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Mechanics of Structure Genome-Based Nonlinear Shell Analysis

In this paper, a mechanics of structure genome (MSG)-based nonlinear shell theory is introduced. The theory uses an implicit algorithm combining the Euler’s and Newton’s method that can be applied for shell modeling as well as 3D homogenization. This theory has been implemented into the general-purpose constitutive modeling code SwiftComp, which was originally developed for linear analyses. For the convenience of implementing different nonlinear material models, the SwiftComp user material (SCUMAT), which has a similar interface to the Abaqus user subroutine UMAT, is developed. The capability of the MSG-based nonlinear shell is validated with numerical examples with different material models. A 2-step nonlinear homogenization, with a micromechanics step and a shell analysis step, is demonstrated.

Yufei Long↗

NASA NTRS1991

Implicit solution of three-dimensional internal turbulent flows

The scalar form of the approximate factorization method was used to develop a new code for the solution of three dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form were iterated in time until a steady solution was reached. Evidence was given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at the domain boundaries was proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects were accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. The flow in a developing S-duct was then solved in the laminar regime in a Reynolds number (Re) of 790 and in the turbulent regime at Re equals 40,000 by using the Baldwin-Lomax model. The Stanitz elbow was then solved by using an invicid version of the same code at M sub inlet equals 0.4. Grid dependence and convergence rate were investigated, showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re equals 2.5 times 10(exp 6) was solved with the Baldwin-Lomax and the q-omega models. Both approaches show satisfactory agreement with experiments, although the q-omega model was slightly more accurate.

Michelassi, V.↗

NASA NTRS1990

Implicit solution of three-dimensional internal turbulent flows

The scalar form of the approximate factorization method was used to develop a new code for the solution of three-dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form are iterated in time until a steady solution is reached. Evidence is given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at domain boundaries is proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects are accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. For the first, an investigation on the model behavior in case of multiple boundaries is performed. The flow in a developing S-duct is then solved in the laminar regime at Reynolds number (Re) 790 and in the turbulent regime at Re=40,000 using the Baldwin-Lomax model . The Stanitz elbow is then solved using an inviscid version of the same code at M(sub inlet)=0.4. Grid dependence and convergence rate are investigated showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re=2.5x10(exp 6) is solved with the Baldwin-Lomax and the q-omega models. Both approaches showed satisfactory agreement with experiments, although the q-omega model is slightly more accurate.

Michelassi, V.↗

DOE OSTI2026

Confinement and String Breaking in the Compact Abelian Higgs Model

While real-time simulation of Quantum Chromodynamics remains technologically out of reach, simplified models for studying elements of QCD phenomenology abound. This work presents a simple model, a spin-1 truncation of the Compact Abelian Higgs Model simulated on qutrit sites, in which confinement and string breaking is accessible to current simulation methods. In the low-energy regime of 1+1D scalar electrodynamics, the heavy modes are integrated out, producing a spin chain effective Hamiltonian in which Gauss' law is implicitly satisfied. We study the spectrum of string-like excitations using DMRG methods on the order of 100 sites. We demonstrate that an added, local chemical potential, playing a role analogous to external charges, permits parameter-dependent measurements of physical features of interest like the string tension and effective meson mass. Varying the chemical potential also permits a characterization of string stability not assessed in prior studies of confining lattice models.

Senseman, Blake [Iowa U.]↗

NASA NTRS1982

Development of mixed time partition procedures for thermal analysis of structures

The computational methods used to predict and optimize the thermal-structural behavior of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a difficult yet critical factor in the efficient solution of such problems. Therefore mixed time integration methods for transient thermal analysis of structures are being developed. This proposed methodology would be readily adaptable to existing computer programs for structural thermal analysis.

Liu, W. K.↗

NASA NTRS1971

Implicit determination of multispectral scanner data variation over extended areas.

Description of a method by which variations in aerial multispectral scanner data can be accounted for when there is insufficient ground truth information. The data are suitably filtered and smoothed along the flight line, and the reduced results are presented in a form such that the investigator can readily determine the preprocessing that should be used and the spatial extent to which it should be applied. An algorithm is developed for the detection of cloud-shadowed areas.

Kriegler, F. J.↗

NASA NTRS2012

Measurement System Characterization in the Presence of Measurement Errors

In the calibration of a measurement system, data are collected in order to estimate a mathematical model between one or more factors of interest and a response. Ordinary least squares is a method employed to estimate the regression coefficients in the model. The method assumes that the factors are known without error; yet, it is implicitly known that the factors contain some uncertainty. In the literature, this uncertainty is known as measurement error. The measurement error affects both the estimates of the model coefficients and the prediction, or residual, errors. There are some methods, such as orthogonal least squares, that are employed in situations where measurement errors exist, but these methods do not directly incorporate the magnitude of the measurement errors. This research proposes a new method, known as modified least squares, that combines the principles of least squares with knowledge about the measurement errors. This knowledge is expressed in terms of the variance ratio - the ratio of response error variance to measurement error variance.

Commo, Sean A.↗

NASA NTRS2005

Efficient Credit Assignment through Evaluation Function Decomposition

Evolutionary methods are powerful tools in discovering solutions for difficult continuous tasks. When such a solution is encoded over multiple genes, a genetic algorithm faces the difficult credit assignment problem of evaluating how a single gene in a chromosome contributes to the full solution. Typically a single evaluation function is used for the entire chromosome, implicitly giving each gene in the chromosome the same evaluation. This method is inefficient because a gene will get credit for the contribution of all the other genes as well. Accurately measuring the fitness of individual genes in such a large search space requires many trials. This paper instead proposes turning this single complex search problem into a multi-agent search problem, where each agent has the simpler task of discovering a suitable gene. Gene-specific evaluation functions can then be created that have better theoretical properties than a single evaluation function over all genes. This method is tested in the difficult double-pole balancing problem, showing that agents using gene-specific evaluation functions can create a successful control policy in 20 percent fewer trials than the best existing genetic algorithms. The method is extended to more distributed problems, achieving 95 percent performance gains over tradition methods in the multi-rover domain.

Agogino, Adrian↗

NASA NTRS1992

Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate

Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.

Joslin, Ronald D.↗

NASA NTRS1995

Flow simulations about steady-complex and unsteady moving configurations using structured-overlapped and unstructured grids

The limiting factor in simulating flows past realistic configurations of interest has been the discretization of the physical domain on which the governing equations of fluid flow may be solved. In an attempt to circumvent this problem, many Computational Fluid Dynamic (CFD) methodologies that are based on different grid generation and domain decomposition techniques have been developed. However, due to the costs involved and expertise required, very few comparative studies between these methods have been performed. In the present work, the two CFD methodologies which show the most promise for treating complex three-dimensional configurations as well as unsteady moving boundary problems are evaluated. These are namely the structured-overlapped and the unstructured grid schemes. Both methods use a cell centered, finite volume, upwind approach. The structured-overlapped algorithm uses an approximately factored, alternating direction implicit scheme to perform the time integration, whereas, the unstructured algorithm uses an explicit Runge-Kutta method. To examine the accuracy, efficiency, and limitations of each scheme, they are applied to the same steady complex multicomponent configurations and unsteady moving boundary problems. The steady complex cases consist of computing the subsonic flow about a two-dimensional high-lift multielement airfoil and the transonic flow about a three-dimensional wing/pylon/finned store assembly. The unsteady moving boundary problems are a forced pitching oscillation of an airfoil in a transonic freestream and a two-dimensional, subsonic airfoil/store separation sequence. Accuracy was accessed through the comparison of computed and experimentally measured pressure coefficient data on several of the wing/pylon/finned store assembly's components and at numerous angles-of-attack for the pitching airfoil. From this study, it was found that both the structured-overlapped and the unstructured grid schemes yielded flow solutions of comparable accuracy for these simulations. This study also indicated that, overall, the structured-overlapped scheme was slightly more CPU efficient than the unstructured approach.

Newman, James C., III↗

NASA NTRS1981

Recent advances in the development of implicit schemes for the equations of fluid dynamics

Innovations and extensions of implicit schemes for equations of fluid dynamics are presented. The notation and theory for linear multistep methods are reviewed, and extensions of work by Beam and Warming (1979) include the implementation of one-leg methods, ADI methods for equations with mixed derivatives, flux vector splitting, the P-dimensional wave equation, and boundary conditions. Numerical experiments indicate that implicit treatment of the boundary conditions is necessary for unconditional stability, and the improvement and implementation of the boundary condition theory should improve the implicit algorithms for gas dynamic equations.

Warming, R. F.↗

DOE OSTI2025

Fast HARDI Uncertainty Quantification and Visualization with Spherical Sampling

In this paper, we study uncertainty quantification and visualization of orientation distribution functions (ODF), which corresponds to the diffusion profile of high angular resolution diffusion imaging (HARDI) data. The shape inclusion probability (SIP) function is the state‐of‐the‐art method for capturing the uncertainty of ODF ensembles. The current method of computing the SIP function with a volumetric basis exhibits high computational and memory costs, which can be a bottleneck to integrating uncertainty into HARDI visualization techniques and tools. We propose a novel spherical sampling framework for faster computation of the SIP function with lower memory usage and increased accuracy. In particular, we propose direct extraction of SIP isosurfaces, which represent confidence intervals indicating spatial uncertainty of HARDI glyphs, by performing spherical sampling of ODFs. Our spherical sampling approach requires much less sampling than the state‐of‐the‐art volume sampling method, thus providing significantly enhanced performance, scalability, and the ability to perform implicit ray tracing. Our experiments demonstrate that the SIP isosurfaces extracted with our spherical sampling approach can achieve up to 8164× speedup, 37282× memory reduction, and 50.2% less SIP isosurface error compared to the classical volume sampling approach. We demonstrate the efficacy of our methods through experiments on synthetic and human‐brain HARDI datasets.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

One-sweep moment-based semi-implicit-explicit integration for gray thermal radiation transport

Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT is coupled to other physics such as hydrodynamics, plasmas, etc., and the timescales one is interested in capturing are often much slower than the radiation timescale. As a result, TRT is treated implicitly, and due to its stiffness and high dimensionality, is often a dominant computational cost in multiphysics simulations. Here we develop a new approach for implicit-explicit (IMEX) integration of gray TRT in the deterministic SN setting, which requires only one sweep per stage, with the simplest first-order method requiring only one sweep per time step. The partitioning of equations is done via a moment-based high-order low-order formulation of TRT, where the streaming operator and first two moments are used to capture the asymptotic stiff regimes of the streaming limit and diffusion limit. Absorption-reemission is treated explicitly, and although stiff, is sufficiently damped by the implicit solve that we achieve stable accurate time integration without incorporating the coupling of the high order and low order equations implicitly. Due to nonlinear coupling of the high-order and low-order equations through temperature-dependent opacities, to facilitate IMEX partitioning and higher-order methods, we use a semi-implicit integration approach amenable to nonlinear partitions. In conclusion, results are demonstrated on thick Marshak and crooked pipe benchmark problems, demonstrating orders of magnitude improvement in accuracy and wallclock compared with the standard first-order implicit integration typically used.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1992

Navier-Stokes analysis of three-dimensional unsteady flows inside turbine stages

This study presents a numerical method for solving the 3D Navier-Stokes equations for unsteady, viscous flow through multiple turbomachinery blade rows. The method solves the fully 3D Navier-Stokes equations with an implicit scheme which is based on a control volume approach. A two-equation turbulence model with a low Reynolds number modification is employed. A third-order accurate upwinding scheme is used to approximate convection terms, while a second order accurate central difference scheme is used for the discretization of viscous terms. A second-order accurate scheme is employed for the temporal discretization. The numerical method is applied to study the unsteady flowfield of the High Pressure Fuel side Turbo-Pump (HPFTP) of the Space Shuttle Main Engine (SSME). The stage calculation is performed by coupling the stator and the rotor flowfields at each time step through an over-laid grid. Numerical results for the complete geometry with the vane trailing edge cutback are presented and compared with the available experimental data.

Hah, C.↗

DOE OSTI2024

Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model

In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Sparse chronology strategy for integrating seasonal energy storage in capacity expansion models

Here, this study develops the sparse chronology method to enhance the representative period framework in capacity expansion models, enabling the effective integration of long-duration energy storage modeling. Traditional representative period methods cannot capture the state of charge of seasonal energy storage systems because they do not establish effective inter-day linkages to connect the state of charge between periods. The sparse chronology approach addresses this limitation by establishing inter-day linkages that allow state of charge to shift inter-seasonally. At the same time, it groups identical representative days into partitions, applying constraints sparsely and implicitly to reduce computational load further. Validation results demonstrate that this method successfully simulates long-duration energy storage patterns, achieving close alignment with a continuous yearly benchmark model, with seasonal trends and state of charge cycles clearly represented. The computational load analysis reveals that the sparse chronology method efficiently applies constraints on maximum and minimum state of charge limits within the representative day framework, eliminating the need for detailed constraints on each individual day. By partitioning representative days and constraining only the start and end of each partition, the method significantly decreases computational requirements. Simulation results show that sparse chronology closely approximates the continuous yearly method's accuracy, even with as few as 20 representative days, achieving correlation values with the benchmark of nearly 0.9 in state of charge plots. Furthermore, it maintains computational efficiency, requiring only 4 % of the solver time compared to the continuous yearly method with 20 representative days. This approach allows capacity expansion models to incorporate long-duration energy storage with high temporal, spatial, and technological resolution, enabling more detailed modeling for large-scale power systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1982

Conservative supra-characteristics method for splitting the hyperbolic systems of gasdynamics for real and perfect gases

A conservative flux difference splitting is presented for the hyperbolic systems of gasdynamics. The stable robust method is suitable for wide application in a variety of schemes, explicit or implicit, iterative or direct, for marching in either time or space. The splitting is modeled on the local quasi one dimensional characteristics system for multi-dimensional flow similar to Chakravarthy's nonconservative split coefficient matrix method; but, as the result of maintaining global conservation, the method is able to capture sharp shocks correctly. The embedded characteristics formulation is cast in a primitive variable the volumetric internal energy (rather than the pressure) that is effective for treating real as well as perfect gases. Finally the relationship of the splitting to characteristics boundary conditions is discussed and the associated conservative matrix formulation for a computed blown wall boundary condition is developed as an example. The theoretical development employs and extends the notion of Roe of constructing stable upwind difference formulae by sending split simple one sided flux difference pieces to appropriate mesh sites. The developments are also believed to have the potential for aiding in the analysis of both existing and new conservative difference schemes.

Lombard, C. K.↗

NASA NTRS1983

A finite element method for diffusion dominated unsteady viscous flows

A general conforming finite element scheme for computing viscous flows is presented which is of second-order accuracy in space and time. Viscous terms are treated implicitly and advection terms are treated explicitly in the time marching segment of the algorithm. A method for solving the algebraic equations at each time step is given. The method is demonstrated on two test problems, one of them being a plane vortex flow for which asymptotic methods are used to obtain suitable numerical boundary conditions at each time step.

Gunzburger, M. D.↗