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At least 271 records · Page 15

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NASA NTRS1985

AOTV bluff body flow - Relaxation algorithm

Preliminary investigations have led to the consideration of two classes of energy efficient aeroassisted orbital transfer vehicle (AOTV) concepts, with high and low L/D. The AOTV represent reentry space vehicles which are to fly hypersonically in the continuum upper reaches of the atmosphere. Problems arise in connection with convective and nonequilibrium radiative heating. As the possibilities for obtaining needed information by experimentation are limited, reliance must be placed on computational techniques to simulate testing of design concepts. A new relaxation algorithm for the compressible Navier-Stokes equations has been developed in the context of recent work with a conservative flux difference eigenvector split implicit upwind scheme CSCM (conservative supracharacteristics method). Attention is given to the CSCM implicit method, and early results for axisymmetric bluff body flow including complete forebody and base flow for a free flight range model drag brake AOTV.

Lombard, C. K.↗

NASA NTRS1982

Stability of mixed time integration schemes for transient thermal analysis

A current research topic in coupled-field problems is the development of effective transient algorithms that permit different time integration methods with different time steps to be used simultaneously in various regions of the problems. The implicit-explicit approach seems to be very successful in structural, fluid, and fluid-structure problems. This paper summarizes this research direction. A family of mixed time integration schemes, with the capabilities mentioned above, is also introduced for transient thermal analysis. A stability analysis and the computer implementation of this technique are also presented. In particular, it is shown that the mixed time implicit-explicit methods provide a natural framework for the further development of efficient, clean, modularized computer codes.

Liu, W. K.↗

NASA NTRS1985

A fully implicit scheme for the barotropic primitive equations

An efficient implicit finite-difference method is developed and tested for a global barotropic model. The scheme requires, at each time step, the solution of only one-dimensional block-tridiagonal linear systems. This additional computation is offset by the use of a time step chosen independently of the mesh spacing. The method is second-order accurate in time and fourth-order accurate in space. Present experience indicates that this implicit method is practical for numerical simulation on fine meshes.

Cohn, S. E.↗

NASA NTRS1978

A comparison of the Method of Lines to finite difference techniques in solving time-dependent partial differential equations

Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.

Kurtz, L. A.↗

NASA NTRS1997

Flowfield-Dependent Mixed Explicit-Implicit (FDMEL) Algorithm for Computational Fluid Dynamics

Despite significant achievements in computational fluid dynamics, there still remain many fluid flow phenomena not well understood. For example, the prediction of temperature distributions is inaccurate when temperature gradients are high, particularly in shock wave turbulent boundary layer interactions close to the wall. Complexities of fluid flow phenomena include transition to turbulence, relaminarization separated flows, transition between viscous and inviscid incompressible and compressible flows, among others, in all speed regimes. The purpose of this paper is to introduce a new approach, called the Flowfield-Dependent Mixed Explicit-Implicit (FDMEI) method, in an attempt to resolve these difficult issues in Computational Fluid Dynamics (CFD). In this process, a total of six implicitness parameters characteristic of the current flowfield are introduced. They are calculated from the current flowfield or changes of Mach numbers, Reynolds numbers, Peclet numbers, and Damkoehler numbers (if reacting) at each nodal point and time step. This implies that every nodal point or element is provided with different or unique numerical scheme according to their current flowfield situations, whether compressible, incompressible, viscous, inviscid, laminar, turbulent, reacting, or nonreacting. In this procedure, discontinuities or fluctuations of an variables between adjacent nodal points are determined accurately. If these implicitness parameters are fixed to certain numbers instead of being calculated from the flowfield information, then practically all currently available schemes of finite differences or finite elements arise as special cases. Some benchmark problems to be presented in this paper will show the validity, accuracy, and efficiency of the proposed methodology.

Garcia, S. M.↗

NASA NTRS1993

A multigrid nonoscillatory method for computing high speed flows

A multigrid method using different smoothers has been developed to solve the Euler equations discretized by a nonoscillatory scheme up to fourth order accuracy. The best smoothing property is provided by a five-stage Runge-Kutta technique with optimized coefficients, yet the most efficient smoother is a backward Euler technique in factored and diagonalized form. The singlegrid solution for a hypersonic, viscous conic flow is in excellent agreement with the solution obtained by the third order MUSCL and Roe's method. Mach 8 inviscid flow computations for a complete entry probe have shown that the accuracy is at least as good as the symmetric TVD scheme of Yee and Harten. The implicit multigrid method is four times more efficient than the explicit multigrid technique and 3.5 times faster than the single-grid implicit technique. For a Mach 8.7 inviscid flow over a blunt delta wing at 30 deg incidence, the CPU reduction factor from the three-level multigrid computation is 2.2 on a grid of 37 x 41 x 73 nodes.

Li, C. P.↗

NASA NTRS1980

Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles. Part 2: Applications

A computer implemented numerical method for predicting the flow in and about an isolated three dimensional jet exhaust nozzle is summarized. The approach is based on an implicit numerical method to solve the unsteady Navier-Stokes equations in a boundary conforming curvilinear coordinate system. Recent improvements to the original numerical algorithm are summarized. Equations are given for evaluating nozzle thrust and discharge coefficient in terms of computed flowfield data. The final formulation of models that are used to simulate flow turbulence effect is presented. Results are presented from numerical experiments to explore the effect of various quantities on the rate of convergence to steady state and on the final flowfield solution. Detailed flowfield predictions for several two and three dimensional nozzle configurations are presented and compared with wind tunnel experimental data.

Thomas, P. D.↗

NASA NTRS2000

Discontinuous dual-primal mixed finite elements for elliptic problems

We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.

Bottasso, Carlo L.↗

DOE OSTI2025

Evaluation of Density-Functional Tight-Binding Methods for Simulation of Protic Molecular Ion Pairs

In this work, we benchmark the accuracy of the density-functional tight-binding (DFTB) method, namely the long-range corrected second-order (LC-DFTB2) and third-order (DFTB3) models, for predicting energetics of imidazolium-based ionic liquid (IL) ion pairs. We compare the DFTB models against popular density functionals such as LC-ωPBE and B3LYP, using ab initio domain-based local pair-natural orbital coupled cluster (DLPNO-CC) energies as reference. Calculations were carried out in the gas phase, as well as in aqueous solution using implicit solvent methods. We find that the LC-DFTB2 model shows excellent performance in the gas phase and agrees well with reference energies in implicit solvent, often outperforming DFTB3 predictions for complexation energetics. Our study identifies a range of opportunities for use of the LC-DFTB method and quantifies its sensitivity to protonation states and the types of chemical interactions between ion pairs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1984

Supersonic nonlinear potential analysis

The NCOREL computer code was established to compute supersonic flow fields of wings and bodies. The method encompasses an implicit finite difference transonic relaxation method to solve the full potential equation in a spherical coordinate system. Two basic topic to broaden the applicability and usefulness of the present method which is encompassed within the computer code NCOREL for the treatment of supersonic flow problems were studied. The first topic is that of computing efficiency. Accelerated schemes are in use for transonic flow problems. One such scheme is the approximate factorization (AF) method and an AF scheme to the supersonic flow problem is developed. The second topic is the computation of wake flows. The proper modeling of wake flows is important for multicomponent configurations such as wing-body and multiple lifting surfaces where the wake of one lifting surface has a pronounced effect on a downstream body or other lifting surfaces.

Siclari, M. J.↗

NASA NTRS1988

General methods for determining the linear stability of coronal magnetic fields

A time integration of a linearized plasma equation of motion has been performed to calculate the ideal linear stability of arbitrary three-dimensional magnetic fields. The convergence rates of the explicit and implicit power methods employed are speeded up by using sequences of cyclic shifts. Growth rates are obtained for Gold-Hoyle force-free equilibria, and the corkscrew-kink instability is found to be very weak.

Craig, I. J. D.↗

NASA NTRS1993

Virtual-pulse time integral methodology: A new explicit approach for computational dynamics - Theoretical developments for general nonlinear structural dynamics

The present paper describes a new explicit virtual-pulse time integral methodology for nonlinear structural dynamics problems. The purpose of the paper is to provide the theoretical basis of the methodology and to demonstrate applicability of the proposed formulations to nonlinear dynamic structures. Different from the existing numerical methods such as direct time integrations or mode superposition techniques, the proposed methodology offers new perspectives and methodology of development, and possesses several unique and attractive computational characteristics. The methodology is tested and compared with the implicit Newmark method (trapezoidal rule) through a nonlinear softening and hardening spring dynamic models. The numerical results indicate that the proposed explicit virtual-pulse time integral methodology is an excellent alternative for solving general nonlinear dynamic problems.

Chen, Xiaoqin↗

NASA NTRS1995

Three-dimensional aerodynamic shape optimization using discrete sensitivity analysis

An aerodynamic shape optimization procedure based on discrete sensitivity analysis is extended to treat three-dimensional geometries. The function of sensitivity analysis is to directly couple computational fluid dynamics (CFD) with numerical optimization techniques, which facilitates the construction of efficient direct-design methods. The development of a practical three-dimensional design procedures entails many challenges, such as: (1) the demand for significant efficiency improvements over current design methods; (2) a general and flexible three-dimensional surface representation; and (3) the efficient solution of very large systems of linear algebraic equations. It is demonstrated that each of these challenges is overcome by: (1) employing fully implicit (Newton) methods for the CFD analyses; (2) adopting a Bezier-Bernstein polynomial parameterization of two- and three-dimensional surfaces; and (3) using preconditioned conjugate gradient-like linear system solvers. Whereas each of these extensions independently yields an improvement in computational efficiency, the combined effect of implementing all the extensions simultaneously results in a significant factor of 50 decrease in computational time and a factor of eight reduction in memory over the most efficient design strategies in current use. The new aerodynamic shape optimization procedure is demonstrated in the design of both two- and three-dimensional inviscid aerodynamic problems including a two-dimensional supersonic internal/external nozzle, two-dimensional transonic airfoils (resulting in supercritical shapes), three-dimensional transport wings, and three-dimensional supersonic delta wings. Each design application results in realistic and useful optimized shapes.

Burgreen, Gregory W.↗

DOE OSTI2024

Digital bead modeling for wire-arc directed energy deposition

Prediction of 2D cross-section and full 3D geometry for stacked weld beads is critical for the outcome of wire-arc directed energy deposition (DED) parts; however, most additive path planning software packages model beads as extrusions of a rectangle. Weld beads are not rectangular, and the resulting shape is dependent upon physics effects at the moment of deposition. Physics phenomena such as the geometry of the underlying surface, the heat input of the welding mode, and the direction of gravity contribute to bead shape. Here, this paper presents a novel implicit modeling method that discretizes a 2D area or 3D volume of space into pixels or voxels and constructs fields based on these physics phenomena. The fields are combined using a weighting scheme trained on 3D scan measurements of welds and wire-arc DED prints. Pixels or voxels are added until the known amount of deposited volume has been achieved. Thereby, a strong conservation of mass principle is applied to the process. Utilizing machine learning techniques, the present model can be trained on a database of scans allowing for the representation of a wide variety of prints. Results show that this method can produce predictions with realistic bead morphology and sub-millimeter form error.

Bead geometry modeling↗

NASA NTRS1992

Progress in unstructured-grid methods development for unsteady aerodynamic applications

The development of unstructured-grid methods for the solution of the equations of fluid flow and what was learned over the course of the research are summarized. The focus of the discussion is on the solution of the time-dependent Euler equations including spatial discretizations, temporal discretizations, and boundary conditions. An example calculation with an implicit upwind method using a CFL number of infinity is presented for the Boeing 747 aircraft. The results were obtained in less than one hour CPU time on a Cray-2 computer, thus, demonstrating the speed and robustness of the capability. Additional calculations for the ONERA M6 wing demonstrate the accuracy of the method through the good agreement between calculated results and experimental data for a standard transonic flow case.

Batina, John T.↗

NASA NTRS1989

Numerical modeling of a vortex stabilized arcjet thruster

A numerical method to solve the equations governing a vortex stabilized arcjet thruster is being developed. The model will allow the effects of swirling flow and geometry on arcjet thruster performance to be determined. The propellant flow equations, i.e., the axisymmetric, thin layer, Navier-Stokes equations, are solved using a Gauss-Siedel line-relaxation procedure. An implicit FTCS method is used to solve the electromagnetic field equations. A grid generation scheme was developed for an arbitrary arcjet geometry. The model will allow the radial and axial components of velocity and current distributions to be determined from a region upstream of the cathode, through the constrictor, to the exit plane of the nozzle.

Keith, Theo G., Jr.↗

NASA NTRS1985

Intermediate boundary conditions for LOD, ADI and approximate factorization methods

A general approach to determining the correct intermediate boundary conditions for dimensional splitting methods is presented. The intermediate solution U is viewed as a second order accurate approximation to a modified equation. Deriving the modified equation and using the relationship between this equation and the original equation allows us to determine the correct boundary conditions for U*. This technique is illustrated by applying it to locally one dimensional (LOD) and alternating direction implicit (ADI) methods for the heat equation in two and three space dimensions. The approximate factorization method is considered in slightly more generality.

Leveque, R. J.↗

NASA NTRS1992

An implicit multigrid scheme for hypersonic strong-interaction flowfields

An implicit multigrid method for the compressible Navier-Stokes equations is applied to a series of two-dimensional, steady, laminar hypersonic flows over a compression ramp, including both attached and separated flow conditions. The algorithm uses upwind-biased differencing for the convective and pressure terms and central differencing for the shear-stress and heat-transfer terms. An implicit spatially factored scheme is used to advance the solution in terms on a given mesh, and a V-cycle multigrid strategy is used to accelerate convergence. The multigrid algorithm provided an order of magnitude decrease in the computational time required to obtain a converged position of the separation location and enabled a substantially grid-independent result to be obtained for each of the flows considered.

Thomas, James L.↗