is otherwise hidden due to time-constant and other broadening or distortion effects caused by the experiment. Three different approaches to deconvolution and their subsequent application to recorded data from three analytical instruments are considered. To demonstrate the efficacy of deconvolution, the use of these approaches to solve the convolution integral for the gas chromatograph, magnetic mass spectrometer, and the time-of-flight mass spectrometer are described. Other possible applications of these types of numerical treatment of data to yield superior results from analog signals of the physical parameters normally measured in aerospace simulation facilities are suggested and briefly discussed.

Wood, G. M.↗

NASA NTRS1994

Effect of stratification and geometrical spreading on sonic boom rise time

The purpose of our investigation is to determine the effect of unsteadiness (not associated with turbulence) on rise time. The unsteadiness considered here is due to (1) geometrical spreading, (2) stratification, which includes variation in density, temperature, and relative humidity, and (3) N shaped waveform. A very general Burgers equation, which includes all these effects, is the propagation model for our study. The equation is solved by a new computational algorithm in which all the calculations are done in the time domain. The present paper is a progress report in which some of the factors contributing to unsteadiness are studied, namely geometrical spreading and variation in relative humidity. The work of Pierce and Kang, which motivated our study, is first reviewed. We proceed with a discussion of the Burgers equation model and the algorithm for solving the equation. Some comparison tests to establish the validity of the algorithm are presented. The algorithm is then used to determine the distance required for a steady-state shock, on encountering an abrupt change in relative humidity, to reach a new steady state based on the new humidity. It is found that the transition distance for plane shocks of amplitude 70 Pa is about 4 km when the change in relative humidity is 10 percent. Shocks of amplitude 140 Pa require less distance. The effect of spherical and cylindrical spreading is also considered. We demonstrate that a spreading shock wave never reaches steady state and that its rise time will be less than the equivalent steady state shock. Finally we show that an N wave has a slightly shorter rise time than a step shock of the same amplitude.

Cleveland, Robin O.↗

NASA NTRS1992

Fault tolerance of artificial neural networks with applications in critical systems

This paper investigates the fault tolerance characteristics of time continuous recurrent artificial neural networks (ANN) that can be used to solve optimization problems. The principle of operations and performance of these networks are first illustrated by using well-known model problems like the traveling salesman problem and the assignment problem. The ANNs are then subjected to 13 simultaneous 'stuck at 1' or 'stuck at 0' faults for network sizes of up to 900 'neurons'. The effects of these faults is demonstrated and the cause for the observed fault tolerance is discussed. An application is presented in which a network performs a critical task for a real-time distributed processing system by generating new task allocations during the reconfiguration of the system. The performance degradation of the ANN under the presence of faults is investigated by large-scale simulations, and the potential benefits of delegating a critical task to a fault tolerant network are discussed.

Protzel, Peter W.↗

NASA NTRSDate not supplied

Effects of Communication Delay on Human Spaceflight Missions

Missions onboard the International Space Station rely on the real-time availability of a large ground team of system experts to command the vehicle, solve safety-critical problems, and guide the crew during complex operations. Also, in Low Earth Orbit (LEO), supplies can be sent and crews evacuated quite quickly if needed. Future missions Beyond Low Earth Orbit (BLEO) will not have this 24/7, real-time safety net as communication latency increases, resupply difficulty increases, and evacuation opportunities diminish. There are few, if any, terrestrial analogs for human spaceflight missions BLEO that reflect the conditions—including extreme environments, long mission durations, and small crew sizes – that make these missions so high risk. Studies on specific conditions, such as communication delays and asynchronous interactions, have been performed in NASA Earth-based analog missions and have found that communication delays can disrupt ground-crew interactions and adversely impact team performance. However, there are gaps and limitations in studies conducted to date, notably on human spacecraft system failure response and recovery, the impacts of shorter lunar-relevant communication delays on complex operations, and the effectiveness of countermeasures. The work presented here breaks down real anomalies that occurred on ISS and Apollo missions and creates example scenarios fort Lunar Surface and Mars missions to explore the impact of communication delays of varying length on onboard operations and mission outcomes. Our analyses indicate that short communication delays (e.g., seconds to a minute) adversely impact the ability for ground to provide real-time oversight and guidance and to catch quickly emerging problems in time. Longer communication delays (e.g., up to 40 minutes on Mars missions) call for a shift of responsibility for tactical operations from ground to crew; crew must make time-critical decisions independently and respond to time-critical vehicle anomalies to prevent consequences.

human-systems integration↗

NASA NTRSDate not supplied

Effects of Communication Delay on Human Spaceflight Missions

Missions onboard the International Space Station rely on the real-time availability of a large ground team of system experts to command the vehicle, solve safety-critical problems, and guide the crew during complex operations. Also, in Low Earth Orbit (LEO), supplies can be sent and crews evacuated quite quickly if needed. Future missions Beyond Low Earth Orbit (BLEO) will not have this 24/7, real-time safety net as communication latency increases, resupply difficulty increases, and evacuation opportunities diminish. There are few, if any, terrestrial analogs for human spaceflight missions BLEO that reflect the conditions—including extreme environments, long mission durations, and small crew sizes – that make these missions so high risk. Studies on specific conditions, such as communication delays and asynchronous interactions, have been performed in NASA Earth-based analog missions and have found that communication delays can disrupt ground-crew interactions and adversely impact team performance. However, there are gaps and limitations in studies conducted to date, notably on human spacecraft system failure response and recovery, the impacts of shorter lunar-relevant communication delays on complex operations, and the effectiveness of countermeasures. The work presented here breaks down real anomalies that occurred on ISS and Apollo missions and creates example scenarios fort Lunar Surface and Mars missions to explore the impact of communication delays of varying length on onboard operations and mission outcomes. Our analyses indicate that short communication delays (e.g., seconds to a minute) adversely impact the ability for ground to provide real-time oversight and guidance and to catch quickly emerging problems in time. Longer communication delays (e.g., up to 40 minutes on Mars missions) call for a shift of responsibility for tactical operations from ground to crew; crew must make time-critical decisions independently and respond to time-critical vehicle anomalies to prevent consequences.

human-systems integration↗

NASA NTRS1992

Mapping unstructured grid computations to massively parallel computers

Investigated here is this mapping problem: assign the tasks of a parallel program to the processors of a parallel computer such that the execution time is minimized. First, a taxonomy of objective functions and heuristics used to solve the mapping problem is presented. Next, we develop a highly parallel heuristic mapping algorithm, called Cyclic Pairwise Exchange (CPE), and discuss its place in the taxonomy. CPE uses local pairwise exchanges of processor assignments to iteratively improve an initial mapping. A variety of initial mapping schemes are tested and recursive spectral bipartitioning (RSB) followed by CPE is shown to result in the best mappings. For the test cases studied here, problems arising in computational fluid dynamics and structural mechanics on unstructured triangular and tetrahedral meshes, RSB and CPE outperform methods based on simulated annealing. Much less time is required to do the mapping and the results obtained are better. Compared with random and naive mappings, RSB and CPE reduce the communication time two fold for the test problems used. Finally, we use CPE in two applications on a CM-2. The first application is a data parallel mesh-vertex upwind finite volume scheme for solving the Euler equations on 2-D triangular unstructured meshes. CPE is used to map grid points to processors. The performance of this code is compared with a similar code on a Cray-YMP and an Intel iPSC/860. The second application is parallel sparse matrix-vector multiplication used in the iterative solution of large sparse linear systems of equations. We map rows of the matrix to processors and use an inner-product based matrix-vector multiplication. We demonstrate that this method is an order of magnitude faster than methods based on scan operations for our test cases.

Hammond, Steven Warren↗

NASA NTRS1972

On the numerical solution of two-dimensional, laminar compressible flows with imbedded shock waves.

The complete, time-dependent Navier-Stokes equations are expressed in conservation form and solved by employing an explicit finite difference numerical technique which incorporates artificial viscosity terms of the form first suggested by Rusanov for numerical stability in the vicinity of shock waves. Surface boundary conditions are developed in a consistent and unique manner through the use of a physically oriented extrapolation procedure. From numerical experimentation an extended range for the explicit stability parameter is established. Also employed is an additional convergence parameter which relates incremental spatial steps. Convergence of the transient solution to a steady state flow was obtained after 400 to 500 time steps.

Goodrich, W. D.↗