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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

High-Order Mesh hr-adaptivity for Surface Fitting to Implicit Geometries

We present an ℎ𝑟-adaptivity framework for morphing a given mesh to fit a target surface prescribed as the zero isocontour of a discrete function. In this framework, high-order meshing is posed as a variational minimization problem that depends on the mesh quality prescribed via the target matrix optimization paradigm (TMOP) and position of a subset of mesh nodes with respect to the target surface. The proposed formulation ensures that the variational problem is converged and mesh quality degradation near the surface is limited, even when the mesh topology is incompatible with the target surface. Additionally, a mesh subset-based approach and ℎ-refinement is introduced to efficiently increase fitting accuracy while reducing the computational cost of the mesh morphing problem. The ℎ𝑟-adaptivity technique extends to different element types in two- and three-dimensions, and can be used in existing finite element and spectral element frameworks to obtain high-order body-fitted meshes. Various numerical experiments demonstrate the robustness and accuracy of the fitting approach for problems of practical interest such as Lagrangian hydrodynamics and topology optimization.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

Calculation of precision satellite orbits with nonsingular elements /VOP formulation/

Review of some results obtained in an effort to develop efficient, high-precision trajectory computation processes for artificial satellites by optimum selection of the form of the equations of motion of the satellite and the numerical integration method. In particular, the matching of a Gaussian variation-of-parameter (VOP) formulation is considered which is expressed in terms of equinoctial orbital elements and partially decouples the motion of the orbital frame from motion within the orbital frame. The performance of the resulting orbit generators is then compared with the popular classical Cowell/Gauss-Jackson formulation/integrator pair for two distinctly different orbit types - namely, the orbit of the ATS satellite at near-geosynchronous conditions and the near-circular orbit of the GEOS-C satellite at 1000 km.

Velez, C. E.↗
NASA NTRS1992

A variational method for finite element stress recovery: Applications in one-dimension

It is well-known that stresses (and strains) calculated by a displacement-based finite element analysis are generally not as accurate as the displacements. In addition, the calculated stress field is typically discontinuous at element interfaces. Because the stresses are typically of more interest than the displacements, several procedures have been proposed to obtain a smooth stress field, given the finite element stresses, and to improve the accuracy. Hinton and Irons introduced global least squares smoothing of discrete data defined on a plane using a finite element formulation. Tessler and co-workers recently developed a conceptually similar formulation for smoothing of two-dimensional data based on a discrete least square approximation with a penalty constraint. The penalty constraint results in a stress field which is C(exp 1)-continuous, a result not previously obtained. The approach requires additional, 'smoothing' finite element analysis and for their two-dimensional application, they used a conforming C(exp 0)-continuous triangular finite element based on a conforming plate element. This paper presents the results of a detailed investigation into the application of Tessler's smoothing procedure to the smoothing of finite element stresses from one-dimensional problems. Although the one-dimensional formulation has some practical applicability, such as in truss, beam, axisymmetric mechanics, and one-dimensional heat conduction, the primary motivation for developing the one-dimensional smoothing case is to explore the characteristics of the general smoothing strategy. In particular, it is used to describe the behavior of the method and to explore the suitability of criteria proposed for the smoothing analysis. Prior to presenting numerical results, the variational formulation of the smoothing strategy is presented and a criterion for the smoothing analysis is described.

Riggs, H. Ronald↗
NASA NTRS1994

Advanced data assimilation in strongly nonlinear dynamical systems

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Miller, Robert N.↗
DOE OSTI2021

Fully variational incremental CASSCF

We report the complete-active-space self-consistent field (CASSCF) method is a canonical electronic structure theory that holds a central place in conceptualizing and practicing first principles simulations. For application to realistic molecules, however, the CASSCF must be approximated to circumvent its exponentially scaling computational costs. Applying the many-body expansion - also known as the method of increments - to CASSCF (iCASSCF) has been shown to produce a polynomially scaling method that retains much of the accuracy of the parent theory and is capable of treating full valence active spaces. Due to an approximation made in the orbital gradient, the orbital parameters of the original iCASSCF formulation could not be variationally optimized, which limited the accuracy of its nuclear gradient. Herein, a variational iCASSCF is introduced and implemented, where all parameters are fully optimized during energy minimization. This method is able to recover electronic correlations from the full valence space in large systems, produce accurate gradients, and optimize stable geometries as well as transition states. Demonstrations on challenging test cases, such as the oxoMn(salen)Cl complex with 84 electrons in 84 orbitals and the automerization of cyclobutadiene, show that the fully variational iCASSCF is a powerful tool for describing challenging molecular chemistries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1987

Equation-of-state spinning fluids in the Einstein-Cartan theory

The relativistic fluid equations may be completed in two physically distinct methods. One method assumes the mass, rho, (or particle number) is conserved, while the other method assumes an equation of state of the form P = P(rho). A variational principle for the mass conservation method both with and without an intrinsic spin for the fluid was constructed earlier (Ray and Smalley, 1982 and 1983). A variational principle for the fluid described by an equation of state both with and without spin is formulated. In all cases the variational principle is set in the Einstein-Cartan metric-torsion U4 geometry. The results for general relativity follow as a special case.

Ray, John R.↗
NASA NTRS1971

A Stability Analysis of Cylindrical Panels Using a Finite Element Formulation

A cylindrical finite element suitable for the linear stability analysis of cylindrical shells is developed. Energy principles and variational methods lead to a problem formulation which lends itself to physical interpretations of the governing matrices of the finite element. By properly grouping the terms which result from taking the second variation of the potential energy of the element, it is possible to identify three distinct types of matrices. The first matrix is the conventional stiffness matrix; the second is an initial stress stiffness matrix; and the third is an initial displacement stiffness matrix. With the assumption of linearity, the buckling problem is stated in terms of the classical linear real eigenvalue equation. This problem formulation was programmed on the CDC 6600 series computer. The computer program is used to analyze the buckling of a variety of structures. Columns, arches, flat plates and curved panels with and without cutouts are considered.

Snyder, R. E.↗
DOE OSTI2021

Extending a 10‐node composite tetrahedral finite element for solid mechanics

Abstract We propose to extend the composite tetrahedral finite element first introduced by Thoutireddy et al. (2002) and recently reformulated by Ostien et al. (2016). We generalize the gradient operator and mass matrix to curved domains through analytical expressions weighted by subtetrahedra Jacobians. Optimal integration weights are constructed to increase the accuracy of Gaussian quadrature. We preserve the variational structure of the formulation through a new five‐field functional with additional, independent fields for the Jacobian and the pressure. This approach not only obviates volumetric locking but also yields symmetry. A deleterious soft mode, common to both the quadratic and composite tetrahedral element with constant pressure formulations is effectively stabilized through a novel convex energy penalty function. Numerous numerical examples spanning a patch test to the impact of a Taylor bar demonstrate the accuracy, robustness, and convergence of the extended composite tetrahedral element for application to structural metals.

Foulk III, James W.↗
DOE OSTI2024

Scalable semidefinite programming approach to variational embedding for quantum many-body problems

In quantum embedding theories, a quantum many-body system is divided into localized clusters of sites which are treated with an accurate ‘high-level’ theory and glued together self-consistently by a less accurate ‘low-level’ theory at the global scale. The recently introduced variational embedding approach for quantum many-body problems combines the insights of semidefinite relaxation and quantum embedding theory to provide a lower bound on the ground-state energy that improves as the cluster size is increased. The variational embedding method is formulated as a semidefinite program (SDP), which can suffer from poor computational scaling when treated with black-box solvers. Here, we exploit the interpretation of this SDP as an embedding method to develop an algorithm which alternates parallelizable local updates of the high-level quantities with updates that enforce the low-level global constraints. Moreover, we show how translation invariance in lattice systems can be exploited to reduce the complexity of projecting a key matrix to the positive semidefinite cone.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Scalable Multiphysics Block Preconditioning for Low Mach Number Compressible Resistive MHD with Application to Magnetic Confinement Fusion

This study investigates multiphysics block preconditioners that are critical in devising scalable Newton–Krylov iterative solvers for longer time-scale fully implicit fluid plasma models. The specific model of interest is the visco-resistive, low Mach number, compressible magnetohydrodynamics (MHD) model. This model describes the dynamics of conducting fluids in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics. The specific application of interest that motivates this study is the macroscopic simulation of longer time-scale stability and disruptions of magnetic confinement fusion devices, specifically the ITER Tokamak. The computational solution of the governing balance equations for mass, momentum, heat transfer, and magnetic induction for resistive MHD systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena as well as the significant range of time and length scales that the interactions of these physical mechanisms produce. To handle the range of time and spatial scales of interest, a fully implicit unstructured variational multiscale finite element formulation is employed. For the scalable solution of the Newton linearized systems, fully coupled block preconditioners are designed to leverage algebraic multigrid subsolves. In conclusion, results are presented for the strong and weak scaling of the method as well as the robustness of these techniques for a large range of Lundquist numbers.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Void growth in an elastic-plastic medium.

The uniaxial deformation of an elastic-plastic medium containing a doubly periodic square array of circular cylindrical voids is studied under plane-strain conditions. Both the effects of geometrical nonlinearities resulting from large deformation and physical nonlinearities arising from plastic material behavior are included in formulating the problem. A variational principle is used as the basis for implementing a finite-element solution. Results are obtained for the change in void shape and size under increasing overall strain, the overall tensile behavior of the material with voids, and the development of the plastic zone about a void.

Needleman, A.↗
NASA NTRS1974

Vehicle control for fuel optimization

The problem of predicting the minimum fuel trajectory for a six degree of freedom vehicle which has a motion characterized by the first order differential equations of translational and rotational dynamics is considered. The thrust direction and center of gravity of the vehicle are assumed to be fixed with respect to the vehicle. Thrust magnitude and the control moment are used as control variables and appear linearly in the equation of motion. Pontryagin's Maximum Principle is used to solve the variational problem. With this formulation, the extremal controls are bang-bang with the exception of the singular case.

Dannenberg, K. D.↗
NASA NTRS1974

A dual extremum principle for a population equation

A dual extremum principle for the Verhulst-Pearl population equation is constructed using a complementary variational technique. The dual formulation utilizes a minimum principle recently developed by Leitmann to convert the functional optimization problem into a parameter optimization problem.

Chan, W. L.↗
NASA NTRS1976

A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique

The equations of radiative transfer in anisotropically scattering media are reformulated as linear operator equations in a single independent variable. The resulting equations are suitable for solution by a variety of standard mathematical techniques. The operators appearing in the resulting equations are in general nonsymmetric; however, it is shown that every bounded linear operator equation can be embedded in a symmetric linear operator equation and a variational solution can be obtained in a straightforward way. For purposes of demonstration, a Rayleigh-Ritz variational method is applied to three problems involving simple phase functions. It is to be noted that the variational technique demonstrated is of general applicability and permits simple solutions for a wide range of otherwise difficult mathematical problems in physics.

Cheyney, H., III↗
NASA NTRS1976

Optimal perturbation models for averaged orbit generation

Averaging techniques applied to the variation of parameters (VOP) formulation of the equations of motion are being investigated as methods for long-term prediction of artificial satellite orbits. Analytically averaged equations were compared with numerically averaged equations with respect to accuracy and efficiency for computation of zonal and nonresonant third-body perturbations. Numerically averaged equations were also evaluated for computation of long-period effects from resonant third-body, tesseral harmonic, and atmospheric drag perturbations. Guidelines will be presented for application of averaged VOP equations to a broad class of orbits.

Long, A. C.↗
NASA NTRS1979

Antenna feedhorn software upgrade

The HYBRIDHORN computer program was developed to serve as an item of general purpose antenna feedhorn design and analysis software. The formulation contains a small flare angle approximation which is subject to question for designs such as the S- and X-band feedhorn. Additionally, the original formulation did not allow azimuthal variation indexes other than unity. The HYBRIDHORN program was upgraded to correct both of these deficiencies. A large flare angle formulation was found. In the upgrade, all of the major program elements were converted to Univac 1108 compatible structured FORTRAN (SFTRAN) for ease of software maintenance. The small and large angle formulations are described and sample numerical results are presented.

Potter, P. D.↗
NASA NTRS1981

On Hybrid and mixed finite element methods

Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.

Pian, T. H. H.↗
NASA NTRS1986

A higher order theory of laminated composite cylindrical shells

A new higher order theory has been proposed for the analysis of composite cylindrical shells. The formulation allows for arbitrary variation of inplane displacements. Governing equations are presented in the form of a hierarchy of sets of partial differential equations. Each set describes the shell behavior to a certain degree of approximation. The natural frequencies of simply-supported isotropic and laminated shells and stresses in a ring loaded composite shell have been determined to various orders of approximation and compared with three dimensional solutions. These numerical studies indicate the improvements achievable in estimating the natural frequencies and the interlaminar shear stresses in laminated composite cylinders.

Krishna Murthy, A. V.↗