Results for “discretization methods” — Page 95

NASA NTRS1993

Solution of elastic-plastic stress analysis problems by the p-version of the finite element method

The solution of small strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus. Numerical examples which include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors are presented.

Szabo, Barna A.↗

NASA NTRS1994

Parallelized direct execution simulation of message-passing parallel programs

As massively parallel computers proliferate, there is growing interest in findings ways by which performance of massively parallel codes can be efficiently predicted. This problem arises in diverse contexts such as parallelizing computers, parallel performance monitoring, and parallel algorithm development. In this paper we describe one solution where one directly executes the application code, but uses a discrete-event simulator to model details of the presumed parallel machine such as operating system and communication network behavior. Because this approach is computationally expensive, we are interested in its own parallelization specifically the parallelization of the discrete-event simulator. We describe methods suitable for parallelized direct execution simulation of message-passing parallel programs, and report on the performance of such a system, Large Application Parallel Simulation Environment (LAPSE), we have built on the Intel Paragon. On all codes measured to date, LAPSE predicts performance well typically within 10 percent relative error. Depending on the nature of the application code, we have observed low slowdowns (relative to natively executing code) and high relative speedups using up to 64 processors.

Dickens, Phillip M.↗

NASA NTRS1995

A numerical solution method for acoustic radiation from axisymmetric bodies

A new and very efficient numerical method for solving equations of the Helmholtz type is specialized for problems having axisymmetric geometry. It is then demonstrated by application to the classical problem of acoustic radiation from a vibrating piston set in a stationary infinite plane. The method utilizes 'Green's Function Discretization', to obtain an accurate resolution of the waves using only 2-3 points per wave. Locally valid free space Green's functions, used in the discretization step, are obtained by quadrature. Results are computed for a range of grid spacing/piston radius ratios at a frequency parameter, omega R/c(sub 0), of 2 pi. In this case, the minimum required grid resolution appears to be fixed by the need to resolve a step boundary condition at the piston edge rather than by the length scale imposed by the wave length of the acoustic radiation. It is also demonstrated that a local near-field radiation boundary procedure allows the domain to be truncated very near the radiating source with little effect on the solution.

Caruthers, John E.↗

NASA NTRS1993

Wing-Body Aeroelasticity Using Finite-Difference Fluid/Finite-Element Structural Equations on Parallel Computers

This paper presents a procedure for computing the aeroelasticity of wing-body configurations on multiple-instruction, multiple-data (MIMD) parallel computers. In this procedure, fluids are modeled using Euler equations discretized by a finite difference method, and structures are modeled using finite element equations. The procedure is designed in such a way that each discipline can be developed and maintained independently by using a domain decomposition approach. A parallel integration scheme is used to compute aeroelastic responses by solving the coupled fluid and structural equations concurrently while keeping modularity of each discipline. The present procedure is validated by computing the aeroelastic response of a wing and comparing with experiment. Aeroelastic computations are illustrated for a High Speed Civil Transport type wing-body configuration.

Byun, Chansup↗

NASA NTRS1996

Simulation of Two-Fluid Flows by the Least-Squares Finite Element Method Using a Continuum Surface Tension Model

In this paper a numerical procedure for simulating two-fluid flows is presented. This procedure is based on the Volume of Fluid (VOF) method proposed by Hirt and Nichols and the continuum surface force (CSF) model developed by Brackbill, et al. In the VOF method fluids of different properties are identified through the use of a continuous field variable (color function). The color function assigns a unique constant (color) to each fluid. The interfaces between different fluids are distinct due to sharp gradients of the color function. The evolution of the interfaces is captured by solving the convective equation of the color function. The CSF model is used as a means to treat surface tension effect at the interfaces. Here a modified version of the CSF model, proposed by Jacqmin, is used to calculate the tension force. In the modified version, the force term is obtained by calculating the divergence of a stress tensor defined by the gradient of the color function. In its analytical form, this stress formulation is equivalent to the original CSF model. Numerically, however, the use of the stress formulation has some advantages over the original CSF model, as it bypasses the difficulty in approximating the curvatures of the interfaces. The least-squares finite element method (LSFEM) is used to discretize the governing equation systems. The LSFEM has proven to be effective in solving incompressible Navier-Stokes equations and pure convection equations, making it an ideal candidate for the present applications. The LSFEM handles all the equations in a unified manner without any additional special treatment such as upwinding or artificial dissipation. Various bench mark tests have been carried out for both two dimensional planar and axisymmetric flows, including a dam breaking, oscillating and stationary bubbles and a conical liquid sheet in a pressure swirl atomizer.

Wu, Jie↗

NASA NTRS1996

Wing-Body Aeroelasticity on Parallel Computers

This article presents a procedure for computing the aeroelasticity of wing-body configurations on multiple-instruction, multiple-data parallel computers. In this procedure, fluids are modeled using Euler equations discretized by a finite difference method, and structures are modeled using finite element equations. The procedure is designed in such a way that each discipline can be developed and maintained independently by using a domain decomposition approach. A parallel integration scheme is used to compute aeroelastic responses by solving the coupled fluid and structural equations concurrently while keeping modularity of each discipline. The present procedure is validated by computing the aeroelastic response of a wing and comparing with experiment. Aeroelastic computations are illustrated for a high speed civil transport type wing-body configuration.

Guruswamy, Guru P.↗

NASA NTRS2000

Transonic Flow Computations Using Nonlinear Potential Methods

This presentation describes the state of transonic flow simulation using nonlinear potential methods for external aerodynamic applications. The presentation begins with a review of the various potential equation forms (with emphasis on the full potential equation) and includes a discussion of pertinent mathematical characteristics and all derivation assumptions. Impact of the derivation assumptions on simulation accuracy, especially with respect to shock wave capture, is discussed. Key characteristics of all numerical algorithm types used for solving nonlinear potential equations, including steady, unsteady, space marching, and design methods, are described. Both spatial discretization and iteration scheme characteristics are examined. Numerical results for various aerodynamic applications are included throughout the presentation to highlight key discussion points. The presentation ends with concluding remarks and recommendations for future work. Overall. nonlinear potential solvers are efficient, highly developed and routinely used in the aerodynamic design environment for cruise conditions. Published by Elsevier Science Ltd. All rights reserved.

Holst, Terry L.↗

NASA NTRS2002

Incorporation of Condensation Heat Transfer in a Flow Network Code

Pure water is distilled from waste water in the International Space Station. The distillation assembly consists of an evaporator, a compressor and a condenser. Vapor is periodically purged from the condenser to avoid vapor accumulation. Purged vapor is condensed in a tube by coolant water prior to entering the purge pump. The paper presents a condensation model of purged vapor in a tube. This model is based on the Finite Volume Method. In the Finite Volume Method, the flow domain is discretized into multiple control volumes and a simultaneous analysis is performed.

Anthony, Miranda↗

NASA NTRS2004

Product-oriented Software Certification Process for Software Synthesis

The purpose of this document is to propose a product-oriented software certification process to facilitate use of software synthesis and formal methods. Why is such a process needed? Currently, software is tested until deemed bug-free rather than proving that certain software properties exist. This approach has worked well in most cases, but unfortunately, deaths still occur due to software failure. Using formal methods (techniques from logic and discrete mathematics like set theory, automata theory and formal logic as opposed to continuous mathematics like calculus) and software synthesis, it is possible to reduce this risk by proving certain software properties. Additionally, software synthesis makes it possible to automate some phases of the traditional software development life cycle resulting in a more streamlined and accurate development process.

Nelson, Stacy↗

NASA NTRS2007

Model Checking Abstract PLEXIL Programs with SMART

We describe a method to automatically generate discrete-state models of abstract Plan Execution Interchange Language (PLEXIL) programs that can be analyzed using model checking tools. Starting from a high-level description of a PLEXIL program or a family of programs with common characteristics, the generator lays the framework that models the principles of program execution. The concrete parts of the program are not automatically generated, but require the modeler to introduce them by hand. As a case study, we generate models to verify properties of the PLEXIL macro constructs that are introduced as shorthand notation. After an exhaustive analysis, we conclude that the macro definitions obey the intended semantics and behave as expected, but contingently on a few specific requirements on the timing semantics of micro-steps in the concrete executive implementation.

Siminiceanu, Radu I.↗

NASA NTRS2006

Progressive Failure Analysis of Composite Stiffened Panels

A new progressive failure analysis capability for stiffened composite panels has been developed based on the combination of the HyperSizer stiffened panel design/analysis/optimization software with the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC). MAC/GMC discretizes a composite material s microstructure into a number of subvolumes and solves for the stress and strain state in each while providing the homogenized composite properties as well. As a result, local failure criteria may be employed to predict local subvolume failure and the effects of these local failures on the overall composite response. When combined with HyperSizer, MAC/GMC is employed to represent the ply level composite material response within the laminates that constitute a stiffened panel. The effects of local subvolume failures can then be tracked as loading on the stiffened panel progresses. Sample progressive failure results are presented at both the composite laminate and the composite stiffened panel levels. Deformation and failure model predictions are compared with experimental data from the World Wide Failure Exercise for AS4/3501-6 graphite/epoxy laminates.

Bednarcyk, Brett A.↗

NASA NTRSDate not supplied

Modeling Deformable Linear Objects for Autonomous Robotic Outfitting of Lunar Surface Systems

The construction of in-space facilities is a significant capability for the establishment of a long-term human presence in space. Autonomous robotic technologies are a critical tool to enabling the construction and maintenance of such permanent facilities. This paper evaluates the outfitting portion of the construction process, focusing on modeling required for robotic manipulation of cable-like objects, referred to as Deformable Linear Objects (DLOs). DLOs contain a high degree of variability, which makes accurate real-time autonomous operations a difficult task. Different modeling methods for DLOs such as discrete mass-spring systems and Cosserat elastic rod models range in problem complexity and accuracy, a trade-off that must be understood to fully realize autonomous cable routing technologies. This paper validates different DLO models through simulation and a hardware experiment, highlighting the size of the state space and accuracy of different approaches. The development of DLO manipulation models for outfitting enables an autonomous architecture for the construction of lunar surface systems.

Amy M Quartaro↗

NASA NTRS2022

Chance-Constrained System Identification of Nonlinear Discrete Systems with Safety and Stability Guarantees

This paper presents a discrete-time nonlinear system identification method while satisfying the stability and safety properties of the system with high probability. An Extreme Learning Machine (ELM) is used with a Gaussian assumption on the function reconstruction error. A quadratically constrained quadratic program (QCQP) is developed with probabilistic safety and stability constraints that are only required to be satisfied at sampled points inside the invariant region. The proposed method is validated using two simulation examples: a two degrees-of-freedom (DoF) robot manipulator with constraints on joint angles whose trajectories are guaranteed to remain inside a safe set and on motion trajectories data of a hand-drawn shape.

Iman Salehi↗

NASA NTRSDate not supplied

Modeling Deformable Linear Objects for Autonomous Robotic Outfitting of Lunar Surface Systems

The construction of in-space facilities is a significant capability for the establishment of a long-term human presence in space. Autonomous robotic technologies are a critical tool to enabling the construction and maintenance of such permanent facilities. This paper evaluates the outfitting portion of the construction process, focusing on modeling required for robotic manipulation of cable-like objects, referred to as Deformable Linear Objects (DLOs). DLOs contain a high degree of variability, which makes accurate real-time autonomous operations a difficult task. Different modeling methods for DLOs such as discrete mass-spring systems and Cosserat elastic rod models range in problem complexity and accuracy, a trade-off that must be understood to fully realize autonomous cable routing technologies. This paper validates different DLO models through simulation and a hardware experiment, highlighting the size of the state space and accuracy of different approaches. The development of DLO manipulation models for outfitting enables an autonomous architecture for the construction of lunar surface systems.

Deformable Modeling↗

NASA NTRSDate not supplied

Aerothermal Shape Optimization of Actively-Cooled Battery Packs using Conjugate Heat Transfer

Thermal management for battery is important for electric aircraft because battery temperature is critically important to vehicle safety, and it also has direct impact on the efficiency of the battery system. Because ambient air is a readily available resource for aircraft, this paper considers an active cooling concept with forced convection of ambient air through the battery pack. Conjugate heat transfer analysis is used to solve the coupled aero-thermal problem, which consists of a finite-volume computational fluid dynamics solver for the fluid domain, and a conduction heat transfer solver for the solid domain. A mixed Neumann and Dirichlet boundary condition is developed for the fluid-solid interface, which allows the solid domain to completely submerge in the fluid domain. A gradient-based optimization method is adopted, and the discrete adjoint approach implemented in DAFoam is used to efficiently compute the gradients. The aero-thermal coupling for primal analysis and gradient computation is handled using the OpenMDAO-based MPhys framework. A constant heat source is prescribed for the battery cells, and the battery shape (design variable) is optimized to minimize cooling pump power and battery weight (composite objective function) while keeping the battery temperature below a threshold (constraint). The optimized design achieves a 44.6% and 1.5% reduction in the cooling pump power and battery weight, respectively, and the maximal temperature constraint is satisfied. This work has the potential to reduce battery-pack weight, improve performance, and reduce the weight of thermal management systems for electric vertical take-off and landing aircraft.

thermal management↗

NASA NTRSDate not supplied

Aerothermal Shape Optimization of Actively-Cooled Battery Packs Using Conjugate Heat Transfer

Thermal management for battery is important for electric aircraft because battery temperature is critically important to vehicle safety, and it also has direct impact on the efficiency of the battery system. Because ambient air is a readily available resource for aircraft, this paper considers an active cooling concept with forced convection of ambient air through the battery pack. Conjugate heat transfer analysis is used to solve the coupled aero-thermal problem, which consists of a finite-volume computational fluid dynamics solver for the fluid domain, and a conduction heat transfer solver for the solid domain. A mixed Neumann and Dirichlet boundary condition is developed for the fluid-solid interface, which allows the solid domain to completely submerge in the fluid domain. A gradient-based optimization method is adopted, and the discrete adjoint approach implemented in DAFoam is used to efficiently compute the gradients. The aero-thermal coupling for primal analysis and gradient computation is handled using the OpenMDAO-based MPhys framework. A constant heat source is prescribed for the battery cells, and the battery shape (design variable) is optimized to minimize cooling pump power and battery weight (composite objective function) while keeping the battery temperature below a threshold (constraint). The optimized design achieves a 44.6% and 1.5% reduction in the cooling pump power and battery weight, respectively, and the maximal temperature constraint is satisfied. This work has the potential to reduce battery-pack weight, improve performance, and reduce the weight of thermal management systems for electric vertical take-off and landing aircraft.

heat transfer↗

DOE OSTI2011

Uniform DT 3T burn: computations and sensitivities

A numerical model was developed in C to integrate the nonlinear deutrium-tritium (DT) burn equations in a three temperature (3T) approximation for spatially uniform test problems relevant to Inertial Confinement Fusion (ICF). Base model results are in excellent agreement with standard 3T results. Data from NDI, SESAME, and TOPS databases is extracted to create fits for the reaction rate parameter, the Planck opacity, and the coupling frequencies of the plasma temperatures. The impact of different fits (e.g., TOPS versus SESAME opacity data, higher order polynomial fits ofNDI data for the reaction rate parameter) were explored, and sensitivity to several model inputs are presented including: opacity data base, Coulomb logarithm, and Bremsstrahlung. Sensitivity to numerical integration time step size, and the relative insensitivity to the discretized numerics and numerical integration method was demonstrated. Variations in the IC for densities and temperatures were explored, showing similar DT burn profiles in most cases once ignition occurs. A coefficient multiplying the Compton coupling term (default, A = 1) can be adjusted to approximate results from more sophisticated models. The coefficient was reset (A = 0.4) to match the maximum temperatures resulting from standard multi-group simulations of the base case test problem. Setting the coefficient to a larger value, (A = 0.6) matches maximum ion temperatures in a kinetic simulation of a high density ICF-like regime. Matching peak temperatures does not match entire temperature-time profiles, indicating the Compton coefficient is density and time dependent as the photon distribution evolves. In the early time burn during the ignition of the DT, the present model with modified Compton coupling provides a very simple method to obtain a much improved match to the more accurate solution from the multi-group radiation model for these DT burn regimes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

Detailed Simulations of Shock-Bifurcation and Ignition of an Argon-diluted Hydrogen/Oxygen Mixture in a Shock Tube

Detailed simulations of the bifurcation and ignition of an Argon-diluted Hydrogen/Oxygen mixture in the two-stage weak ignition regime are performed. An adaptive mesh-refinement (AMR) technique is employed to resolve all relevant physical scales that are associated with the viscous boundary-layer, the reaction front, and the shock-wave. A high-order hybrid WENO/central-differencing method is used as spatial discretization scheme, and a detailed chemical mechanism is employed to describe the combustion of the H2/O2 mixture. The operating conditions considered in this study are p = 5 bar and T = 1100 K, and fall in the third explosion limit. The computations show that the mixing of the thermally stratified fluid, carrying different momentum and enthalpy, introduces inhomogeneities in the core-region behind the reflected shock. These inhomogeneities act as localized ignition kernels. During the induction period, these kernels slowly expand and eventually transition to a detonation wave that rapidly consumes the unburned mixture.In competition with this detonation wave are the presence of secondary ignition kernels that appear in the unreacted core-region between reflected shock and detonation wave.

Ihme, Matthias↗