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At least 1,279 records · Page 71

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NASA NTRS1989

Computing Viscoplastic Behavior Of A Material

Finite-element implementation developed for Robinson's unified model of viscoplasticity. Implemented via MARC general-purpose finite-element computer program by incorporating all of nonlinearity of material into initial load vector and treating vector as pseudo body force in finite-element equilibrium equations. In technique, each finite increment split into several equal subincrements, constitutive equations integrated by explicit Euler forward-difference method. HYPELA subroutine in MARC includes adaptive integration scheme selecting optimal sizes of subincrements. Spline function smooths discontinuous boundaries in Robinson's model to facilitate finite-element numerical calculations. Method used to calculate elastic, plastic, and creep deformations in solid materials at various temperatures; also used to study thermomechanical behavior of such things as hot pressure vessels and highly stressed components in engines.

Arya, V. K.↗

DOE OSTI2022

Comparison of three state-of-the-art crystal plasticity based deformation twinning models for magnesium alloys

In magnesium alloys, deformation twinning and its interactions with dislocation slip are responsible for a sigmoidal shape stress–strain behavior and an asymmetrical tension–compression yield strength in magnesium alloys. The sensitivity of twinning to the underlying microstructure renders the crystal plasticity method the most commonly adopted modeling approach for magnesium-twinning. This paper compares three state-of-the-art crystal plasticity-based twinning models from the literature, namely the elastic-viscoplastic self-consistent twinning-detwinning (EVPSC-TDT) model, crystal plasticity finite element model based on enhanced predominate twin reorientation approach (CPFE-ePTR), and the crystal plasticity finite element model based on “discrete twinning” approach (CPFE-DT). A polycrystalline microstructure is simulated with all three methods to compare the resulting stress–strain curves and lattice strains to those from the experimentally measured data. All three methods showed the capability of capturing the experimental results with different levels of accuracy. Additionally, the EVPSC-TDT method avoids solving the finite element matrices and showed the highest computational efficiency. The CPFE-ePTR model shows a higher accuracy in capturing the lattice strain. The CPFE-DT relies on high-resolution finite element mesh and is much slower than the other two methods, but it captured the local deformation concentration and stress reversal phenomena near the twin band, which was not possible with the other two methods. Based on the comparison, guidance for the selection of the appropriate model based on the specific modeling target is provided in this paper.

36 MATERIALS SCIENCE↗

NASA NTRS2006

Magnetic Field Solver

The Magnetic Field Solver computer program calculates the magnetic field generated by a group of collinear, cylindrical axisymmetric electromagnet coils. Given the current flowing in, and the number of turns, axial position, and axial and radial dimensions of each coil, the program calculates matrix coefficients for a finite-difference system of equations that approximates a two-dimensional partial differential equation for the magnetic potential contributed by the coil. The program iteratively solves these finite-difference equations by use of the modified incomplete Cholesky preconditioned-conjugate-gradient method. The total magnetic potential as a function of axial (z) and radial (r) position is then calculated as a sum of the magnetic potentials of the individual coils, using a high-accuracy interpolation scheme. Then the r and z components of the magnetic field as functions of r and z are calculated from the total magnetic potential by use of a high-accuracy finite-difference scheme. Notably, for the finite-difference calculations, the program generates nonuniform two-dimensional computational meshes from nonuniform one-dimensional meshes. Each mesh is generated in such a way as to minimize the numerical error for a benchmark one-dimensional magnetostatic problem.

Ilin, Andrew V.↗

NASA NTRS2008

Vibration Response Models of a Stiffened Aluminum Plate Excited by a Shaker

Numerical models of structural-acoustic interactions are of interest to aircraft designers and the space program. This paper describes a comparison between two energy finite element codes, a statistical energy analysis code, a structural finite element code, and the experimentally measured response of a stiffened aluminum plate excited by a shaker. Different methods for modeling the stiffeners and the power input from the shaker are discussed. The results show that the energy codes (energy finite element and statistical energy analysis) accurately predicted the measured mean square velocity of the plate. In addition, predictions from an energy finite element code had the best spatial correlation with measured velocities. However, predictions from a considerably simpler, single subsystem, statistical energy analysis model also correlated well with the spatial velocity distribution. The results highlight a need for further work to understand the relationship between modeling assumptions and the prediction results.

Cabell, Randolph H.↗

DOE OSTI2024

Neutron transport methods for multiphysics heterogeneous reactor core simulation in Griffin

Griffin is a reactor physics application based on the Multiphysics Object-Oriented Simulation Environment (MOOSE). This work discloses the methods, algorithms, and implementation for simulating heterogeneous reactor dynamics models. Griffin utilizes a discontinuous finite-element method with discrete ordinates (DFEM-S ) to discretize the field variable of the multigroup neutron transport equation. Multiphysics feedback is handled using two-step tabulated cross-section methodology. Feedback quantities are evaluated using the MOOSE-MultiApp system to couple various engineering phenomena, such as heat conduction and thermal fluids. The multiphysics DFEM-S system is solved using fixed-point iteration with a fully asynchronous parallel sweeper, unstructured coarse-mesh finite difference acceleration, and a multi-timescale improved quasi-static method scheme. The implementation is applied to a multiphysics microreactor model, with two transients: one initiated by a single heat-pipe failure and another by control drum rotation. Importantly, these examples demonstrate the ability of Griffin to tractably solve the neutron transport equation considering seven independent variables and feedback.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1987

Solving finite element equations on concurrent computers

This paper discusses the development of a concurrent algorithm for the solution of systems of equations arising in finite element applications. The approach is based on a hybrid of direct elimination method and preconditioned conjugate iteration. Two different preconditioners are used; diagonal scaling and a concurrent implementation of incomplete LU factorization. First, an automatic procedure is used to partition the finite element mesh into sub-structures. The particular mesh partition is chosen to minimize an estimate of the cost for evaluating the solution using this algorithm on a concurrent computer. These procedures are implemented in a finite element program on the JPL/CalTech MARK III hypercube computer. An overview of the structure of this program is presented. The performance of the solution method is demonstrated with the aid of a number of numerical test runs, and its advantages for concurrent implementations are discussed. Efficiency and speed-up factors over sequential machines for the numerical examples are highlighted.

Nour-Omid, B.↗

NASA NTRS1994

Computation of turbulent boundary layers employing the defect wall-function method

In order to decrease overall computational time requirements of spatially-marching parabolized Navier-Stokes finite-difference computer code when applied to turbulent fluid flow, a wall-function methodology, originally proposed by R. Barnwell, was implemented. This numerical effort increases computational speed and calculates reasonably accurate wall shear stress spatial distributions and boundary-layer profiles. Since the wall shear stress is analytically determined from the wall-function model, the computational grid near the wall is not required to spatially resolve the laminar-viscous sublayer. Consequently, a substantially increased computational integration step size is achieved resulting in a considerable decrease in net computational time. This wall-function technique is demonstrated for adiabatic flat plate test cases from Mach 2 to Mach 8. These test cases are analytically verified employing: (1) Eckert reference method solutions, (2) experimental turbulent boundary-layer data of Mabey, and (3) finite-difference computational code solutions with fully resolved laminar-viscous sublayers. Additionally, results have been obtained for two pressure-gradient cases: (1) an adiabatic expansion corner and (2) an adiabatic compression corner.

Brown, Douglas L.↗

NASA NTRS1994

An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients

The primary accomplishments of the project are as follows: (1) Using the transonic small perturbation equation as a flowfield model, the project demonstrated that the quasi-analytical method could be used to obtain aerodynamic sensitivity coefficients for airfoils at subsonic, transonic, and supersonic conditions for design variables such as Mach number, airfoil thickness, maximum camber, angle of attack, and location of maximum camber. It was established that the quasi-analytical approach was an accurate method for obtaining aerodynamic sensitivity derivatives for airfoils at transonic conditions and usually more efficient than the finite difference approach. (2) The usage of symbolic manipulation software to determine the appropriate expressions and computer coding associated with the quasi-analytical method for sensitivity derivatives was investigated. Using the three dimensional fully conservative full potential flowfield model, it was determined that symbolic manipulation along with a chain rule approach was extremely useful in developing a combined flowfield and quasi-analytical sensitivity derivative code capable of considering a large number of realistic design variables. (3) Using the three dimensional fully conservative full potential flowfield model, the quasi-analytical method was applied to swept wings (i.e. three dimensional) at transonic flow conditions. (4) The incremental iterative technique has been applied to the three dimensional transonic nonlinear small perturbation flowfield formulation, an equivalent plate deflection model, and the associated aerodynamic and structural discipline sensitivity equations; and coupled aeroelastic results for an aspect ratio three wing in transonic flow have been obtained.

Carlson, Leland A.↗

NASA NTRS1974

Solution of an eigenvalue problem for the Laplace operator on a spherical surface

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (also referred to as the membrane eigenvalue problem for the vibration equation) on the unit spherical surface are developed. Two specific types of spherical surface domains are considered: (1) the interior of a spherical triangle, i.e., the region bounded by arcs of three great circles, and (2) the exterior of a great circle arc extending for less than pi radians on the sphere (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is derived. The symmetric (generally five-point) finite difference equations that develop are written in matrix form and then solved by the iterative method of point successive overrelaxation. Upon convergence of this iterative method, the fundamental eigenvalue is approximated by iteration utilizing the power method as applied to the finite Rayleigh quotient.

Walden, H.↗

NASA NTRS1987

On the accuracy of the pseudocompressibility method in solving the incompressible Navier-Stokes equations

The method of pseudocompressibility is tested for its accuracy in solving the incompressible Navier-Stokes equations. An implicit, finite difference computer code is used to solve the equations in a three-dimensional, curvilinear coordinate system. The code employs artificial compressibiity for solving the pressure field, coupled with an implicit, approximate factorization scheme. This coupling is known as the pseudocompressibility method and introduces pressure waves of finite speed into the fluid medium that would otherwise have an infinite sound speed. The waves die out as the solution converges, and the steady state solution approaches a divergence-free condition. These waves, however, limit the time accuracy of the computations. The effects of these waves are analysed and criteria are set for choosing the pseudocompressibility parameter that governs the pressure wave speed; test cases are presented that verify these criteria. The code is tested by computing laminar flow over a two-dimensional, backward-facing step and over a two-dimensional, impulsively started circular cylinder.

Rogers, S. E.↗

NASA NTRS1988

Power flow in a beam using a 5-accelerometer probe

A method to determine structure-borne power flow is examined which uses central finite differences to approximate the field variables required to calculate the shear and bending components of flexural vibration. An experimental study using a beam driven by a shaker was performed with the aim of comparing estimates using this proposed five-accelerometer method and the conventional two-accelerometer, free-field method. The advantages and disadvantages of the new method are pointed out.

Downing, J. Micah↗

DOE OSTI2026

Comparative analysis of plasticity-based GND density estimation methods in crystal plasticity finite element models

In crystal plasticity finite element (CPFE) simulations, accurately quantifying geometrically necessary dislocations (GNDs) is critical for capturing strain gradients in polycrystals. We compare different methods for quantifying GNDs, all of which originate from the Nye tensor, which is computed as the curl of the plastic deformation gradient. The projection technique directly decomposes the Nye tensor onto individual screw and edge dislocation components to compute GNDs. This approach requires converting a nine-component Nye tensor into densities for a larger number of dislocation systems, a fundamentally underdetermined (non-unique) process, which is resolved using L2 minimization. In contrast, when employing CPFE analysis, one could directly compute dislocation densities on each slip system using shear gradients. Projection and slip gradient methods are compared with respect to their prediction of GNDs with changing grain size, strain, and grain neighborhoods, including multigrain junctions. Although these techniques match analytical GND densities for single slip, single crystal deformation, and are consistent with anticipated overall GND trends, we find that the GND densities from projection techniques are significantly lower than those predicted from CPFE-based slip gradients in polycrystals. A suggested improvement of only using the active dislocation systems in the projection technique almost entirely resolved this mismatch.

Crystal plasticity↗

NASA NTRS1996

On DGS Relaxation: The Stokes Problem

Multigrid methods have proven to be efficient methods for solving partial differential equations (especially those of elliptic type). There is also growing experience with multigrid solvers for fluids problems, e.g., the Stokes and Navier-Stokes equations (using both finite element and finite difference discretizations). It is also well known that at the heart of any multigrid method is the smoother. In this work we look at a smoother introduced by Brandt and Dinar (DGS relaxation), and we examine some of its properties and consider some possible modifications to it. It is well known that multigrid performance using DGS relaxation is sensitive to the treatment of boundaries; this issue is addressed.

Meir, A. J.↗

NASA NTRS1976

Polynominal Interpolation Methods for Viscous Flow Calculations

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and by Hermitian (Taylor series) finite-difference discretization. The similarities and special features of these different developments are discussed. The governing systems apply for both uniform and variable meshes. Hybrid schemes resulting from two different polynomial approximations for the first and second derivatives lead to a nonuniform mesh extension of the so-called compact or Pad? difference technique (Hermite 4). A variety of fourth-order methods are described and the Hermitian approach is extended to sixth-order (Hermite 6). The appropriate spline boundary conditions are derived for all procedures. For central finite differences, this leads to a two-point, second-order accurate generalization of the commonly used three-point end-difference formula. Solutions with several spline and Hermite procedures are presented for the boundary layer equations, with and without mass transfer, and for the incompressible viscous flow in a driven cavity. Divergence and nondivergence equations are considered for the cavity. Among the fourth-order techniques, it is shown that spline 4 has the smallest truncation error. The spline 4 procedure generally requires one-quarter the number of mesh points in a given coordinate direction as a central finite-difference calculation of equal accuracy. The Hermite 6 procedure leads to remarkably accurate boundary layer solutions.

Rubin, S. G.↗

DOE OSTI2022

An immersed interface method for the 2D vorticity-velocity Navier-Stokes equations with multiple bodies

We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by nonconvex immersed bodies, multiply connected domains, and the calculation of force distributions on immersed surfaces. The immersed interface method is re-interpreted as a polynomial extrapolation of flow quantities and boundary conditions into the immersed solid bodies, reducing computational cost and enabling simulations with nonconvex bodies that could not be discretized with previous immersed interface methods. In the flow, the vorticity transport equation is discretized using a conservative finite difference scheme and explicit Runge-Kutta time integration. The velocity reconstruction problem is transformed to a scalar Poisson equation that is discretized with conservative finite differences, and solved using an FFT-accelerated iterative algorithm. The use of conservative differencing throughout leads to exact enforcement of a discrete Kelvin's theorem, allowing for simulations with multiply connected domains and outflow boundaries that have challenged other immersed interface vortex methods. We also explore novel methods for recovering time-dependent pressure distributions on immersed bodies within a vorticity-based method and present a novel control volume formulation for recovering aerodynamic moments from only the vorticity and velocity fields. The method achieves second order spatial accuracy and third order temporal accuracy, and is validated on a variety of 2D flows in internal and free-space domains.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A matrix-free hyperviscosity formulation for high-order ALE hydrodynamics

The numerical approximation of compressible hydrodynamics is at the core of high-energy density (HED) multiphysics simulations as shocks are the driving force in experiments like inertial confinement fusion (ICF). In this work, we describe our extension of the hyperviscosity technique, originally developed for shock treatment in finite difference simulations, for use in arbitrarily high-order finite element methods for Lagrangian hydrodynamics. Hyperviscosity enables shock capturing while preserving the high-order properties of the underlying discretization away from the shock region. Specifically, we compute a high-order term based on a product of the mesh length scale to a high power scaled by a hyper-Laplacian operator applied to a scalar field. We then form the total artificial viscosity by taking a non-linear blend of this term and a traditional artificial viscosity term. We also present a matrix-free formulation for computing the finite element based hyper-Laplacian operator. Such matrix-free methods have superior performance characteristics compared to traditional full matrix assembly approaches and offer advantages for GPU based HPC hardware. We demonstrate the numerical convergence of our method and its application to complex, multi-material ALE simulations on high-order (curved) meshes.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

Measurements of skin friction on the wall of a hypersonic nozzle.

Direct skin friction measurements obtained on the wall of a Mach 19.8 nozzle are presented. These measurements of skin friction and values deduced from the profile data are compared with predictions from a finite difference theory and also with several 'flat-plate' prediction methods for skin friction.

Harvey, W. D.↗

NASA NTRS1972

Numerical calculations of flow fields

The solutions to the equations of motion for inviscid fluid flow around a pointed elliptic cone at incidence are presented. The numerical method used, MacCormack's second order preferential predictor-corrector finite difference approximation, is applied to the fluid flow equations derived in conservation-law form. The entropy boundary condition, hitherto unused for elliptic cone problems, is investigated and compared to reflection boundary condition solutions. The stagnation streamline movement of the inclined elliptic cone is noted and surface pressure coefficients are plotted. Also presented are solutions for an elliptic cone and a circular cone at zero incidence and a circular cone at a small angle of attack. Comparisons are made between these present solutions and previously published theory.

Anderson, D. M.↗