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At least 397 records · Page 22

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NASA NTRS2016

Overview of the CHarring Ablator Response (CHAR) Code

An overview of the capabilities of the CHarring Ablator Response (CHAR) code is presented. CHAR is a one-, two-, and three-dimensional unstructured continuous Galerkin finite-element heat conduction and ablation solver with both direct and inverse modes. Additionally, CHAR includes a coupled linear thermoelastic solver for determination of internal stresses induced from the temperature field and surface loading. Background on the development process, governing equations, material models, discretization techniques, and numerical methods is provided. Special focus is put on the available boundary conditions including thermochemical ablation, surface-to-surface radiation exchange, and flowfield coupling. Finally, a discussion of ongoing development efforts is presented.

Amar, Adam J.↗

NASA NTRS2016

Overview of the CHarring Ablator Response (CHAR) Code

An overview of the capabilities of the CHarring Ablator Response (CHAR) code is presented. CHAR is a one-, two-, and three-dimensional unstructured continuous Galerkin finite-element heat conduction and ablation solver with both direct and inverse modes. Additionally, CHAR includes a coupled linear thermoelastic solver for determination of internal stresses induced from the temperature field and surface loading. Background on the development process, governing equations, material models, discretization techniques, and numerical methods is provided. Special focus is put on the available boundary conditions including thermochemical ablation and contact interfaces, and example simulations are included. Finally, a discussion of ongoing development efforts is presented.

Amar, Adam J.↗

NASA NTRSDate not supplied

Understanding Variability in Mechanical Behavior of Adhesively Bonded Sandwich Joints due to Stochastic Material Damage

A mesoscale progressive damage analysis was applied to the analysis of recently tested adhesively bonded sandwich panels, in which ten nominally identical tension loaded panels failed in three different failure modes, with peakloads ranging from 13.0 –16.1 kips. A parametric finite element model for progressive damage analysis of an adhesively bonded joint (ABJ) considering matrix and fiber damage, and delamination cracks in unidirectional and fabric composite sections of the joint, as well as core crushing, and adhesive fracture was developed. The model was developed using Abaqus/Explicit and utilized continuum damage mechanics material models for intralaminar damage in the facesheet and doubler plies, cohesive elements for delamination and adhesive debonding, and discretized cells considering plasticity to model crushing of the aluminum honeycomb core. Analysis predictions obtained with a pristine model agreed well with the average experimental peak load, strain in the joint, and post-test damage states. Then, various methods to incorporate stochastic material variability into ABJ model were evaluated. These methods included simulation of pre-existing matrix damage, pre-existing adhesive porosity, and uniform modification of adhesive properties. These material and manufacturing defects changed the damage mode predictions in some cases. The analysis of stochastic strength due to the considered defects revealed unintuitive damage mode interaction in the ABJ, explaining some structure-property relationships observed experimentally.

Richard Larson↗

NASA NTRS2002

A Discontinuous Galerkin Discretization of the Eikonal Equation on Curved Piecewise Isoparametric Triangulated Manifolds

This viewgraph presentation provides information on optimizing the travel distance between two points on a curved surface. The presentation addresses the single source shortest path problem, fast algorithms for estimating the eikonal equation, fast schemes and barrier theorems, and the discontinuous Galerkin method, including hyperbolic causality, finite element method, scalars, and marching the discontinuous Galerkin Eikonal approximation.

Barth, TIm↗

NASA NTRS1985

High-speed compressible flow and other advection-dominated problems of fluid dynamics

Finite element methods are described for modeling high speed compressible flows with strong advection, problems important to aerodynamics. The situations are characterized by high pressure and temperature gradients, transients and the appearance of discontinuities, factors which require mesh refinement during computations. Techniques are developed for temporal and spatial discretization of a model problem. Several observations are made regarding the explicit and implicit features of the calculations, the use of the Lax-Wendroff scheme to produce a mass-matrix for obtaining accurate results for transients, methods of performing stability analyses, and simplification techniques. Examples are provided of solving the nonlinear shallow-water equations and describing compressible flows, particularly transonic flows. Domain splitting is defined for improving the calculations at each time step and in different parts of the flow regime while simultaneously advancing the calculations towards a solution.

Zienkiewicz, O. C.↗

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 NTRS1982

Algebraic grid generation

The numerical solution of partial differential equations about irregular geometries and with varying characteristic scales has created the need for coordinate systems and associated transformations which reflect both geometric and physical requirements. The process of finding coordinate transformations in discrete representations is called 'grid generation'. The present investigation is concerned with three algebraic grid generation methods. The methods include transfinite interpolation, the multisurface method, and the two-boundary technique. Interpolation formulas, in terms of homotopic mappings and constraints in terms of point positions and/or derivatives are the essential elements of the techniques. The methods are relatively simple to understand, they are explicit and do not require extensive computational effort, and they have a high degree of generality.

Smith, R. E.↗

NASA NTRS1988

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Mostrel, M. M.↗

NASA NTRS1990

Finite-element schemes for extended integrations of atmospheric models

Of the two finite-element models presently used to investigate the effect of the conservation of integral invariants, by means of finite-element discretization schemes of the shallow-water equations, in order to serve as a paradigm of long-term atmospheric-model integrations, the first employs rectangular elements and conserves total energy, while the second uses triangular elements and a high-accuracy two-stage Numerov-Galerkin method. Attention is given to critical times for numerical nonlinear instability, as well as to the determination of the critical degree of dissipation entailed by the achievement of stable long-term integrations. Relative computational efficiency and accuracy comparisons are presented for the two finite-element schemes.

Steppeler, J.↗

NASA NTRS1992

A new method for transonic static aeroelasticity problems

A new method has been developed to calculate the steady flow and structural deformations for fluid/structure interaction problems. The discretized fluid dynamic and structural equations are regarded as a single set of coupled, nonlinear, algebraic equations. The equilibrium solution is directly obtained using Newton's method. The governing equations used for the fluid flow are the two-dimensional Navier-Stokes equations, and a finite-element model is used to represent the structure. This paper describes the analytical method and presents sample calculations demonstrating the technique. The results show rapid convergence and good agreement with experimental data.

Felker, Fort F.↗

NASA NTRS2001

Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws

We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.

Barth, Timothy↗

NASA NTRS2009

Silicon Wafer-Scale Substrate for Microshutters and Detector Arrays

The silicon substrate carrier was created so that a large-area array (in this case 62,000+ elements of a microshutter array) and a variety of discrete passive and active devices could be mounted on a single board, similar to a printed circuit board. However, the density and number of interconnects far exceeds the capabilities of printed circuit board technology. To overcome this hurdle, a method was developed to fabricate this carrier out of silicon and implement silicon integrated circuit (IC) technology. This method achieves a large number of high-density metal interconnects; a 100-percent yield over a 6-in. (approximately equal to 15-cm) diameter wafer (one unit per wafer); a rigid, thermally compatible structure (all components and operating conditions) to cryogenic temperatures; re-workability and component replaceability, if required; and the ability to precisely cut large-area holes through the substrate. A method that would employ indium bump technology along with wafer-scale integration onto a silicon carrier was also developed. By establishing a silicon-based version of a printed circuit board, the objectives could be met with one solution. The silicon substrate would be 2 mm thick to survive the environmental loads of a launch. More than 2,300 metal traces and over 1,500 individual wire bonds are required. To mate the microshutter array to the silicon substrate, more than 10,000 indium bumps are required. A window was cut in the substrate to allow the light signal to pass through the substrate and reach the microshutter array. The substrate was also the receptacle for multiple unpackaged IC die wire-bonded directly to the substrate (thus conserving space over conventionally packaged die). Unique features of this technology include the implementation of a 2-mmthick silicon wafer to withstand extreme mechanical loads (from a rocket launch); integrated polysilicon resistor heaters directly on the substrate; the precise formation of an open aperture (approximately equal to 3x3cm) without any crack propagation; implementation of IR transmission blocking techniques; and compatibility with indium bump bonding. Although designed for the microshutter arrays for the NIRSpec instrument on the James Webb Space Telescope, these substrates can be linked to microshutter applications in the photomask generation and stepper equipment used to make ICs and microelectromechanical system (MEMS) devices.

Jhabvala, Murzy↗

NASA NTRS2015

2nd-Order CESE Results For C1.1: Transonic Ringleb Flow

The Conservation Element and Solution Element (CESE) method was used as implemented in the NASA research code ez4d (an unstructured Navier-Stokes solver coded in C++ with serial and parallel versions available.) The CESE method is a time-accurate formulation with flux-conservation in both space and time. The method treats the discretized derivatives of space and time identically and while the 2nd-order accurate version was used, high-order versions exist.

Numerical Analysis↗

NASA NTRS2022

The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows

The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the non-local, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, as roughness elements, steps, gaps, or corners. To solve the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 107 to 108. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear system. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE.

Boundary Layer Stability↗

NASA NTRS1984

Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics

A possible technique is explored for extending to multidimensional flows some of the upwind-differencing methods that are highly successful in the one-dimensional case. Emphasis is on the two-dimensional case, and the flow domain is assumed to be divided into polygonal computational elements. Inside each element, the flow is represented by a local superposition of elementary solutions consisting of plane waves not necessarily aligned with the element boundaries.

Roe, P. L.↗

NASA NTRS1986

Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics

Roe, P. L.↗

NASA NTRS1981

Dynamic stability of a rotor blade using finite element analysis

The aeroelastic stability of flap bending, lead-lag bending, and torsion of a helicopter rotor blade in hover is examined using a finite element formulation based on the principle of virtual work. Quasi-steady two-dimensional airfoil theory is used to obtain the aerodynamic loads. The rotor blade is discretized into beam elements, each with ten modal degrees of freedom. The resulting nonlinear equations of motion are solved for steady-state blade deflections through an iterative procedure. The flutter solution is calculated assuming blade motion to be a small perturbation about the steady solution. The normal mode method based on the coupled rotating natural modes about the steady deflections is used to reduce the number of equations in the flutter eigenanalysis. Results are presented for hingeless and articulated rotor blade configurations.

Sivaneri, N. T.↗

NASA NTRSDate not supplied

Assessment of Edge-Based Viscous Method for Corner-Flow Solutions on Graphics Processing Units

A highly efficient, edge-based viscous (EBV) discretization method has been recently implemented in a practical, unstructured-grid, node-centered, finite-volume flow solver and evaluated for Reynolds-averaged Navier-Stokes (RANS) formulations. In comparison to a well-established cell-based viscous (CBV) method, the EBV method has demonstrated multifold acceleration of all viscous-kernel computations on general unstructured mixed-element grids. The viscous kernels include evaluation of viscous fluxes, diffusion terms in turbulence models, and the corresponding Jacobian terms. In this paper, an EBV implementation of a nonlinear extension of the Spalart-Allmaras turbulence model, SA-neg-QCR2000, is presented and verified. The SA-neg-QCR2000 model is used for simulating turbulent corner flows. Previously reported EBV computations have been conducted on traditional computing architectures based on central processing units (CPU). This paper assesses benefits of the EBV method on modern high-performance computing architectures based on graphics processing units (GPU). The GPU implementations of the CBV and EBV methods are verified by comparing solutions and iterative convergence with those observed in CPU computations on the same grids. A comprehensive assessment of the EBV speedup on CPU and GPU architectures is presented for established benchmark corner flows, namely, a supersonic flow through a long square duct and a subsonic flow around a NASA juncture flow model.

CFD↗