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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 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

On the prescription of boundary conditions for nonlocal Poisson's and peridynamics models

We introduce a technique to automatically convert local boundary conditions into nonlocal volume constraints for nonlocal Poisson’s and peridynamic models. The proposed strategy is based on the approximation of nonlocal Dirichlet or Neumann data with a local solution obtained by using available boundary, local data. The corresponding nonlocal solution converges quadratically to the local solution as the nonlocal horizon vanishes, making the proposed technique asymptotically compatible. The proposed conversion method does not have any geometry or dimensionality constraints and its computational cost is negligible, compared to the numerical solution of the nonlocal equation. The consistency of the method and its quadratic convergence with respect to the horizon is illustrated by several two-dimensional numerical experiments conducted by meshfree discretization for both the Poisson’s problem and the linear peridynamic solid model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Asymptotic Expansion of the Impedance Per Unit Length for Rectangular Conductors

An iteration method is introduced to obtain the asymptotic form of the impedance per unit length of a rectangular conductor when the half side lengths are large compared to the skin depth. The first terms of the asymptotic expansion are extracted in closed form. The manner in which the corner corrections fit into the expansion are illustrated. The asymptotic results are compared to a numerical solution in the square limit. The odd corner correction for a right angle edge is also discussed.

42 ENGINEERING↗
DOE OSTI2022

Augmented Gaussian random field: Theory and computation

We propose the novel augmented Gaussian random field (AGRF), which is a universal framework incorporating the data of observable and derivatives of any order. Rigorous theory is established. We prove that under certain conditions, the observable and its derivatives of any order are governed by a single Gaussian random field, which is the aforementioned AGRF. As a corollary, the statement "the derivative of a Gaussian process remains a Gaussian process" is validated, since the derivative is represented by a part of the AGRF. Moreover, a computational method corresponding to the universal AGRF framework is constructed. Both noiseless and noisy scenarios are considered. Formulas of the posterior distributions are deduced in a nice closed form. A significant advantage of our computational method is that the universal AGRF framework provides a natural way to incorporate arbitrary order derivatives and deal with missing data. We use four numerical examples to demonstrate the effectiveness of the computational method. The numerical examples are composite function, damped harmonic oscillator, Korteweg-De Vries equation, and Burgers' equation.

Mathematics↗
DOE OSTI2022

Numerical Analysis of Liquid Metal MHD Flow and Heat Transfer for Open-Surface Li Divertor in FNSF

Within the ongoing U.S.-based program on the development of liquid metal plasma-facing components, numerical simulations and analyses are performed to address the feasibility of the open-surface Li divertor. In the previous scoping studies (Smolentsev, 2021), heat-removal capabilities of the divertor were assessed using a simplified flow model for a slug-type velocity profile and constant flow thickness. Here, new analyses take into account forces acting on the flowing Li layer. Three reduced-order mathematical models are applied under the conditions of the U.S. Fusion Nuclear Science Facility (FNSF) to access magnetohydrodynamic (MHD) flow development effects, velocity distribution, and surface waves: 1) fully developed MHD flow; 2) quasi-2-D developing MHD flow; and 3) multiphase MHD flow. The obtained results for MHD flows and the surface heat flux computed with the plasma code scrape-off layer plasma simulation for ITER (SOLPS-ITER) are then used as input data to compute the temperature distribution in the divertor by solving the convection–diffusion energy equation.

Smolentsev, Sergey↗
DOE OSTI2020

HPC4Mobilty w/ UCB

The purpose of this project is to examine the energy impact of urban-scale traffic for the Los Angeles Basin by developing and implementing a scalable traffic assignment model. An energy optimization function will be posed and when integrated into the optimization code for travel assignment it can be mathematically proven to converge. The energy optimization function can then be compared to the typical travel time optimization that is traditionally used in traffic assignment models. The analysis will begin with static traffic assignment models with the routing for all origin and destinations computed in parallel on high performance computing facilities. Convergence of the numerical methods rely on the solution of convex programs (or extensions of these). This step will mostly consist of demonstrating the ability to parallelize the Frank Wolfe algorithm on various platforms. This work will contribute to LBNL’s efforts to develop new processes, analytical tools, program designs, and business models to advance the state of the art in next-generation sustainable transportation solutions.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

BBN-simple: How to bake a universe-sized cake

Big Bang Nucleosynthesis (BBN), the process of creation of lightest elements in the early universe, is a highly robust, precise, and ultimately successful theory that forms one of the three pillars of the standard hot-Big-Bang cosmological model. Existing theoretical treatments of BBN and the associated computer codes are accurate and flexible, but are typically highly technical and opaque, and not suitable for pedagogical understanding of the BBN. Here we present BBN-simple - a from-scratch numerical calculation of the lightest element abundances pitched at an advanced undergraduate or beginning graduate level. We review the physics of the early universe relevant for BBN, provide information about the reaction rates, and discuss computational-mathematics background that is essential in setting up a BBN calculation. Here, we calculate the abundances of the principal nuclear species in a standard cosmological model, and find a reasonably good agreement with public precision-level BBN codes.

Big bang nucleosynthesis↗
DOE OSTI2022

Theory of In-Cloud Activation of Aerosols and Microphysical Quasi-Equilibrium in a Deep Updraft

The microphysical quasi-equilibrium in an ascending adiabatic parcel is elucidated by an analytical theory in 0D with drastic simplifications. The theory predicts how in-cloud activation is most likely to be triggered by the onset of precipitation during sufficient ascent, with the ascent only needing to approach almost twice the cloud-base updraft speed aloft. The precipitation and cloud condensate mass fields are coupled in a closed system in a simplified version of the model. The initial state of no precipitation is unstable with respect to a perturbation. In the 2D phase space of both mass fields, there is a neutral line. Unstable growth of precipitation mass drives the system to cross the line into a regime of stability. An attractor is then approached consisting of precipitation mass balanced by accretion of cloud mass and fallout. The cloud-particle number concentration also approaches a stable equilibrium governed by the balance between in-cloud activation aloft from the inexorably increasing supersaturation during vertical acceleration and accretion of cloud droplets by precipitation. Dimensionless numbers characterizing the microphysical equilibria and their stability are derived mathematically, including a condensation–precipitation efficiency and an in-cloud activation efficiency. The theory explains common observations of the orders of magnitude of liquid water content in convective and stratiform clouds. Finally, sensitivity tests of the numerically integrated theoretical equations are documented with respect to variations in cloud condensation nucleus (CCN) aerosols and updraft speed. In conclusion, it is shown that this theory of in-cloud activation, with an increasing supersaturation during ascent, applies to both ice-only and liquid-only cloud.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Random Knotting in Fractal Ring Polymers

Many ring polymer systems of physical and biological interest exhibit both pronounced topological effects and nontrivial self-similarity, but the relationship between these two phenomena has not yet been clearly established. Here, we use theory and simulation to formulate such a connection by studying a fundamental topological property—the random knotting probability—for ring polymers with varying fractal dimension, d f . Using straightforward scaling arguments, we generalize a classic mathematical result, showing that the probability of a trivial knot decays exponentially with chain size, N, for all fractal dimensions: P 0 (N) ∝ exp(–N/N 0 ). However, no such simple considerations can account for the dependence of the knotting length, N 0 , on d f , necessitating a more involved analytical calculation. This analysis reveals a complicated double-exponential dependence, which is well supported by numerical data. By contrast, functional forms typical of simple scaling theories fail to adequately describe the observations. These findings are equally valid for two-dimensional ring polymer systems, where “knotting” is defined as the intersection of any two segments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Convex Programs for Minimal-Area Problems

The minimal-area problem that defines string diagrams in closed string field theory asks for the metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2π. This is an extremal length problem in conformal geometry as well as a problem in systolic geometry. Here, we consider the analogous minimal-area problem for homology classes of curves and, with the aid of calibrations and the max flow-min cut theorem, formulate it as a local convex program. We derive an equivalent dual program involving maximization of a concave functional. These two programs give new insights into the form of the minimal-area metric and are amenable to numerical solution. We explain how the homology problem can be modified to provide the solution to the original homotopy problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Stability Analysis of Interface Conditions for Ocean-Atmosphere Coupling

In this paper, we analyze the stability of different coupling strategies for multidomain PDEs that arise in general circulation models used in climate simulations. We focus on fully coupled ocean–atmosphere models that are needed to represent and understand the complicated interactions of these two systems, becoming increasingly important in climate change assessment in recent years. Numerical stability issues typically arise because of different time-stepping strategies applied to the coupled PDE system. In particular, the contributing factors include using large time steps, lack of accurate interface flux, and single-iteration coupling. We investigate the stability of the coupled ocean–atmosphere models for various interface conditions such as the Dirichlet–Neumann condition and the bulk interface condition, which is unique to climate modeling. By analyzing a simplified model, we demonstrate here how the parameterization of the bulk condition and other numerical and physical parameters affect the coupling stability and establish stability conditions for different coupling strategies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Optimization-based, property-preserving finite element methods for scalar advection equations and their connection to Algebraic Flux Correction

In this paper, we continue our efforts to exploit optimization and control ideas as a common foundation for the development of property-preserving numerical methods. Here we focus on a class of scalar advection equations whose solutions have fixed mass in a given Eulerian region and constant bounds in any Lagrangian volume. Our approach separates discretization of the equations from the preservation of their solution properties by treating the latter as optimization constraints. This relieves the discretization process from having to comply with additional restrictions and makes stability and accuracy the sole considerations in its design. A property-preserving solution is then sought as a state that minimizes the distance to an optimally accurate but not property-preserving target solution computed by the scheme, subject to constraints enforcing discrete proxies of the desired properties. Furthermore, we consider two such formulations in which the optimization variables are given by the nodal solution values and suitably defined nodal fluxes, respectively. A key result of the paper reveals that a standard Algebraic Flux Correction (AFC) scheme is a modified version of the second formulation obtained by shrinking its feasible set to a hypercube. In conclusion, we present numerical studies illustrating the optimization-based formulations and comparing them with AFC

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques

Here, we study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in terms of number of random inputs and their probability distributions, which can be either known in closed form or provided through samples. We derive novel multifidelity Monte Carlo estimators which rely on a shared subspace between the high-fidelity and low-fidelity models where the parameters follow the same probability distribution, i.e., a standard Gaussian. We build the shared space employing normalizing flows to map different probability distributions into a common one, together with linear and nonlinear dimensionality reduction techniques, active subspaces and autoencoders, respectively, which capture the subspaces where the models vary the most. We then compose the existing low-fidelity model with these transformations and construct modified models with an increased correlation with the high-fidelity model, which therefore yield multifidelity estimators with reduced variance. A series of numerical experiments illustrate the properties and advantages of our approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations

Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a semi-discrete entropy inequality under appropriate boundary conditions. Here in this work, we describe a discretization of viscous terms in the compressible Navier-Stokes equations which enables a simple and explicit imposition of entropy stable no-slip and reflective (symmetry) wall boundary conditions for discontinuous Galerkin (DG) discretizations. Specifically, we derive methods for imposing adiabatic no-slip and reflective (symmetry) boundary conditions for modal entropy stable DG formulations which preserve a semi-discrete entropy inequality. Numerical results confirm the robustness and accuracy of the proposed approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A mass conservative, well balanced, tangency preserving and energy decaying method for the shallow water equations on a sphere

Here a fully discrete surface finite element method is proposed for solving the viscous shallow water equations in a bounded Lipschitz domain on the sphere based on a general triangular mesh. The method consists of a modified Crank–Nicolson method in time and a Galerkin surface finite element method in space for the fluid thickness H and the fluid velocity u. A finite element space tangential to the sphere at all finite element nodes is proposed to approximate the fluid velocity u. The proposed method has second-order accuracy in time and first-order accuracy in space, and preserves mass conservation, well balancedness, tangency of velocity to the sphere, and energy decay. Numerical experiments are presented to illustrate the accuracy of the proposed method and the preservation of the physical properties, including mass conservation, well balancedness, and energy decay. A numerical simulation of ocean mesoscale activity on a circular basin with a continental shelf is provided.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Data-driven models of nonautonomous systems

Nonautonomous dynamical systems are characterized by time-dependent inputs, which complicates the discovery of predictive models describing the spatiotemporal evolution of the state variables of quantities of interest from their temporal snapshots. When dynamic mode decomposition (DMD) is used to infer a linear model, this difficulty manifests itself in the need to approximate the time-dependent Koopman operators. Our approach is to approximate the original nonautonomous system with a modified system derived via a local parameterization of the time-dependent inputs. The modified system comprises a sequence of local parametric systems, which are subsequently approximated by a parametric surrogate model using the DRIPS (dimension reduction and interpolation in parameter space) framework. The offline step of DRIPS relies on DMD to build a linear surrogate model, endowed with reduced-order bases for the observables mapped from training data. The online step interpolates on suitable manifolds to construct a sequence of iterative parametric surrogate models; the target/test parameter points on these manifolds are specified by a local parameterization of the test time-dependent inputs. Here, we use numerical experimentation to demonstrate the robustness of our method and compare its performance with that of deep neural networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Necessary and sufficient conditions for quadratic stabilizability of switched systems on non-uniform time domains

In this paper, we consider the quadratic stabilizability via state feedback for a particular class of switched systems that evolve on a non-uniform time domain by introducing time scales theory. The system considered switches between a continuous-time subsystem with variable lengths and a discrete-time subsystem with variable discrete step sizes. Necessary and sufficient conditions are derived to guarantee the quadratic stability of this class of switched systems via a switching state feedback law based on the existence of a common positive definite matrix satisfying the quadratic stabilizability condition by considering that the two subsystems are unstable. By state feedback, we mean that the switching among subsystems depends on the system states. Current results for this kind of state switching feedback control are derived only for switched systems evolving on a continuous time domain or a discrete time domain with fixed step’s size. These results are not applicable for the particular class of switched systems where there is a mixing between the continuous and discrete dynamics. This motivates the derivation of a new and more general state feedback control law for switched systems in this work. Here, a numerical example illustrating the results is presented.

42 ENGINEERING↗
DOE OSTI2023

On the dual advantage of placing observations through forward sensitivity analysis

The four-dimensional variational data assimilation methodology for assimilating noisy observations into a deterministic model has been the workhorse in forecasting centres for over three decades. While this method provides a computationally efficient framework for dynamic data assimilation, it is largely silent on the important question concerning the minimum number and placement of observations. To answer this question, we demonstrate the dual advantage of placing the observations where the square of the sensitivity of the model solution with respect to the unknown control variables, called forward sensitivities, attains its maximum. By following this approach, we can force the observability Gramian to be of full rank, which in turn guarantees efficient recovery of the optimal values of the control variables, which is the first of the two advantages of this strategy. We further show that the proposed strategy of placing observations has another inherent optimality: the square of the sensitivity of the optimal estimates of the control with respect to the observations (used to obtain these estimates) attains its minimum value, a second advantage that is a direct consequence of the above strategy for placing observations. Our analytical framework and numerical experiments on linear and nonlinear systems confirm the effectiveness of our proposed strategy.

97 MATHEMATICS AND COMPUTING↗