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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.

Steger, J. L.↗
NASA NTRS1996

Hyperbolic Methods for Surface and Field Grid Generation

This chapter describes the use of hyperbolic partial differential equation methods for structured surface grid generation and field grid generation. While the surface grid generation equations are inherently three dimensional, the field grid generation equations can be formulated in two or three dimensions. The governing equations are derived from orthogonality relations and cell area/volume constraints; and are solved numerically by marching from an initial curve or surface. The marching step size and marching distance can be prescribedly the user. Exact specifications of the side and outer boundaries are not possible with a one sweep marching scheme but limited control is achievable. Excellent orthogonality and grid clustering characteristics are provided by hyperbolic methods with one to two orders of magnitude savings in time over typical elliptic methods. Since hyperbolic grid generation methods do not require the exact specifications of the side and outer boundaries of a grid, these methods are particularly well suited for the overlapping grid approach for solving problems on complex configurations. Grid generation software based on hyperbolic methods and their applications on several complex configurations will be described.

Chan, William M.↗
NASA NTRS1989

Assessment of numerical methods for the solution of fluid dynamics equations for nonlinear resonance systems

The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.

Przekwas, A. J.↗
NASA NTRS1983

On the symmetric form of systems of conservation laws with entropy

The present investigation has the objective to review the general structure of system of conservation laws with entropy, giving particular attention to a presentation of symmetric formulations of the equations of gas dynamics. Systems of hyperbolic conservation laws are considered, taking into account the case in which a system of equations is symmetric hyperbolic, questions of symmetrization, and entropy functions. The Euler equations for a polytropic gas in conservation form are considered. The symmetric form retains the conservation properties of the equations. Weak solutions remain, therefore, unchanged. Of particular computational interest is the possibility of using the symmetric form.

Harten, A.↗
NASA NTRS2022

Continuum Covariance Propagation for Understanding Variance Loss in Advective Systems

Motivated by the spurious variance loss encountered during covariance propagation in atmospheric and other large-scale data assimilation systems, we consider the problem for state dynamics governed by the continuity and related hyperbolic partial differential equations. This loss of variance has been attributed to reduced-rank representations of the covariance matrix, as in ensemble methods for example, or else to the use of dissipative numerical methods. Through a combination of analytical work and numerical experiments, we demonstrate that significant variance loss, as well as gain, typically occurs during covariance propagation, even at full rank. The cause of this unusual behavior is a discontinuous change in the continuum covariance dynamics as correlation lengths become small, for instance in the vicinity of sharp gradients in the velocity field. This discontinuity in the covariance dynamics arises from hyperbolicity: the diagonal of the kernel of the covariance operator is a characteristic surface for advective dynamics. Our numerical experiments demonstrate that standard numerical methods for evolving the state are not adequate for propagating the covariance, because16they do not capture the discontinuity in the continuum covariance dynamics as correlations lengths tend to zero. Our analytical and numerical results show that this leads to significant, spurious variance loss in certain regions, and gain in others. The results suggest that developing local covariance propagation methods designed specifically to capture covariance evolution near the diagonal may prove a useful alternative to current methods of covariance propagation.

covariance propagation↗
DOE OSTI2020

In situ compression artifact removal in scientific data using deep transfer learning and experience replay

The massive amount of data produced during simulation on high-performance computers has grown exponentially over the past decade, exacerbating the need for streaming compression and decompression methods for efficient storage and transfer of this data---key to realizing the full potential of large-scale computational science. Lossy compression approaches such as JPEG when applied to scientific simulation data realized as a stream of images can achieve good compression rates but at the cost of introducing compression artifacts and loss of information. This paper develops a unified framework for in situ compression artifact removal in which the fully convolutional neural network architectures are combined with scalable training, transfer learning, and experience replay to achieve superior accuracy and efficiency while significantly decreasing the storage footprint as compared with the traditional optimization-based approaches. We demonstrate the proposed approach and compare it with compressed sensing postprocessing and other baseline deep learning models using climate simulations and nuclear reactor simulations, both of which are driven by hyperbolic partial differential equations. Our approach when applied to remove the compression artifacts on the JPEG-compressed nuclear reactor simulation data (using a transfer-trained model that was pretrained on the climate simulation data and updated incrementally as the nuclear reactor simulation progressed), achieved a significant improvement---mean peak signal-to-noise ratio of 42.438 as compared with 27.725 obtained with the compressed sensing approach.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Efficient grid generation

Because the governing equations in fluid dynamics contain partial differentials and are too difficult in most cases to solve analytically, these differentials are generally replaced by finite difference terms. These terms contain terms in the solution at nearby states. This procedure discretizes the field into a finite number of states. These states, when plotted, form a grid, or mesh, of points. It is at these states, or field points, that the solution is found. The optimum choice of states, the x, y, z coordinate values, minimizes error and computational time. But the process of finding these states is made more difficult by complex boundaries, and by the need to control step size differences between the states, that is, the need to control the spacing of field points. One solution technique uses a different set of state variables, which define a different coordinate system, to generate the grid more easily. A new method, developed by Dr. Joseph Steger, combines elliptic and hyperbolic partial differential equations into a mapping function between the physical and computational coordinate systems. This system of equations offers more control than either equation provides alone. The Steger algorithm was modified in order to allow bodies with stronger concavities to be used, offering the possibility of generating a single grid about multiple bodies. Work was also done on identifying areas where grid breakdown occurs.

Seki, Rycichi↗
DOE OSTI2024

Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks

We develop a weakly intrusive framework to simulate the propagation of uncertainty in solutions of generic hyperbolic partial differential equation systems on graph-connected domains with nodal coupling and boundary conditions. The method is based on the Stochastic Finite Volume (SFV) approach and can be applied for uncertainty quantification (UQ) of the dynamical state of fluid flow over actuated transport networks. The numerical scheme has specific advantages for modeling intertemporal uncertainty in time-varying boundary parameters, which cannot be characterized by strict upper and lower (interval) bounds. We describe the scheme for a single pipe, and then formulate the controlled junction Riemann problem (JRP) that enables the extension to general network structures. In conclusion, we demonstrate the method's capabilities and performance characteristics using a standard benchmark test network.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Medial axis and local thickness computation using the Fast Sweeping Method

This report describes an efficient and robust voxel-based methodology for computing the medial axis, local thickness, and distance-to-skeleton of arbitrary three-dimensional geometries. It is assumed that the object can be represented by an exact or approximate signed distance function on a discrete grid. The gradient of such function is used to formulate a hyperbolic partial differential equation (PDE) that models the collapse of the position vector in space. By exploiting the causality property of the PDE, the Fast Sweeping Method is able to obtain the solution in a finite number of sweeps independent of the mesh resolution. The intersection of characteristic lines leads to the formation of shocks and a discrete bisector function is used to identify the medial axis. The same PDE approach is used to compute the local thickness inside the object and obtain the distance-to-skeleton field. Multiple examples are given in two and three dimensions along with a resolution study. The methodology has optimal complexity and yields subsecond computational times for geometries with over a million zones on a single core. The methodology is also capable of parallelization across shared and distributed memory architectures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Mixed gauge-global symmetries, elliptic modes, and black hole thermodynamics in Hořava-Lifshitz gravity

In Hořava-Lifshitz gravity, a putative consistent theory of quantum gravity for which there is evidence for both black hole thermodynamics and a holographic construction, spacetime is endowed with a preferred dynamical spacelike foliation. The theory has a leaf reparameterization symmetry that is neither global nor local gauge, hyperbolic and elliptic equations of motion, a lack of splittability, and universal horizon black hole solutions. The reparameterization symmetry is “mixed”: it is a local symmetry in one coordinate yet global on each leaf. More broadly it is an example of both unfree and projectable gauge symmetries. The mixed symmetry and associated charge has not yet been accounted for in calculations of universal horizon thermodynamics in Hořava-Lifshitz gravity. This has led to problems, in particular the failure of the first law in a class of asymptotically AdS solutions where the normal to the leaves of the foliation is not aligned with the time translation Killing vector at infinity. We show how the dynamics of the charge corresponding to this symmetry coupled with the other features above resolves this issue. We then briefly comment how this mixed symmetry, the corresponding charge, and the elliptic equations of motion also conspire to evade recent holographic arguments for only local gauge fields in consistent theories of quantum gravity due to the lack of splittability of the elliptic equation and associated mode.

Global Symmetries↗
DOE OSTI2023

Canonical and noncanonical Hamiltonian operator inference

Here, a method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a straightforward linear solve given snapshot data and gray-box knowledge of the system Hamiltonian. Examples involving several hyperbolic partial differential equations show that the proposed method yields reduced models which, in addition to being accurate and stable with respect to the addition of basis modes, preserve conserved quantities well outside the range of their training data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms

The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic computational plasma physics. This motivates exploring whether a future error-corrected quantum computer could perform these simulations more efficiently than any classical computer. In this work, we describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) and detail three specific cases of this method that correspond to previously studied mappings. Then we explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation). Using a number of qubits only logarithmic in the number of variables of the nonlinear system, a quantum computer could simulate truncated systems to approximate output quantities if the nonlinearity is sufficiently weak. Other aspects of the computational efficiency of the three detailed embedding strategies are also discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Required toroidal confinement for fusion and omnigeneity

Deuterium–tritium (DT) burning requires a long energy confinement times compared to collision times, so the particle distribution functions must approximate local Maxwellians. Non-equilibrium thermodynamics is applicable, which gives relations among transport, entropy production, the collision frequency, and the deviation from a Maxwellian. The distribution functions are given by the Fokker–Planck equation, which is an advection–diffusion equation. A large hyperbolic operator, the Vlasov operator with the particle trajectories as its characteristics, equals a small diffusive operator, the collision operator. The collisionless particle trajectories would be chaotic in stellarators without careful optimization. This would lead to rapid entropy production and transport—far beyond what is consistent with a self-sustaining DT burn. Omnigeneity is the weakest general condition that is consistent with a sufficiently small entropy production associated with the thermal particle trajectories. Omnigeneity requires that the contours of constant magnetic field strength be unbounded in at least one of the two angular coordinates in magnetic surfaces and that there be a symmetry in the field-strength wells along the field lines. Even in omnigenous plasmas, fluctuations due to microturbulence can produce chaotic particle trajectories and the gyro-Bohm transport is seen in many stellarator and tokamak experiments. The higher the plasma temperature above 10 keV, the smaller the transport must be compared to gyro-Bohm for a self-sustaining DT burn. The hot alphas of DT fusion heat the electrons. When the ion–electron equilibration time is long compared to the ion energy confinement time, a self-sustaining DT burn is not possible, which sets a limit on the electron temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Ameliorating the Courant-Friedrichs-Lewy condition in spherical coordinates: A double FFT filter method for general relativistic MHD in dynamical spacetimes

Numerical simulations of merging compact objects and their remnants form the theoretical foundation for gravitational wave and multimessenger astronomy. While Cartesian-coordinate-based adaptive mesh refinement is commonly used for simulations, spherical-like coordinates are more suitable for nearly spherical remnants and azimuthal flows due to lower numerical dissipation in the evolution of fluid angular momentum, as well as requiring fewer numbers of computational cells. However, the use of spherical coordinates to numerically solve hyperbolic partial differential equations can result in severe Courant-Friedrichs-Lewy (CFL) stability condition time step limitations, which can make simulations prohibitively expensive. This paper addresses this issue for the numerical solution of coupled spacetime and general relativistic magnetohydrodynamics evolutions by introducing a double fast Fourier transform (FFT) filter and implementing it within the fully message passing interface (mpi)-parallelized sphericalnr framework in the einstein toolkit. In conclusion, we demonstrate the effectiveness and robustness of the filtering algorithm by applying it to a number of challenging code tests, and show that it passes these tests effectively, demonstrating convergence while also increasing the time step significantly compared to unfiltered simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Canonical and Noncanonical Hamiltonian Operator Inference

SAND2024-08577O Canonical and Noncanonical Hamiltonian Operator Inference is research code that applies old and new model reduction algorithms to well-known and publicly available "toy" problems. It applies operator inference (OpInf) methods for model reduction to several benchmark hyperbolic partial differential equations: linear wave, Korteweg-de Vries, Benjamin-Bona-Mahoney, and linear elasticity. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
NASA NTRS1971

Numerical solution of flowfields behind rectangular wings

The numerical solution of flow fields behind rectangular wings is described. Subjects discussed are: (1) evaluation of various differencing methods applied to the hyperbolic partial differential equations encountered in gas dynamics, (2) application of the numerical differencing techniques to the wedge flow, two dimensional shock reflection for the three dimensional finite thickness wing at zero degrees angle of attack, and (3) calculation of preliminary results for wedge flows using optimum differencing methods.

Anderson, D.↗