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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Departures of the electron energy distribution from a Maxwellian in hydrogen. I - Formulation and solution of the electron kinetic equation. II - Consequences

The problem of calculating the steady-state free-electron energy distribution in a hydrogen gas is considered in order to study departures of that distribution from a Maxwellian at sufficiently low degrees of ionization. A model kinetic equation is formulated and solved analytically for the one-particle electron distribution function in a steady-state partially ionized hydrogen gas, and it is shown that the formal solution can be accurately approximated by using the WKB method. The solutions obtained indicate that the high-energy tail of the distribution is susceptible to distortion by imbalanced inelastic collisions for ionization fractions not exceeding about 0.1 and that such departures from a Maxwellian can lead to significant changes in the collisional excitation and ionization rates of ground-state hydrogen atoms. Expressions for the electron-hydrogen collision rates are derived which explicitly display their dependence on the hydrogen departure coefficients. The results are applied in order to compare self-consistent predictions with those based on the a priori assumption of a Maxwellian distribution for models of the thermal ionization equilibrium of hydrogen in the optically thin limit, spectral-line formation by a gas consisting of two-level atoms, and radiative transfer in finite slabs by a gas of four-level hydrogen atoms.

Shoub, E. C.↗
NASA NTRS1989

Some fast elliptic solvers on parallel architectures and their complexities

The discretization of separable elliptic partial differential equations leads to linear systems with special block triangular matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconsistant coefficients. A method was recently proposed to parallelize and vectorize BCR. Here, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches, including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational complexity lower than that of parallel BCR.

Gallopoulos, E.↗
DOE OSTI2023

Cosmology from random entanglement

We construct entangled microstates of a pair of holographic CFTs whose dual semiclassical description includes big bang-big crunch AdS cosmologies in spaces without boundaries. The cosmology is supported by inhomogeneous heavy matter and it partially purifies the bulk entanglement of two disconnected auxiliary AdS spacetimes. We show that the island formula for the fine grained entropy of one of the CFTs follows from a standard gravitational replica trick calculation. In generic settings, the cosmology is contained in the entanglement wedge of one of the two CFTs. We then investigate properties of the cosmology-to-boundary encoding map, and in particular, its non-isometric character. Restricting our attention to a specific class of states on the cosmology, we provide an explicit, and state-dependent, boundary representation of operators acting on the cosmology. Finally, under genericity assumptions, we argue for a non-isometric to approximately-isometric transition of the cosmology-to-boundary map for “simple” states on the cosmology as a function of the bulk entanglement, with tensor network toy models of our setup as a guide.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Parameterizations of Entrainment-Mixing Mechanisms and their Effects on Cloud Droplet Spectral Width Based on Numerical Simulations

Entrainment-mixing mechanisms significantly affect cloud droplet number concentration, radius, and spectral shape. Quantitative examination of entrainment-mixing effects on cloud droplet spectral width is lacking. Here, we examine the effects of entrainment-mixing processes on cloud microphysics by 12,218 different setups, each simulated 10 times using the Explicit Mixing Parcel Model (EMPM) driven by the observational data from the Third Tibetan Plateau Atmospheric Scientific Experiment (TIPEX-III) campaign. Parameterizations of entrainment-mixing mechanisms are developed by relating homogeneous mixing degree to transition scale number that depends on the dissipation rate and droplet evaporation time scale. The correlation between relative dispersion of cloud droplet size distribution and homogeneous mixing degree changes from negative to positive with the decreasing homogeneous mixing degree. The different relationships are closely related to the competition between complete and partial droplet evaporation and the number concentration of small droplets, which are quantitatively described by two newly introduced dimensionless numbers. The competition is significantly affected by relative humidity and mixing fraction of entrained air as well as turbulence dissipation rate, but not much by cloud droplet number concentration. Especially, when relative humidity and dissipation rate are high, there is only a negative correlation. This study sheds new light on generalizing the homogeneous/inhomogeneous concept by considering relative dispersion, and also provides parameterizations of entrainment-mixing processes and relative dispersion for atmospheric models.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1989

Some fast elliptic solvers on parallel architectures and their complexities

The discretization of separable elliptic partial differential equations leads to linear systems with special block tridiagonal matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconstant coefficients. A method was recently proposed to parallelize and vectorize BCR. In this paper, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational compelxity lower than that of parallel BCR.

Gallopoulos, E.↗
NASA NTRS1996

Implicit Extrapolation Methods for Variable Coefficient Problems

Implicit extrapolation methods for the solution of partial differential equations are based on applying the extrapolation principle indirectly. Multigrid tau-extrapolation is a special case of this idea. In the context of multilevel finite element methods, an algorithm of this type can be used to raise the approximation order, even when the meshes are nonuniform or locally refined. Here previous results are generalized to the variable coefficient case and thus become applicable for nonlinear problems. The implicit extrapolation multigrid algorithm converges to the solution of a higher order finite element system. This is obtained without explicitly constructing higher order stiffness matrices but by applying extrapolation in a natural form within the algorithm. The algorithm requires only a small change of a basic low order multigrid method.

Jung, M.↗
DOE OSTI2024

On Properties of Adjoint Systems for Evolutionary PDEs

We investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the adjoint system associated with an evolutionary partial differential equation has an infinite-dimensional Hamiltonian structure, which is useful for connecting the fully continuous, semi-discrete, and fully discrete levels. We subsequently address the question of discretize-then-optimize versus optimize-then-discrete for both semi-discretization and time integration, by characterizing the commutativity of discretize-then-optimize methods versus optimize-then-discretize methods uniquely in terms of an adjoint-variational quadratic conservation law. For Galerkin semi-discretizations and one-step time integration methods in particular, we explicitly construct these commuting methods by using structure-preserving discretization techniques.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Explicit expressions of the potential and its derivatives at the origin in terms of the scattering data

The quantum mechanical theory of scattering of a particle by a spherically symmetrical potential is presented. As in the inverse scattering problem, the input of the calculation is the scattering and bound-state data, and the output is data on the potential. The results discussed are explicit expressions for the values of the potential and its derivatives at the origin in terms of the scattering and boundstate data. Various methods to obtain these results are outlined. The presentation is aimed at introducing these various approaches. The simplest scattering problem (nonrelativistic S-wave scattering on a holomorphic potential without bound states) is used as the basis for discussion, and technicalities are omitted whenever possible without loss of clarity. A complete compilation is given of the results obtained to date in this field, including the treatment of higher partial waves and the Klein-Gordon and Dirac equations.

Calogero, F.↗
DOE OSTI2021

A scalable exponential-DG approach for nonlinear conservation laws: With application to Burger and Euler equations

In this work, we propose an Exponential DG framework for partial differential equations. We decompose 7 governing equations into linear and nonlinear parts to which we apply the discontinuous Galerkin 8 (DG) spatial discretization. In particular, we construct the linear part using Jacobian that effectively 9 capture stiff characteristics in the system. The former is integrated analytically, whereas the latter 10 is approximated. This approach i) is stable with a large Courant number (Cr > 1); ii) supports 11 high-order solutions both in time and space; iii) is computationally favorable compared to IMEX 12 DG methods with no preconditioner; iv) becomes comparable to explicit RKDG methods on uniform 13 mesh and beneficial on non-uniform grid for Euler equations; v) is scalable in a modern massively 14 parallel computing architecture due to its explicit nature of exponential time integrators and com15 pact communication stencil of DG method. Numerical results demonstrate the performance of our 16 proposed methods through various examples. We also discuss the stability and convergence analysis 17 for our exponential DG scheme in the context of Burgers equation.

42 ENGINEERING↗
DOE OSTI2021

NRC Multiphysics Analysis Capability Deployment (FY2021 - Part 2)

This report details the progress and activities of Idaho National Laboratory (INL) on the Nuclear Regulatory Commission (NRC) project “Development and Modeling Support for Advanced Non-Light Water Reactors.” Task 4b was completed for this report. INL developed a sample problem showing how to use Serpent 2 to calculate macroscopic cross sections for use in Griffin for a typical sodium fast reactor Unprotected Loss of Flow (ULOF) transient. The complicating factor is the relatively large axial gradient of the coolant (and hence fuel) temperature and its evolution during the transient. A 3D Griffin model of the Advanced Burner Test Reactor (ABTR) is coupled to the System Analysis Module (SAM) to perform the ULOF transient. The model includes various explicit feedback mechanisms for fast reactors, including Doppler, radial expansion from the displacement of the support plate, and axial expansion from the displacement of the fuel pins. The results for the ULOF transient are consistent with published values. We observed small effects in the transient results that arise from the superhomogenization equivalence correction of uniform and nonuniform temperature data sets, but they diminish as more dominant reactivity mechanisms are added to the model. Potential improvements to the neutronics model include: adding the differential control rod and sodium feedback mechanisms, implementing cross section re-homogenization based on the partial volume of the various materials, and enhancing the kinetics parameters. Furthermore, the fluids model only includes four subchannels to represent the entire active core due to performance limitations in SAM when attempting to model one subchannel per assembly.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1982

Algebraic grid generation

The numerical solution of partial differential equations about irregular geometries and with varying characteristic scales has created the need for coordinate systems and associated transformations which reflect both geometric and physical requirements. The process of finding coordinate transformations in discrete representations is called 'grid generation'. The present investigation is concerned with three algebraic grid generation methods. The methods include transfinite interpolation, the multisurface method, and the two-boundary technique. Interpolation formulas, in terms of homotopic mappings and constraints in terms of point positions and/or derivatives are the essential elements of the techniques. The methods are relatively simple to understand, they are explicit and do not require extensive computational effort, and they have a high degree of generality.

Smith, R. E.↗
NASA NTRS1999

Automatic Data Distribution for CFD Applications on Structured Grids

Development of HPF versions of NPB and ARC3D showed that HPF has potential to be a high level language for parallelization of CFD applications. The use of HPF requires an intimate knowledge of the applications and a detailed analysis of data affinity, data movement and data granularity. Since HPF hides data movement from the user even with this knowledge it is easy to overlook pieces of the code causing low performance of the application. In order to simplify and accelerate the task of developing HPF versions of existing CFD applications we have designed and partially implemented ADAPT (Automatic Data Distribution and Placement Tool). The ADAPT analyzes a CFD application working on a single structured grid and generates HPF TEMPLATE, (RE)DISTRIBUTION, ALIGNMENT and INDEPENDENT directives. The directives can be generated on the nest level, subroutine level, application level or inter application level. ADAPT is designed to annotate existing CFD FORTRAN application performing computations on single or multiple grids. On each grid the application can considered as a sequence of operators each applied to a set of variables defined in a particular grid domain. The operators can be classified as implicit, having data dependences, and explicit, without data dependences. In order to parallelize an explicit operator it is sufficient to create a template for the domain of the operator, align arrays used in the operator with the template, distribute the template, and declare the loops over the distributed dimensions as INDEPENDENT. In order to parallelize an implicit operator, the distribution of the operator's domain should be consistent with the operator's dependences. Any dependence between sections distributed on different processors would preclude parallelization if compiler does not have an ability to pipeline computations. If a data distribution is "orthogonal" to the dependences of an implicit operator then the loop which implements the operator can be declared as INDEPENDENT.

Frumkin, Michael↗
NASA NTRS1998

Three-Dimensional High-Lift Analysis Using a Parallel Unstructured Multigrid Solver

A directional implicit unstructured agglomeration multigrid solver is ported to shared and distributed memory massively parallel machines using the explicit domain-decomposition and message-passing approach. Because the algorithm operates on local implicit lines in the unstructured mesh, special care is required in partitioning the problem for parallel computing. A weighted partitioning strategy is described which avoids breaking the implicit lines across processor boundaries, while incurring minimal additional communication overhead. Good scalability is demonstrated on a 128 processor SGI Origin 2000 machine and on a 512 processor CRAY T3E machine for reasonably fine grids. The feasibility of performing large-scale unstructured grid calculations with the parallel multigrid algorithm is demonstrated by computing the flow over a partial-span flap wing high-lift geometry on a highly resolved grid of 13.5 million points in approximately 4 hours of wall clock time on the CRAY T3E.

Mavriplis, Dimitri J.↗
NASA NTRS1971

Two examples in the time optimal control theory of distributed parameter systems.

The behavior of hyperbolic and parabolic partial differential equations is contrasted by studying the point-to-point time-optimal control problem for the equation of heat conduction and the equation of motion of a vibrating string. A maximal principle is obtained for the time-optimal control of the one-dimensional heat equation, and it is proven that time optimal controls are weakly bang-bang. The bang-bang principle is proven to be invalid for hyperbolic equations because of the finite speed of wave propagation. In the case of boundary value control of the vibrating spring, the latter is demonstrated by deriving an explicit formula for the time optimal control.

Quinn, J. P.↗
DOE OSTI2021

Confinement effects on the solvation structure of solvated alkaline metal cations in a single-digit 1T-MoS 2 nanochannel: A first-principles study

Confinement plays an important role in determining ion transport in porous materials, which, in turn, may influence the performance of many energy storage and desalination devices. In this work, we combined density functional theory (DFT) with an implicit solvation model and ab initio molecular dynamics (AIMD) to investigate the effects of nanoconfinement on several solvated alkaline metal cations in a single-digit 1T-MoS 2 nanochannel. Our DFT calculations with a solvation model indicated that cations with stronger hydration energy introduce a higher number of co-intercalated water molecules into the channel, consistent with early experimental observation obtained for MXene (2D transition metal carbide) channels. The predicted optimal water numbers for the cations were then used for AIMD simulations that explicitly include the effects of the solvent. When compared with the cations in bulk solution, our simulations showed that the hydration structure and coordination number (CN) of the solvated cations confined in the MoS 2 channel can be significantly altered. Further, we found that larger cations with weaker hydration energy (K + , Rb + , and Cs + ) exhibited a distinctive CN decrease under confinement, while smaller cations (Li + and Na + ) retained a similar hydration shell as in the bulk solution. More specifically, the hydration shell of large cations (K + , Rb + , and Cs + ) in MoS 2 showed similar features of the coordination angle to the bulk, which suggests the partially broken hydration shell with no geometry change under confinement. Our simulations provided insights into the change of the hydration structure of alkaline metal cations under confinement, which may have important implications on their transport in the 1T-MoS 2 channel.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Domain-aware Control-oriented Neural Models for Autonomous Underwater Vehicles

Conventional physics-based modeling is a time-consuming bottleneck in control design for complex nonlinear systems like autonomous underwater vehicles (AUVs). In contrast, purely data-driven models, require a large number of observations and lack operational guarantees for safety-critical systems. Data-driven models leveraging available partially characterized dynamics have potential to provide reliable systems models in a typical data-limited scenario for high value complex systems, thereby avoiding months of expensive expert modeling time. In this work we explore this middle-ground between expert-modeled and pure data-driven modeling. We present control-oriented parametric models with varying levels of domain-awareness that exploit known system structure and prior physics knowledge to create constrained deep neural dynamical system models. We employ universal differential equations to construct data-driven blackbox and graybox representations of the AUV dynamics. In addition, we explore a hybrid formulation that explicitly models the residual error related to imperfect graybox models. We compare the prediction performance of the learned models for different distributions of initial conditions and control inputs to assess their suitability for control.

Shaw Cortez, Wenceslao E.↗
DOE OSTI2024

Simulation of gas mixture dynamics in a pipeline network using explicit staggered-grid discretization

Here we develop an explicit staggered finite difference discretization scheme for simulating the transport of highly heterogeneous gas mixtures through pipeline networks. This study is motivated by the proposed blending of hydrogen into natural gas pipelines to reduce end use carbon emissions while using existing pipeline systems throughout their planned lifetimes. Our computational method accommodates an arbitrary number of constituent gases with very different physical properties that may be injected into a network with significant spatiotemporal variation. In this setting, the gas flow physics are highly location- and time- dependent, so that local composition and nodal mixing must be accounted for. The resulting conservation laws are formulated in terms of pressure, partial densities and flows, and volumetric and mass fractions of the constituents. We include non-ideal equations of state that employ linear approximations of gas compressibility factors, so that the pressure dynamics propagate locally according to a variable wave speed that depends on mixture composition and density. We derive compatibility relationships for network edge boundary values that are more complex than for a homogeneous gas. The simulation method is evaluated on initial boundary value problems for a single pipe and a small network, is cross-validated with a lumped element simulation, and used to demonstrate a local monitoring and control policy for maintaining allowable concentration levels.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

On an origin of numerical diffusion: Violation of invariance under space-time inversion

The invariant properties of the convection equation du/dt + adu/dx = 0 (where d is the partial differential operator) with respect to spatial reflection, time reversal, and space-time inversion are studied. Generally, a finite-difference analog of this equation may possess some or none of these properties. It is shown that, under certain conditions, the von Neumann amplification factor of an analog satisfies a special relation for each invariant property this analog possesses. Particularly, an analog is neutrally stable and thus free of numerical diffusion if it possesses the invariant property related to space-time inversion. It is also explained why generally (1) an upwind scheme possesses neither the invariant property related to spatial reflection nor that related to space-time inversion, and (2) an explicit scheme possesses neither the invariant property related to time reversal nor that related to space-time inversion. Extension to the viscous case and a remarkable connection between the current work and a new numerical framework for solving conservation laws are also discussed.

Chang, Sin-Chung↗