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NASA NTRS1989

Heating and acceleration of heavy ions during solar flares

The heating of the various ion species during solar flares is examined in an attempt to develop a unified model incorporating the enrichments in abundances seen by ISEE 3 and some of the characteristics of the soft X-ray line emissions. Problems associated with identifying the initial conditions and the driving mechanisms for the particle acceleration are addressed. The acceleration of heated plasma ions as they propagate upward into the corona is studied via particle simulations.

Winglee, R. M.↗

NASA NTRS2007

Simulations of Boundary-Layer Transition

For incompressible benchmark flows, we have demonstrated the capability of the parabolized stability equations (PSE) to simulate the transition process in excellent agreement with microscopic experiments and direct Navier-Stokes simulations at modest computational cost. Encouraged by these results, we have developed the PSE methodology of three-dimensional boundary-layers in general curvilinear coordinates for the range from low to hypersonic speeds, and for both linear and nonlinear problems. For given initial and boundary conditions, the approach permits simulations from receptivity through linear and secondary instabilities into the late stages of transition where significant changes in skin friction and heat transfer coefficients occur. We have performed transition simulations for a variety of two- and three-dimensional similarity solutions and for realistic flows over swept wings at subsonic and supersonic speeds, the pressure ans suction side of turbine blades at low and medium turbulence levels, and over a blunt cone at Mach number Ma = 8. We present selected results for different transition mechanisms with emphasis on the late stage of transition and the evolution of wall-shear stress and heat transfer.

Herbert, Thorwald↗

NASA NTRS1979

Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems

Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

Skollermo, G.↗

NASA NTRS1996

Artificial Boundary Conditions Based on the Difference Potentials Method

While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems present a wide class of practically important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computationally) expensive. The methods from the second group (local ABC's) are, as a rule, algorithmically simple, numerically cheap, and geometrically universal; however, they usually lack accuracy of computations. In this paper we first present a survey and provide a comparative assessment of different existing methods for constructing the ABC's. Then, we describe a relatively new ABC's technique of ours and review the corresponding results. This new technique, in our opinion, is currently one of the most promising in the field. It enables one to construct such ABC's that combine the advantages relevant to the two aforementioned classes of existing methods. Our approach is based on application of the difference potentials method attributable to V. S. Ryaben'kii. This approach allows us to obtain highly accurate ABC's in the form of certain (nonlocal) boundary operator equations. The operators involved are analogous to the pseudodifferential boundary projections first introduced by A. P. Calderon and then also studied by R. T. Seeley. The apparatus of the boundary pseudodifferential equations, which has formerly been used mostly in the qualitative theory of integral equations and PDE'S, is now effectively employed for developing numerical methods in the different fields of scientific computing.

Tsynkov, Semyon V.↗

NASA NTRS1961

The General Equations of Equilibrium of Rotationally Symmetric Membranes and some Static Solutions for Uniform Centrifugal Loading

The general equations of equilibrium of a rotationally symmetrical body undergoing large arbitrary deflections but small strains are derived by means of the principle of virtual work. All deflections are referred to a reference surface which, in general, may be taken to coincide with any intermediate state of the membrane. Static solutions of the general equations for steadily rotating membranes are considered for the cases in which the final or the initial configuration of the membrane is specified. For problems in which the final configuration is specified, conditions are given under which such a configuration is obtainable from a stress-free initial state. Such conditions being satisfied, it is shown that the stresses and radial displacements are determinate while axial displacements may be obtained by quadrature. For problems in which the initial configuration is given, the determination of the stresses and deflections is reduced to the solution of a second-order nonlinear differential equation for a stress function. An approximate method of solution based on boundary-layer considerations is presented for the case of a spinning sphere of constant thickness. Specific examples are given for both classes of problems.

Simmonds, James G.↗

NASA NTRS2008

Numerical Determination of Critical Conditions for Thermal Ignition

The determination of ignition or thermal explosion in an oxidizing porous body of material, as described by a dimensionless reaction-diffusion equation of the form .tu = .2u + .e-1/u over the bounded region O, is critically reexamined from a modern perspective using numerical methodologies. First, the classic stationary model is revisited to establish the proper reference frame for the steady-state solution space, and it is demonstrated how the resulting nonlinear two-point boundary value problem can be reexpressed as an initial value problem for a system of first-order differential equations, which may be readily solved using standard algorithms. Then, the numerical procedure is implemented and thoroughly validated against previous computational results based on sophisticated path-following techniques. Next, the transient nonstationary model is attacked, and the full nonlinear form of the reaction-diffusion equation, including a generalized convective boundary condition, is discretized and expressed as a system of linear algebraic equations. The numerical methodology is implemented as a computer algorithm, and validation computations are carried out as a prelude to a broad-ranging evaluation of the assembly problem and identification of the watershed critical initial temperature conditions for thermal ignition. This numerical methodology is then used as the basis for studying the relationship between the shape of the critical initial temperature distribution and the corresponding spatial moments of its energy content integral and an attempt to forge a fundamental conjecture governing this relation. Finally, the effects of dynamic boundary conditions on the classic storage problem are investigated and the groundwork is laid for the development of an approximate solution methodology based on adaptation of the standard stationary model.

Luo, W.↗

DOE OSTI2023

Data-driven, structure-preserving approximations to entropy-based moment closures for kinetic equations

In this study, we present a data-driven approach for approximating entropy-based closures of moment systems from kinetic equations. The proposed closure learns the entropy function by fitting the map between the moments and the entropy of the moment system, and thus does not depend on the spacetime discretization of the moment system or specific problem configurations such as initial and boundary conditions. With convex and C 2 approximations, this data-driven closure inherits several structural properties from entropy-based closures, such as entropy dissipation, hyperbolicity, and H-Theorem. We construct convex approximations to the Maxwell–Boltzmann entropy using convex splines and neural networks, test them on the plane source benchmark problem for linear transport in slab geometry, and compare the results to the standard, entropy-based systems which solve a convex optimization problem to find the closure. Numerical results indicate that these data-driven closures provide accurate solutions in much less computation time than that required by the optimization routine.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Where did the tumor start? An inverse solver with sparse localization for tumor growth models

In this work, we present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction–diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of magnetic resonance imaging (MRI) scans drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. Like most cases in clinical practice, we use data from a single time snapshot. Moreover, the precise time relative to the initiation of the tumor is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the structure and magnitude of the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint on the initial condition of the tumor) and that the initial condition magnitude in the maximum norm is equal to one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over a previously existing solver that uses standard two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the two-norm regularized solver.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Fluoride-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model

In this report we present work performed in Fiscal Year 2022 that demonstrates the modeling and simulation of a fully coupled neutronics thermal hydraulics reference plant model for a fluoride-cooled high-temperature pebble-bed reactor. The multiphysics model is developed on the Nuclear Regulatory Commission’s Comprehensive Reactor Analysis Bundle (BlueCRAB) available on the Idaho National Laboratory’s high-performance computer, which natively and seamlessly couples Griffin, Pronghorn, and the BISON Multiphysics Object-Oriented Simulation Environment based applications. Griffin provides reactor physics capabilities, including depletion to the equilibrium core, k-eigenvalue, adjoint, and transient. The unique direct equilibrium core capability in Griffin is based on a streamline methodology to spatially deplete the pebbles into burnup groups. Pronghorn solves the porous medium equations for the fluid regions and conduction in the solid regions and incorporates a fluidic diode model to simulate the transition from forced to natural convection during accident scenarios. MOOSE modules solves thermal conduction problems for the pebbles and tristructural isotropic in the pebble-bed core, thus providing the fuel and moderator spatial fields for each pebble burnup group. The neutronics feedback relies primarily on fuel, moderator, and reflector temperatures as as well as the FLiBe salt density. Here, we present results for the uncoupled equilibrium core and perform comparisons to equivalent Monte Carlo models. The power distributions and kinetic parameters obtained with Griffin are consistent with those computed with Griffin. We demonstrate a noticeable improvement with the use of discrete ordinates method (SN) transport. The coupled steady-state equilibrium core provides the initial condition for two time-dependent problems: a control rod withdrawal event and an unprotected loss of flow event. In both cases, the reactor design is self-stabilizing and the solutions are consistent with the expected physics. Although this model is prototypical regarding BlueCRAB’s capabilities, its results are consistent with published work by Kairos Power and other research entities. Significant improvements to the model are planned in future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1995

Solutions of the benchmark problems by the dispersion-relation-preserving scheme

The 7-point stencil Dispersion-Relation-Preserving scheme of Tam and Webb is used to solve all the six categories of the CAA benchmark problems. The purpose is to show that the scheme is capable of solving linear, as well as nonlinear aeroacoustics problems accurately. Nonlinearities, inevitably, lead to the generation of spurious short wave length numerical waves. Often, these spurious waves would overwhelm the entire numerical solution. In this work, the spurious waves are removed by the addition of artificial selective damping terms to the discretized equations. Category 3 problems are for testing radiation and outflow boundary conditions. In solving these problems, the radiation and outflow boundary conditions of Tam and Webb are used. These conditions are derived from the asymptotic solutions of the linearized Euler equations. Category 4 problems involved solid walls. Here, the wall boundary conditions for high-order schemes of Tam and Dong are employed. These conditions require the use of one ghost value per boundary point per physical boundary condition. In the second problem of this category, the governing equations, when written in cylindrical coordinates, are singular along the axis of the radial coordinate. The proper boundary conditions at the axis are derived by applying the limiting process of r approaches 0 to the governing equations. The Category 5 problem deals with the numerical noise issue. In the present approach, the time-independent mean flow solution is computed first. Once the residual drops to the machine noise level, the incident sound wave is turned on gradually. The solution is marched in time until a time-periodic state is reached. No exact solution is known for the Category 6 problem. Because of this, the problem is formulated in two totally different ways, first as a scattering problem then as a direct simulation problem. There is good agreement between the two numerical solutions. This offers confidence in the computed results. Both formulations are solved as initial value problems. As such, no Kutta condition is required at the trailing edge of the airfoil.

Tam, Christopher K. W.↗

DOE OSTI2020

Estimation of distributions via multilevel Monte Carlo with stratified sampling

We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the joint cumulative distribution function (CDF) of a vector-valued quantity of interest in problems with random input parameters and initial conditions. Our approach combines MLMC with stratified sampling of the input sample space by replacing standard Monte Carlo at each level with stratified Monte Carlo initialized with proportionally allocated samples. We show that the resulting stratified MLMC (sMLMC) algorithm is more efficient than its standard MLMC counterpart due to the additional variance reduction provided by the stratification of the random parameter's domain, especially at the coarsest levels. Additional computational cost savings are obtained by smoothing the indicator function with a Gaussian kernel, which proves to be an efficient and robust alternative to recently developed polynomial-based techniques.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Stability analysis of the Eulerian–Lagrangian finite volume methods for nonlinear hyperbolic equations in one space dimension

In this paper, we construct a novel Eulerian–Lagrangian finite volume (ELFV) method for nonlinear scalar hyperbolic equations in one space dimension. It is well known that the exact solutions to such problems may contain shocks though the initial conditions are smooth, and direct numerical methods may suffer from restricted time step sizes. To relieve the restriction, we propose an ELFV method, where the space-time domain was separated by the partition lines originated from the cell interfaces whose slopes are obtained following the Rakine–Hugoniot junmp condition. Unfortunately, to avoid the intersection of the partition lines, the time step sizes are still limited. To fix this gap, we detect effective troubled cells (ETCs) and carefully design the influence region of each ETC, within which the partitioned space-time regions are merged together to form a new one. Then with the new partition of the space-time domain, we theoretically prove that the proposed first-order scheme with Euler forward time discretization is total-variation-diminishing and maximum-principle-preserving with at least twice larger time step constraints than the classical first order Eulerian method for Burgers’ equation. Numerical experiments verify the optimality of the designed time step sizes.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1996

Aerostructural Vortical Flow Interactions with Applications to F/A-18 and F-117 Tail Buffet

The buffet response of the flexible twin-tail configuration of the F/A-18 and a generic F-111 aircraft are computationally simulated and experimentally validated. The problem is a multidisciplinary one which requires the sequential solution of three sets of equations on a multi-block grid structure. The first set is the unsteady, compressible, full Navier-Stokes equations. The second set is the aeroelastic equations for bending and torsional twin-tail responses. The third set is the grid-displacement equations which are used to update the grid coordinates due to the tail deflections. The computational models consist of a 76 deg. swept back, sharp edged delta wing of aspect ratio of one and a swept-back F/A-18 or F-117 twin-tail. The configuration is pitched at 30 deg. angle-of-attack. The problem is solved for the initial flow conditions with the twin tails kept rigid. Next, the aeroelastic equations of the tails are turned on along with the grid-displacement equations to solve for the bending and torsional tails responses due to the unsteady loads produced by the vortex breakdown flow of the leading-edge vortex cores of the delta wing. Several spanwise locations of the twin tails are investigated. The computational results are validated using several existing experimental data.

Kandil, Osama A.↗

NASA NTRS1996

Twin Tail/Delta Wing Configuration Buffet Due to Unsteady Vortex Breakdown Flow

The buffet response of the twin-tail configuration of the F/A-18 aircraft; a multidisciplinary problem, is investigated using three sets of equations on a multi-block grid structure. The first set is the unsteady, compressible, full Navier-Stokes equations. The second set is the coupled aeroelastic equations for bending and torsional twin-tail responses. The third set is the grid-displacement equations which are used to update the grid coordinates due to the tail deflections. The computational model consists of a 76 deg-swept back, sharp edged delta wing of aspect ratio of one and a swept-back F/A-18 twin-tails. The configuration is pitched at 32 deg angle of attack and the freestream Mach number and Reynolds number are 0.2 and 0.75 x 10(exp 6) respectively. The problem is solved for the initial flow conditions with the twin tail kept rigid. Next, the aeroelastic equations of the tails are turned on along with the grid-displacement equations to solve for the uncoupled bending and torsional tails response due to the unsteady loads produced by the vortex breakdown flow of the vortex cores of the delta wing. Two lateral locations of the twin tail are investigated. These locations are called the midspan and inboard locations.

Kandil, Osama A.↗

NASA NTRS2006

The Effect of Air Density on Atmospheric Electric Fields Required for Lightning Initiation from a Long Airborne Object

The purpose of the work was to determine minimum atmospheric electric fields required for lightning initiation from an airborne vehicle at various altitudes up to 10 km. The problem was reduced to the determination of a condition for initiation of a viable positive leader from a conductive object in an ambient electric field. It was shown that, depending on air density and shape and dimensions of the object, critical atmospheric fields are governed by the condition for leader viability or that for corona onset. To establish quantitative criteria for reduced air densities, available observations of spark discharges in long laboratory gaps were analyzed, the effect of air density on leader velocity was discussed and evolution in time of the properties of plasma in the leader channel was numerically simulated. The results obtained were used to evaluate the effect of pressure on the quantitative relationships between the potential difference near the leader tip, leader current and its velocity; based on these relationships, criteria for steady development of a leader were determined for various air pressures. Atmospheric electric fields required for lightning initiation from rods and ellipsoidal objects of various dimensions were calculated at different air densities. It was shown that there is no simple way to extend critical ambient fields obtained for some given objects and pressures to other objects and pressures.

Bazelyan, E. M.↗

NASA NTRS1985

Analysis of the electromagnetic scattering from an inlet geometry with lossy walls

One of the primary goals is to develop an approximate but sufficiently accurate analysis for the problem of electromagnetic (EM) plane wave scattering by an open ended, perfectly-conducting, semi-infinite hollow circular waveguide (or duct) with a thin, uniform layer of lossy or absorbing material on its inner wall, and with a simple termination inside. The less difficult but useful problem of the EM scattering by a two-dimensional (2-D), semi-infinite parallel plate waveguide with an impedance boundary condition on the inner walls was chosen initially for analysis. The impedance boundary condition in this problem serves to model a thin layer of lossy dielectric/ferrite coating on the otherwise perfectly-conducting interior waveguide walls. An approximate but efficient and accurate ray solution was obtained recently. That solution is presently being extended to the case of a moderately thick dielectric/ferrite coating on the walls so as to be valid for situations where the impedance boundary condition may not remain sufficiently accurate.

Myung, N. H.↗

DOE OSTI2026

Accelerating kinetic plasma simulations with machine-learning-generated initial conditions

Computational models of plasma technologies often solve for the system operating conditions by time-stepping an initial value problem to a quasi-steady solution. However, the strongly nonlinear and multi-timescale nature of plasma dynamics often necessitate millions, or even hundreds of millions, of steps to reach convergence, reducing the effectiveness of these simulations for computer-aided engineering. We consider acceleration of kinetic plasma simulations via data-driven machine-learning-generated initial conditions, which initialize the simulations close to their final quasi-steady-state, thereby reducing the number of steps to reach convergence. Three machine-learning models are developed to predict the density and ion kinetic profiles of capacitively coupled plasma discharges relevant to the microelectronics industry. The models are trained on kinetic simulations over a range of device operating frequencies and pressures. Best performance was observed when simulations were initialized with ion kinetic profiles generated by a convolutional neural network, reducing the mean number of steps to reach convergence by 17.1× when compared to initialization with a zero-dimensional global model. We also outline a workflow for continuous data-driven model improvement and simulation speedup, with the aim of generating sufficient data for full device digital twins.

Artificial neural networks↗

NASA NTRS2011

Thoughts Without Content are Empty, Intuitions Without Concepts are Blind - Determinism and Contingency Revisited

Was the emergence of life a predictable outcome of chemical evolution on earth? Could evolution produce life very different from ours? These are one of the oldest questions in the field of the origin of life that not only have broad philosophical implications but also impact how we approach the problem from the methodological standpoint. Framing the issue in terms of the dichotomy between contingency and determinism is not a fortunate because these two terms in their conventional meaning are neither mutually exclusive nor jointly exhaustive. Determinism, represented in natural sciences by Newtonian physics, relies on the assumption that every event is causally determined by a chain of previous events. In the context of the origin of life it means that once the initial conditions on the early earth have been specified further evolution follows inevitably. Considering uncertainties about conditions on the prebiotic earth, many plausible sets of initial conditions can be defined, each followed by a separate deterministic trajectory. This conventional understanding of determinism does not admit contingency. Further, it has no implications for evaluating how many sets of initial conditions lead to the emergence of life. It appears that a better framing of the problem is as follows: given plausible sets of initial conditions on the early earth how probable and broadly spread are evolutionary trajectories that lead to life? Instead of undertaking an impossible task of specifying microscopic initial conditions for all components of the system one uses a reduced representation of this system and specify only a small set of essential macroscopic parameters, values (or ranges of values) of which can be identified, inferred or estimated from experiment, theory or historical record. The following evolutionary trajectories are still governed by laws of physics and chemistry but become probabilistic and "contingency" is admitted as variations in other variables in the system. A similar reasoning is common in other fields of science, for example in statistical mechanics. Some trajectories lead to life, perhaps in different forms, whereas others do not. Of our true interest is the ratio of these two outcomes. The issue of determinism does not directly enter the picture. The debate about the likelihood of the emergence of life is quite old. One view holds that the origin of life is an event governed by chance, and the result of so many random events (contingencies) is unpredictable. This view was eloquently expressed by Monod. In his book "Chance or Necessity" he argued that life was a product of "nature's roulette." In an alternative view, expressed in particular by deDuve and Morowitz, the origin of life is considered a highly probable or even inevitable event (although its details need not be determined in every respect). Only in this sense the origin of life can be considered a "deterministic event".

Pohorille, Andrew↗