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At least 1,261 records · Page 70

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NASA NTRS2015

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

Mazaheri, Alireza↗

NASA NTRS2015

Improved Discrete Ordinate Solutions in the Presence of an Anisotropically Reflecting Lower Boundary: Upgrades of the DISORT Computational Tool

A successor version 3 of DISORT (DISORT3) is presented with important upgrades that improve the accuracy, efficiency, and stability of the algorithm. Compared with version 2 (DISORT2 released in 2000) these upgrades include (a) a redesigned BRDF computation that improves both speed and accuracy, (b) a revised treatment of the single scattering correction, and (c) additional efficiency and stability upgrades for beam sources. In DISORT3 the BRDF computation is improved in the following three ways: (i) the Fourier decomposition is prepared "off-line", thus avoiding the repeated internal computations done in DISORT2; (ii) a large enough number of terms in the Fourier expansion of the BRDF is employed to guarantee accurate values of the expansion coefficients (default is 200 instead of 50 in DISORT2); (iii) in the post processing step the reflection of the direct attenuated beam from the lower boundary is included resulting in a more accurate single scattering correction. These improvements in the treatment of the BRDF have led to improved accuracy and a several-fold increase in speed. In addition, the stability of beam sources has been improved by removing a singularity occurring when the cosine of the incident beam angle is too close to the reciprocal of any of the eigenvalues. The efficiency for beam sources has been further improved from reducing by a factor of 2 (compared to DISORT2) the dimension of the linear system of equations that must be solved to obtain the particular solutions, and by replacing the LINPAK routines used in DISORT2 by LAPACK 3.5 in DISORT3. These beam source stability and efficiency upgrades bring enhanced stability and an additional 5-7% improvement in speed. Numerical results are provided to demonstrate and quantify the improvements in accuracy and efficiency of DISORT3 compared to DISORT2.

Lin, Z.↗

NASA NTRS2014

Identification of Flights for Cost-Efficient Climate Impact Reduction

The aircraft-induced climate impact has drawn attention in recent years. Aviation operations affect the environment mainly through the release of carbon-dioxide, nitrogen-oxides, and by the formation of contrails. Recent research has shown that altering trajectories can reduce aviation environmental cost by reducing Absolute Global Temperature Change Potential, a climate assessment metric that adapts a linear system for modeling the global temperature response to aviation emissions and contrails. However, these methods will increase fuel consumption that leads to higher fuel costs imposed on airlines. The goal of this work is to identify ights for which the environmental cost of climate impact reduction outweighs the increase in operational cost on an individual aircraft basis. Environmental cost is quanti ed using the monetary social cost of carbon. The increase in operational cost is considering cost of additional fuel usage only. For this paper, an algorithm has been developed that modi es the trajectories of ights to evaluate the e ect of environ- mental cost and operational cost of ights in the United States National Airspace System. The algorithm identi es ights for which the environmental cost of climate impact can be reduced and modi es their trajectories to achieve maximum environmental net bene t, which is the di erence between reduction in environmental cost and additional operational cost. The result shows on a selected day, 16% of the ights among eight major airlines, or 2,043 ights, can achieve environmental net bene t using weather forecast data, resulting in net bene t of around $500,000. The result also suggests that the long-haul ights would be better candidates for cost-ecient climate impact reduction than the short haul ights. The algorithm will help to identify the characteristics of ights that are capable of applying cost-ecient climate impact reduction strategy.

climate impact reduction↗

NASA NTRS2014

Evaluating Tradeoffs Between Environmental Impact and Operational Costs for Enroute Air Traffic

The rapid growth of air traffic has drawn attention to aircraft-induced environmental impact. Aviation operations affect the environment mainly through the release of emissions and by the formation of contrails. Recent research has shown that altering aircraft cruise altitudes can reduce aviation environmental impact by reducing Absolute Global Temperature Change Potential, a climate assessment metric that adapts a linear system for modeling the global temperature response to aviation emissions and contrails. However, these methods will increase fuel consumption that leads to higher operational costs imposed on airlines resulting in reluctance to adopt a new routing strategy. This paper evaluates the tradeoff between environmental impact reduction and the corresponding added operational costs for enroute air traffic. The concept of social cost of carbon and the carbon auction price from California's recent cap-and-trade system were used to provide estimates and a methodology to evaluate environmental costs for carbon dioxide emissions and contrail formations. Depending on the specific environmental policy, the strategy is considered favorable when the reduction in environmental costs exceeds the increase in operational costs. The results show how the net environmental bene t varies with different decision-making time horizons, different carbon and fuel costs, and different days. The study provides guidance towards the development of the environmental reduction strategies.

environmental impact↗

NASA NTRS2020

Multigrid Preconditioning for a Space-Time Spectral-Element Discontinuous-Galerkin Solver

In this work we examine a multigrid preconditioning approach in the context of a high- order tensor-product discontinuous-Galerkin spectral-element solver. We couple multigrid ideas together with memory lean and efficient tensor-product preconditioned matrix-free smoothers. Block ILU(0)-preconditioned GMRES smoothers are employed on the coarsest spaces. The performance is evaluated on nonlinear problems arising from unsteady scale- resolving solutions of the Navier-Stokes equations: separated low-Mach unsteady ow over an airfoil from laminar to turbulent ow. A reduction in the number of ne space iterations is observed, which proves the efficiency of the approach in terms of preconditioning the linear systems, however this gain was not reflected in the CPU time. Finally, the preconditioner is successfully applied to problems characterized by stiff source terms such as the set of RANS equations, where the simple tensor product preconditioner fails. Theoretical justification about the findings is reported and future work is outlined.

Franciolini, Matteo↗

NASA NTRSDate not supplied

Impact of Analytic Derivatives on Optimization of N-Impulse Orbit Transfer

Several formulations are possible for the optimization of N-impulse two-body orbit transfers. One formulation that assumes the firstN−1impulses are design variables and implements Lambert’s algorithm in the final leg is here considered. This paper presents a derivation for the analytic expressions of the gradients needed to optimize this formulation. The impact of using these analytic expressions on the optimization computational cost is also presented. A linear system of equations is developed that approximates the Lambert’s problem solution in a way that is suitable for computing the analytic gradients. The derivations of the analytic gradients, as well as numerical case studies for 2-impulse and 3-impulse orbit transfers, are presented. The numerical case studies highlights a significant reduction in the computational cost, measured in terms of the number of function calls.

Ahmed Ellithy↗

NASA NTRSDate not supplied

Efficient Parametric Uncertainty Analysis of an Earth Entry Vehicle Concept Using Least Angle Regression

The objective of this work was to outline and apply an efficient and accurate parametric un-certainty propagation approach to the analysis of convective heating on an Earth entry vehicle concept. The described approach was based on Least Angle Regression used to solve a sparse and underdetermined linear system in the point-collocation non-intrusive polynomial chaos surrogate method. This approach involved an iterative process to computing the non-zero terms of the underlying polynomial chaos model using only enough samples to converge uncertainty interval predictions and Sobol index values based global nonlinear sensitivity estimates. The Earth entry vehicle was analyzed at three points along a representative trajectory for a Mars return mission. 329 sources of uncertainty were identified in the computational fluid dynamics model used to predict the forebody convective heating. These included uncertainty in flow field chemical rates, collision integrals, heats of formation, surface finite rate char model reaction rates, wall roughness height, and the turbulent Schmidt number. Results from this study showed that convective heating uncertainty as high as 50% of the nominal was predicted with only about 50 evaluations of the computational model. This was far fewer than would be required for a sampling-based approach or a full basis polynomial chaos model, which would have required over 50,000 samples. Additionally, results showed that over 90% of the total convective heating uncertainty was due to uncertainty in the N2catalytic rate on the surface, while the remainder of the uncertainty was attributed to the turbulent Schmidt number and the wall roughness uncertainties.

Thomas K West IV↗

NASA NTRSDate not supplied

Implicit Preconditioning for Explicit Multigrid Solvers on Cut-Cell Cartesian Meshes

This work assesses the effectiveness of linearized implicit Euler preconditioning for multigrid solvers using an unpreconditioned, Jacobian-free Newton Krylov method to converge the linear system of equations. Multigrid convergence rates improve to approximately 0.75 across the cases tested including a Mach 2 supersonic wedge, transonic NACA 0012 airfoil, and ONERA M6 wing. While larger Krylov subspaces increase the convergence rate, they also increase the computational cost, such that 4-8 Krylov vectors often offers the fastest turnaround. Further reductions in computational cost are achieved with a sequential hybrid preconditioner that begins with the explicit multigrid solver before transitioning to the preconditioned algorithm later on. In addition, a novel implementation of dual time stepping is extended to include both common BDF methods as well as high-order implicit Runge-Kutta schemes. This particular formulation, which uses A −1 preconditioning, is amenable to matrix-free solvers, and the L-stable methods are especially suited for meshes with arbitrarily small cut-cells. Asymptotic order of convergence is demonstrated for BDF1, BDF2, SDIRK2, and 3rd-order Radau IIA time integration with unsteady 2D vortex simulations.

ARMD↗

DOE OSTI2021

Critical Literature Review of Quantitative Sustainability Assessment Methods for the Circular Economy

The circular economy (CE) has been proposed to be an operational framework for sustainable development that decouples economic growth from resource consumption. The CE ambition is to maximize the retention of value in products, materials, and resources in the economy over time with the help of CE strategies such as selling a service rather than a product, reusing and repairing products or their components, and recycling. The social, economic, and environmental performances of CE strategies need to be measured against their linear counterparts to avoid strategies that increase circularity but have other unintended externalities. However, there is currently no tool specifically designed to compare circular to linear systems and, thus, various methods from different fields have been applied. This session aims at reviewing, contrasting, and critiquing different methods that have been applied to assess the CE until now, along with an up to date state of the science in this field. Methods from the industrial ecology field have most often been applied to study the CE. However, the transition to CE involves both technological improvements as well as social changes. New business models such as collaborative consumption models (e.g., Uber or Airbnb) are examples of the new patterns of production and consumption of the CE, which may be difficult to analyze from a purely industrial ecology perspective. Methods from complexity science and humanities could therefore complement the industrial ecology perspective to extend the scope of the analysis. Such an approach could also answer a longstanding criticism of the CE which, in contrast with sustainability, solely focuses on the environment and the economy. Moreover, the hybridization of two or more existing methods can yield additional capabilities, which may enable the exploration of additional CE-related research questions. The 90 minutes session will have several presentations and conclude with a moderated, interactive panel discussion on how methods from different fields could be combined to harness their relative strengths.

circular economy↗

DOE OSTI2022

Learning Stochastic Parametric Differentiable Predictive Control Policies

We present a scalable unsupervised learning-based method for obtaining explicit control policies for model predictive control problems for stochastic linear systems with additive uncertainties subject to nonlinear chance constraints. We call the proposed method stochastic parametric differentiable predictive control (SP-DPC), which extends the recently proposed deterministic DPC policy optimization algorithm. We formulate the SP-DPC as a deterministic approximation to the stochastic parametric constrained optimal control problem via independent sampling of the problem's parameters and uncertainties. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. In particular, the computed expectation of the problem's value function is backpropagated through the finite-time closed-loop system rollouts parametrized by a known nominal system dynamics model and neural control policy. We also provide theoretical probabilistic guarantees on closed-loop stability and chance constraints satisfaction for systems controlled by learned neural policies. We demonstrate the computational efficiency and scalability of the proposed policy optimization algorithm in three numerical examples, including systems with a large number of states or subject to nonlinear constraints.

Drgona, Jan↗

DOE OSTI2022

Frequency-domain vs time-domain SP{sub N} equations to simulate neutron noise

Inside the reactor core mechanical vibrations of fuel assemblies can produce high fluctuations around a steady-state configuration, known as neutron noise. This effect can cause the triggering of power reduction measures. Classically, diffusion theory has been used to simulate this behavior. However, this equation has some limitations if the materials of the reactor have strong variations. In this work, we use the diffusive time-dependent simplified spherical harmonics equations that improve the previous results without the necessity of using high computational requirements. In particular, two types of analyses with these equations (SP{sub 3}) are made: a frequency-domain and a time-domain. A numerical neutron noise benchmark tests the methodology and compare both formulations. First, numerical results show a good agreement between the amplitudes and phases of the SP3 equations computed with the frequency-domain and time-domain. Therefore, as the frequency-domain computation only requires to solve a linear system, it is a recommendable option for neutron noise computations. Second, one can conclude that for this type of nuclear systems, where the assemblies are not homogenized, the SP{sub 3} approximation results improve considerably the accuracy of the diffusion theory.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

AUTOMATIC GENERATION OF EVENT TREES AND FAULT TREES: A MODEL-BASED APPROACH

In the past few decades, increasing complexity in modern engineering systems has been driven by the integration of a large number of components and by the fact that the system operations involve many disciplines (e.g., thermal-hydraulics, plant operations, cyber-security). Current safety/reliability modeling approaches to such systems are labor intensive, difficult to learn, and rely heavily on simplistic Boolean logic to depict failure propagation and accident progression. While these methods serve well for simple systems (i.e., linear causal systems with limited small inter- and intra-system interactions), their results are difficult to verify when modeling complex systems (typically performed through the extensive use of modeling assumptions). The development of new methods is addressed to meet these challenges through a model-based system engineering (MBSE) lens. Under MBSE philosophy, every aspect of the system (form or function) is represented by a model that completely characterizes its architecture or behavior. MBSE approach greatly improves the management of design, analysis and verification of complex systems. An integration of Dynamic Probabilistic Risk Assessment (DPRA) methods with MBSE models is proposed to perform safety/reliability analyses of engineering systems. In particular, MBSE representation of the system (performed using Systems Modeling Language [SysML]) is coupled with DPRA methods to automatically generate event trees and fault trees.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth

Matrix chain multiplication -- computing $\mathcal{W} = M^{(0)}\cdots M^{(K-1)}$ where $M^{(k)} \in \mathbb{R}^{P_k \times P_{k+1}}$-- arises in scientific computing, machine learning, and graph analysis. Despite the importance of this problem, for chains of distinct matrices, the classical number of operations grows linearly with the chain length $K$ and polynomially in the matrix dimensions. We present \emph{Two-Tower Matrix Multiplication}, a quantum subroutine that encodes the product $\mathcal{W}$ of the $K$ matrices into a quantum state in circuit depth $\mathcal{O}(\max_{k} \mathrm{polylog} (P_k P_{k+1}))$, which is independent of~$K$ within the QRAM-based state-preparation model, whereas the qubit count is $\mathcal{O}\bigl(\sum_{k} \log P_k \bigr)$; the total gate count remains linear in $K$, so the gain is in the circuit depth. The construction interleaves state-preparation operators across two layers; within each layer, all operators act on disjoint registers and execute in parallel. This subroutine can be specialized for the chain-vector case, which computes the product of $K-1$ matrices applied to a vector. We prove the correctness of the subroutine for all $K$ and provide two implementations using the Qiskit and QCLAB frameworks. The subroutine is applicable to any downstream quantum algorithm that operates on a matrix encoded in the statevector, including norm estimation, graph-matrix powers, linear system solving, and quantum machine learning kernels.

Antonioli, Giacomo [Pisa U.] (ORCID:00090000668703↗

NASA NTRS1977

Closed-loop structural stability for linear-quadratic optimal systems

This paper contains an explicit parametrization of a subclass of linear constant gain feedback maps that will not destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multiinput linear-quadratic feedback optimal designs.

Wong, P. K.↗

NASA NTRS1975

Closed-loop structural stability for linear-quadratic optimal systems

This paper contains an explicit parameterization of a subclass of linear constant gain feedback maps that never destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multi-input linear-quadratic feedback optimal designs.

Wong, P. K.↗

NASA NTRS1976

Closed-loop structural stability for linear-quadratic optimal system

This paper contains an explicit parameterization of a subclass of linear constant gain feedback maps that will not destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multi-input linear-quadratic feedback optimal designs.

Wong, P. K.↗

NASA NTRS1976

Closed-loop structural stability for linear-quadratic optimal systems

Wong, P. K.↗

NASA NTRS1984

Linear distributed parameter systems - Closed-loop exponential stability with a finite-dimensional controller

Theoretical results are presented which characterize the linear distributed parameter system (DPS) which can be (exponentially) stabilized by a finite-dimensional controller. This characterization relies on stabilizing subspaces and the solvability of the nonlinear asymmetric Riccati equation. Also considered are connections with the usual model reduction approaches to finite-dimensional DPS controller design.

Balas, M. J.↗