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DOE OSTI2020

Functional equations and separation of variables for exact g -function

The g-function is a measure of degrees of freedom associated to a boundary of two-dimensional quantum field theories. In integrable theories, it can be computed exactly in a form of the Fredholm determinant, but it is often hard to evaluate numerically. In this paper, we derive functional equations — or equivalently integral equations of the thermodynamic Bethe ansatz (TBA) type — which directly compute the g-function in the simplest integrable theory; the sinh-Gordon theory at the self-dual point. The derivation is based on the classic result by Tracy and Widom on the relation between Fredholm determinants and TBA, which was used also in the context of topological string. We demonstrate the efficiency of our formulation through the numerical computation and compare the results in the UV limit with the Liouville CFT. As a side result, we present multiple integrals of Q-functions which we conjecture to describe a universal part of the g-function, and discuss its implication to integrable spin chains.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1978

User's Manual for Thermal Analysis Program of Axially Grooved Heat Pipe (HTGAP)

A computer program that numerically predicts the steady state temperature distribution inside an axially grooved heat pipe wall for a given groove geometry and working fluid under various heat input and output modes is described. The program computes both evaporator and condenser film coefficients. The program is able to handle both axisymmetric and nonaxisymmetric heat transfer cases. Non-axisymmetric heat transfer results either from non-uniform input at the evaporator or non-uniform heat removal from the condenser, or from both. The presence of a liquid pool in the condenser region under one-g condition also causes non-axisymmetric heat transfer, and its effect on the pipe wall temperature distribution is included in the present program. The hydrodynamic aspect of an axially grooved heat pipe is studied in the Groove Analysis Program (GAP). The present thermal analysis program assumes that the GAP program (or other similar programs) is run first so that the heat transport limit and optimum fluid charge of the heat pipe are known a priori.

Kamotani, Y.↗

DOE OSTI2025

Enhancing the accuracy of XPS calculations: Exploring hybrid basis set schemes for CVS-EOMIP-CCSD calculations

Reliable computational methodologies and basis sets for modeling x-ray spectra are essential for extracting and interpreting electronic and structural information from experimental x-ray spectra. In particular, the trade-off between numerical accuracy and computational cost due to the size of the basis set is a major challenge, since molecular orbitals undergo extreme relaxation in the core-hole state. To gain clarity on the changes in electronic structure induced by the formation of a core-hole, the use of sufficiently flexible basis for expanding the orbitals, particularly for the core region, has been shown to be essential. This work focuses on the refinement of core-hole ionized state calculations using the equation-of-motion coupled cluster family of methods through an extensive analysis on the effectiveness of “hybrid” and mixed basis sets. In this investigation, we utilize the CVS-EOMIP-CCSD method in combination and construct hybrid basis sets piecewise from readily available Dunning’s correlation consistent basis sets in order to calculate x-ray ionization energies (IEs) for a set of small gas phase molecules. Our results provide insights into the impact of basis sets on the CVS-EOMIP-CCSD calculations of K-edge IEs of first-row p-block elements. Furthermore, these insights enable us to understand more about the basis set dependence of the core IEs computed and allow us to establish a protocol for deriving reliable and cost-effective theoretical estimates for computing IEs of small molecules containing such elements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1973

Orbit improvement from satellite imaging data obtainable from outer planet missions.

Equations of motion are established for a dynamical system in which a spacecraft flies close to and interacts with an outer planet and one or more of its satellites. For the computation of the state and mass partials needed in a simultaneous orbit correction of n interacting bodies, a notably compact set of variational equations is derived. The above system of differential equations is integrated numerically on a computer. Spacecraft-satellite direction measurements accurate to plus or minus 10 sec were simulated along three representative trajectories (Mariner/Jupiter/Saturn 1977 missions) approaching Io, Titan, and Iapetus to within 41000, 13000, and 7000 km, respectively. The paper concludes with a brief discussion of the need for future work on the orbits of the satellites of the outer planets.

Aksnes, K.↗

NASA NTRS1993

A numerical implementation of MHD in divergence form

Shock computations are presently undertaken by a numerical implementation of fully relativistic MHD in divergence form, as illustrated by pseudospectral-method computations for the coplanar Riemann MHD problem. Compound waves are noted to persist in relativistic MHD. Attention is given to two limiting cases: (1) where the velocities become nonrelativistic, and (2) where the longitudinal magnetic field becomes zero. Comparisons are made with results for both the singular case of zero longitudinal magnetic field, and nonrelativistic MHD.

Van Putten, Maurice H. P. M.↗

DOE OSTI2021

Validation of numerical models for seismic fluid-structure-interaction analysis of nuclear, safety-related equipment

Seismic design, qualification, and risk assessment of nuclear safety-related vessels filled with liquid will have to consider the interaction between the vessel (tank), the contained liquid, and submerged components, if any. Seismic fluid-structure-interaction (FSI) analysis of nuclear vessels will rely on numerical models, which are required to be verified and validated. This study validates previously-verified numerical models using test data generated from earthquake-simulator experiments involving a cylindrical tank. Two solvers in LS-DYNA for FSI simulations are used for the numerical analysis: Arbitrary-Lagrangian-Eulerian (ALE) and Incompressible Computational Fluid Dynamics (ICFD). Numerical and test results are compared for responses critical to seismic design of advanced reactor vessels: hydrodynamic pressures on the tank wall, reactions at the support, and wave heights of the contained liquid. Analysis is performed for one-, two-, and three-directional seismic inputs with a range of intensity, and rocking motions. The accuracy of the numerical results and different methods for outputting wave heights are discussed. Recommendations for validation of seismic FSI numerical models of advanced reactors are provided. As a result, the validation exercise presented in this study is broadly applicable to cylindrical tanks, regardless of industry sector.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

NASA NTRS1977

Combustion of hydrogen injected into a supersonic airstream (the SHIP computer program)

The mathematical and physical basis of the SHIP computer program which embodies a finite-difference, implicit numerical procedure for the computation of hydrogen injected into a supersonic airstream at an angle ranging from normal to parallel to the airstream main flow direction is described. The physical hypotheses built into the program include: a two-equation turbulence model, and a chemical equilibrium model for the hydrogen-oxygen reaction. Typical results for equilibrium combustion are presented and exhibit qualitatively plausible behavior. The computer time required for a given case is approximately 1 minute on a CDC 7600 machine. A discussion of the assumption of parabolic flow in the injection region is given which suggests that improvement in calculation in this region could be obtained by use of the partially parabolic procedure of Pratap and Spalding. It is concluded that the technique described herein provides the basis for an efficient and reliable means for predicting the effects of hydrogen injection into supersonic airstreams and of its subsequent combustion.

Markatos, N. C.↗

NASA NTRS1985

An Eigensystem Realization Algorithm for Application to Modal Testing

Important features of the Eigensystem Realization Algorithm (ERA) are summarized as follows: (1) from the computational standpoint, the algorithm is attractive, since only simple numerical operations are needed; (2) the computational procedure is numerically stable; (3) the structural dynamics requirements for modal parameter identification and the control design requirements for a reduced-state space model are satisfied; (4) data from more than one test can be used simultaneously to efficiently identify the closely spaced eigenvalues; and (5) no restrictions on number of measurements are imposed.

Juang, J. N.↗

NASA NTRS2000

Determination of the Fracture Parameters in a Stiffened Composite Panel

A modified J-integral, namely the equivalent domain integral, is derived for a three-dimensional anisotropic cracked solid to evaluate the stress intensity factor along the crack front using the finite element method. Based on the equivalent domain integral method with auxiliary fields, an interaction integral is also derived to extract the second fracture parameter, the T-stress, from the finite element results. The auxiliary fields are the two-dimensional plane strain solutions of monoclinic materials with the plane of symmetry at x(sub 3) = 0 under point loads applied at the crack tip. These solutions are expressed in a compact form based on the Stroh formalism. Both integrals can be implemented into a single numerical procedure to determine the distributions of stress intensity factor and T-stress components, T11, T13, and thus T33, along a three-dimensional crack front. The effects of plate thickness and crack length on the variation of the stress intensity factor and T-stresses through the thickness are investigated in detail for through-thickness center-cracked plates (isotropic and orthotropic) and orthotropic stiffened panels under pure mode-I loading conditions. For all the cases studied, T11 remains negative. For plates with the same dimensions, a larger size of crack yields larger magnitude of the normalized stress intensity factor and normalized T-stresses. The results in orthotropic stiffened panels exhibit an opposite trend in general. As expected, for the thicker panels, the fracture parameters evaluated through the thickness, except the region near the free surfaces, approach two-dimensional plane strain solutions. In summary, the numerical methods presented in this research demonstrate their high computational effectiveness and good numerical accuracy in extracting these fracture parameters from the finite element results in three-dimensional cracked solids.

Lin, Chung-Yi↗

DOE OSTI2020

A numerical-homogenization based phase-field fracture modeling of linear elastic heterogeneous porous media

Most porous media, such as geomaterials and biomaterials are highly heterogeneous in nature, and they contain large variations of microscopic pore structures, such as pore sizes, pore distribution, and pore shapes. The oscillation of microscopic structures is a substantial challenge in theoretical characterization and is usually ignored in continuous modeling. However, mechanical behavior of porous media such as deformation and failure, are essentially impacted by the microscopic heterogeneity which needs to be considered in modeling a porous media. Here, this research proposes a numerical modeling framework with a capability to investigate the effect of microscopic heterogeneity on the macroscopic fracture behavior in porous media by using a numerical homogenization technique, combined with the phase-field fracture modeling method. This numerical modeling strategy computes a homogenized elasticity tensor based on microscopic heterogeneous pore structures heterogenous porous domain by solving boundary value problems at microscopic domain. The strain energy and subsequent propagation of macroscopic fractures will be updated using homogenized stiffness information. Using this numerical scheme, the microscopic pore structure’s impact on the fracture behavior through the homogenized elastic tensor will be taken into account. This multiscale technique is benchmarked against classical problems. Finally, the results highlight the importance of the underlying pore structure and reveal that both fracture strength and propagation path can be influenced by the microscopic heterogeneity.

36 MATERIALS SCIENCE↗

NASA NTRS1996

Computation of Static Shapes and Voltages for Micromachined Deformable Mirrors with Nonlinear Electrostatic Actuators

In modeling micromachined deformable mirrors with electrostatic actuators whose gap spacings are of the same order of magnitude as those of the surface deformations, it is necessary to use nonlinear models for the actuators. In this paper, we consider micromachined deformable mirrors modeled by a membrane or plate equation with nonlinear electrostatic actuator characteristics. Numerical methods for computing the mirror deformation due to given actuator voltages and the actuator voltages required for producing the desired deformations at the actuator locations are presented. The application of the proposed methods to circular deformable mirrors whose surfaces are modeled by elastic membranes is discussed in detail. Numerical results are obtained for a typical circular micromachined mirror with electrostatic actuators.

Wang, P. K. C.↗

NASA NTRS1981

On the interaction of a sound pulse with the shear layer of an axisymmetric jet

The behavior of a sound pulse from a simulated source in a jet is investigated both experimentally and numerically. Both approaches show that in the low and medium frequencies the far field acoustic power exhibits and marked amplification as the flow velocity increases. Experimentally this changes to an attenuation at the higher frequencies which cannot be computed by the numerical model. This amplification is traced to shear noise terms which trigger the instability waves that are inherent within the flow.

Maestrello, L.↗

NASA NTRS2015

Polarized Bidirectional Reflectance of Optically Thick Sparse Particulate Layers: an Efficient Numerically Exact Radiative-Transfer Solution

We describe a simple yet efficient numerical algorithm for computing polarized bidirectional reflectance of an optically thick (semi-infinite), macroscopically flat layer composed of statistically isotropic and mirror symmetric random particles. The spatial distribution of the particles is assumed to be sparse, random, and statistically uniform. The 44 Stokes reflection matrix is calculated by iterating the Ambartsumian's vector nonlinear integral equation. The result is a numerically exact solution of the vector radiative transfer equation and as such fully satisfies the energy conservation law and the fundamental reciprocity relation. Since this technique bypasses the computation of the internal radiation field, it is very fast and highly accurate. The FORTRAN implementation of the technique is publicly available on the World Wide Web at http://www.giss.nasa.gov/staff/ mmishchenko/brf. It can be combined with several existing computer programs providing the requisite single-scattering properties of spherical or morphologically complex particles and applied to a wide range of optical characterization problems. Benchmark results obtained with this program can be used for testing alternative solvers of the vector radiative transfer equation.

radiative transfer↗

DOE OSTI2023

Simulation toolkit for digital material characterization of large image-based microstructures

In this paper, an efficient image-based simulation toolkit for material characterization is presented, which is scalable to work from personal computers to workstations. The effective thermal conductivity, elasticity, and permeability are evaluated employing a computational homogenization framework based on the Finite Element Method (FEM). Two complementary open-source packages are presented: one developed in Python, which can convert digital images into voxel meshes (pyTomoviewer); the other developed in Julia, that can run numerical simulations to compute effective material properties (chpack). Also, a CUDA C version of chpack is provided (chfem_gpu). They were designed to deal with large multi-phase models, so strategies were devised to minimize their memory footprint, while avoiding a high toll on execution time. The voxel-based approach significantly simplifies the FEM meshes and allows efficient matrix-free implementations. In that sense, to handle large linear systems of equations, the element-by-element (EBE) technique is adopted, in conjunction with a low-memory implementation of the Preconditioned Conjugate Gradient (PCG) method. Finally, the code was thoroughly tested on an artificial geometry made of a square array of cylinders, for which analytical solutions exist, as well as on a real micro-tomographic reconstruction of FiberForm TM , a carbon preform commonly used in thermal protection systems.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Progress on Understanding Rayleigh–Taylor Flow and Mixing Using Synergy Between Simulation, Modeling, and Experiment

Simultaneous advances in numerical methods and computing, theoretical techniques, and experimental diagnostics have all led independently to better understanding of Rayleigh–Taylor (RT) instability, turbulence, and mixing. In particular, experiments have provided significant motivation for many simulation and modeling studies, as well as validation data. Numerical simulations have also provided data that is not currently measurable or very difficult to measure accurately in RT unstable flows. Thus, simulations have also motivated new measurements in this class of buoyancy-driven flows. This overview discusses simulation and modeling studies synergistic with experiments and examples of how experiments have motivated simulations and models of RT instability, flow, and mixing. First, a brief summary of measured experimental and calculated simulation quantities, of experimental approaches, and of issues and challenges in the simulation and modeling of RT experiments is presented. Implicit large-eddy, direct numerical, and large-eddy simulations validated using RT experimental data are then discussed. This is followed by a discussion of modeling using analytical, modal, buoyancy–drag, and turbulent transport models of RT mixing experiments. The discussion will focus on three-dimensional RT mixing arising from multimode perturbations. Finally, this focused review concludes with a perspective on future simulation, modeling, and experimental directions for further research. Research in simulation and modeling of RT unstable flows, coupled with experiments, has made significant progress over the past several decades. This overview serves as an opportunity to both discuss progress and to stimulate future research on simulation and modeling of this unique class of hydrodynamically unstable turbulent flows.

42 ENGINEERING↗

NASA NTRS1985

Putting the 'super' in supercomputers

Computers used for numerical simulations of physical phenomena, e.g., flowfields, meteorology, structural analysis, etc., replace physical experiments that are too expensive or impossible to perform. The problems considered continually become increasingly more complex and thus demand faster processing times to do all necessary computations. The effects components technologies have on computer speed are leveling off, leaving new architectures and programming as the only currently viable means to upgrade speed. Parallel computations, either in the form of array processors, assembly line processing or multiprocessors are being explored using existing microprocessor technologies. Slower hardware configurations can also be made equivalent to faster supercomputers by economic programming. The availability of rudimentary parallel architecture supercomputers for general industrial use is increasing. Scientific applications continue to drive the development of more sophisticated parallel machines.

Schulbach, C.↗

DOE OSTI2020

An Eulerian multimaterial framework for simulating high-explosive aquarium tests

Aquarium tests of cylindrical high-explosive charges provide optical data of the detonation front velocity and shape, propagation of the shock wave in the surrounding water, and expansion rates of the detonation products behind the front. Data from aquarium experiments is often used for calibration of reactive burn models based on phenomenological equations of state (EOS) and reaction rate laws. This paper presents a multimaterial numerical modeling framework to solve the 2D axisymmetric reactive Euler equations for high-explosive aquarium tests, in particular for ammonium nitrate - fuel oil (ANFO) explosives. An extension of the Ghost Fluid Method (GFM) is used to handle the dynamic material interfaces for the ANFO explosion products, the charge-confining material (polymethyl methacrylate PMMA), and the surrounding water. This study analyzes the sensitivity of calculations (both computational efficiency and numerical accuracy) to different algorithms for the material interface models including the original GFM versus Riemann solver-based strategies. A novel method for defining the left and right states in the interfacial Riemann problem eliminates the need for sorting or nodal interpolation during the projection along the material interface. Numerical tests indicate that populating the interface node values using the Riemann solution mitigate the overheating error observed in steady-state calculations. Solution convergence and computational efficiency are explored as a function of the spatial and temporal order of the schemes. Results from the computational model with analytical equations of state and fitted reaction rate parameters show very good quantitative agreement with experimentally observed detonation front velocity, reaction products expansion, and shock wave propagation in the surrounding water for a cylindrical ANFO charge encased in PMMA. Finally, the proposed modeling framework, in conjunction with experimental tests, provides a reliable tool to assess equations of state and reaction rate expressions for reactive burn models of confined high explosives.

42 ENGINEERING↗

NASA NTRS1972

Orbit improvement from satellite imaging data obtainable from the Mariner/Jupiter/Saturn 1977 missions

Equations of motion are established for a dynamic system in which a spacecraft flies close to and interacts with an outer planet and one or more of its satellites. For the computation of the state and mass partials needed in the orbit corrections, a set of variational equations is derived. These assume a notably compact form through the introduction of a matrix operator D. The above system of differential equations is integrated numerically on a computer.

Aksnes, K.↗