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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Semi-analytical sensitivity analysis for nonlinear transient problems

Efficient analytical sensitivity computations are essential elements of gradient-based optimization schemes; however, they can be difficult to implement. This implementation issue is often resolved by adopting the semi-analytical method which exhibits the efficiency of the analytical methods and the ease of implementation of the finite difference method. However, care must be taken as semi-analytical sensitivities may exhibit errors due to truncation and round-off. Additional errors are introduced if the convergence tolerance of the primal analysis is not sufficiently small. This paper gives a general overview and some new developments of the analytical and semi-analytical sensitivity analyses for nonlinear steady-state, transient, and dynamic problems. We discuss the restrictive assumptions, accuracy, and consistency of these methods. Both adjoint and direct differentiation methods are studied. Numerical examples are provided.

42 ENGINEERING↗
NASA NTRS1976

Large deflections of shallow conical membrane

Large deflections of a shallow elastic conical membrane fixed at the outer edge and loaded by either uniform or hydrostatic pressure are investigated. The overning equations were solved by the method of matched asymptotic expansions and by a finite difference method. Agreement between the two methods was excellent for the small values of the perturbation parameter.

Chang, W. H.↗
NASA NTRS1977

Compressible laminar boundary layers with suction on swept and tapered wings

In this paper we present a numerical method for solving the compressible laminar boundary-layer equations with suction on swept and tapered wings. The method employs an efficient two-point finite-difference method to solve the governing equations, and a very convenient similarity transformation which removes the wall normal velocity as a boundary condition and places it into the governing equations as a parameter. In this way the awkward nonlinear boundary condition which couples all the variables is avoided. To test and demonstrate the method, we present a sample calculation for a typical laminar-flow-control (LFC) wing.

Kaups, K.↗
NASA NTRS1981

Numerical solution of compressible viscous flows at high Reynolds numbers

A new numerical method which was used to reduce the computation time required in fluid dynamics to solve the Navier-Stokes equations at flight Reynolds numbers is described. The method is the implicit analogue of the explicit finite different method. It uses this as its first stage, while the second stage removes the restrictive stability condition by recasting the difference equations in an implicit form. The resulting matrix equations to be solved are either upper or lower block bidiagonal equations. The new method makes it possible and practical to calculate many important three dimensional, high Reynolds number flow fields on computers.

Maccormack, R. W.↗
NASA NTRS1992

A SINDA thermal model using CAD/CAE technologies

The approach to thermal analysis described by this paper is a technique that incorporates Computer Aided Design (CAD) and Computer Aided Engineering (CAE) to develop a thermal model that has the advantages of Finite Element Methods (FEM) without abandoning the unique advantages of Finite Difference Methods (FDM) in the analysis of thermal systems. The incorporation of existing CAD geometry, the powerful use of a pre and post processor and the ability to do interdisciplinary analysis, will be described.

Rodriguez, Jose A.↗
NASA NTRS1987

Development of computational methods for unsteady aerodynamics at the NASA Langley Research Center

The current scope, recent progress, and plans for research and development of computational methods for unsteady aerodynamics at the NASA Langley Research Center are reviewed. Both integral-equations and finite-difference method for inviscid and viscous flows are discussed. Although the great bulk of the effort has focused on finite-difference solution of the transonic small-perturbation equation, the integral-equation program is given primary emphasis here because it is less well known.

Yates, E. Carson, Jr.↗
NASA NTRS1988

Accuracy analysis of the semi-analytical method for shape sensitivity calculation

The semianalytical method, widely used for calculating derivatives of static response with respect to design variables for structures modeled by finite elements, is studied in this paper. The paper shows that the method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. The errors are shown to be associated with the structural model. An error index is developed to test the accuracy of the semianalytical method. It characterizes the difference in errors between a general finite-difference method and the semianalytical method. Moreover, a method for improving the accuracy of the semianalytical method (when possible) is provided. Examples are presented to demonstrate the use of the error index.

Barthelemy, Bruno↗
NASA NTRS1990

Accuracy analysis of the semi-analytical method for shape sensitivity calculation

The semianalytical method of design sensitivity analysis that is widely used for calculating derivatives of static response with respect to design variables for structures modeled by finite elements is studied. It is shown that the method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. Errors are shown to be associated with an incompatibility of the sensitivity field with the structure. An error index is developed to test the accuracy of the semianalytical method. It characterizes the difference in errors between a general finite-difference method and the semianalytical method. A method for improving the accuracy of the semianalytical method (when possible) is provided. Examples are presented to demonstrate the use of the error index.

Barthelemy, Bruno↗
NASA NTRS1992

The solution of coupled Schroedinger equations using an extrapolation method

In this paper, extrapolation to the limit in a finite-difference method is applied to solve a system of coupled Schroedinger equations. This combination results in a method that only requires knowledge of the potential energy functions for the system. This numerical procedure has several distinct advantages over the more conventional methods. Namely, initial guesses for the term values are not needed; assumptions need be made about the behavior of the wavefunctions, such as the slope or magnitude in the nonclassical region; and the algorithm is easy to implement, has a firm mathematical foundation, and provides error estimates. Moreover, the method is less sensitive to round-off error than other methods since a small number of mesh points is used and it can be implemented on small computers. A comparison of the method with another numerical method shows results agreeing within 1 part in 10 exp 4.

Goorvitch, D.↗
NASA NTRS2003

High Order Filter Methods for Shock/Turbulence MHD Flows

Low-dissipative high order filter finite difference methods for shock/turbulence/combustion compressible viscous MHD flows has been constructed. Several variants of the filter approach that cater to different flow types are proposed. These filters provide a natural and efficient way for the minimization of the divergence of the magnetic field (del (raided dot) B) numerical error in the sense that no standard divergence cleaning is required. For certain 2-D MHD test problems, divergence free preservation of the magnetic fields of these filter schemes has been achieved.

Yee, H. C.↗
NASA NTRS1987

Geometrical acoustics and transonic helicopter sound

A new method is presented for predicting the impulsive noise generated by a transonic rotor blade. The method is a combined approach involving computational fluid dynamics and geometrical acoustics. A full-potential finite-difference method is used to obtain the pressure field close to the blade. A Kirchhoff integral formulation is then used to extend these finite-difference results into the far field. This Kirchhoff formula is based on geometrical acoustics approximations. It requires initial data across a plane at the sonic radius in a blade-fixed coordinate system. This data is provided by the finite-difference solution. Acoustic pressure predictions show good agreement with hover experimental data for cases with hover tip Mach numbers of 0.88 through 0.96. The cases above 0.92 tip Mach number are dominated by non-linear transonic effects seen as strong shocks on and off the blade tip. This paper gives the first successful predictions of far-field acoustic pressures for high-speed impulsive noise over a range of Mach numbers after delocalization.

Isom, Morris↗
NASA NTRS1987

Motion and decay of vortex rings submerged in a rotational flow

The interaction between vortex rings of finite strength and an axisymmetric rotational background flow is studied by a singular perturbation method, because it is difficult to use a finite-difference method to analyze the viscous decay in the small core of a vortex ring. The analysis is carried out by combining a composite solution of a vortex ring and an unsteady Euler solution for the background rotational flow. Using the method of averaging, a numerical scheme is developed to obtain an Euler solution in which the grid and time-step sizes depend solely on the length and velocity scales of the background flow. Numerical results are presented to illustrate the interaction between the trajectories and decay rates of the vortex rings and the background rotational flow.

Ishii, K.↗
DOE OSTI2019

Real time time-dependent density functional theory using higher order finite-element methods

We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real time using higher order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this end, we develop an a priori mesh adaption technique, based on the semidiscrete (discrete in space but continuous in time) error estimate on the time-dependent Kohn-Sham orbitals, to construct an efficient finite-element discretization. Subsequently, we obtain the full-discrete error estimate to guide our choice of the time step. We employ spectral finite elements along with special reduced order quadrature to render the overlap matrix diagonal, thereby simplifying the inversion of the overlap matrix that features in the evaluation of the discrete time-evolution operator. We use the second-order Magnus operator as the time-evolution operator, wherein the action of the discrete Magnus operator, expressed as exponential of a matrix, on the Kohn-Sham orbitals is obtained efficiently through an adaptive Lanczos iteration. We observe close to optimal rates of convergence of the dipole moment with respect to spatial and temporal discretization, for both pseudopotential and all-electron calculations. We demonstrate a staggering 100-fold reduction in the computational time afforded by higher order finite elements over linear finite elements, for both pseudopotential and all-electron calculations. Further, for similar level of accuracy, we obtain significant computational savings by our approach as compared to state-of-the-art finite-difference methods. Here, we also demonstrate the competence of higher order finite elements for all-electron benchmark systems. Lastly, we observe good parallel scalability of the proposed method on many hundreds of processors.

36 MATERIALS SCIENCE↗
NASA NTRS1980

The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations

The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented. This new method is based on the mathematical theory of characteristics. The development of the method from characteristic theory is presented. Boundary point calculation procedures consistent with the SCM method used at interior points are explained. The split coefficient matrices that define the method for steady supersonic and unsteady inviscid flows are given for several examples. The SCM method is used to compute several flow fields to demonstrate its accuracy and versatility. The similarities and differences between the SCM method and the lambda-scheme are discussed.

Chakravarthy, S. R.↗
NASA NTRS1990

A numerical method for phase-change problems

A highly accurate and efficient finite-difference method for phase-change problems with multiple moving boundaries of irregular shape is developed by employing a coordinate transformation that immobilizes moving boundaries and preserves the conservative forms of the original governing equations. The numerical method is first presented for one-dimensional phase-change problems (involving large density variation between phases, heat generation, and multiple moving boundaries) and then extended to solve two-dimensional problems (without change of densities between phases). Numerical solutions are obtained non-iteratively using an explicit treatment of the interfacial mass and energy balances and an implicit treatment of the temperature field equations. The accuracy and flexibility of the present numerical method are verified by solving some phase-change problems and comparing the results with existing analytical, semi-analytical and numerical solutions. Results indicate that one- and two-dimensional phase-change problems can be handled easily with excellent accuracies.

Kim, Charn-Jung↗
NASA NTRS2004

Adaptive Low Dissipative High Order Filter Methods for Multiscale MHD Flows

Adaptive low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous MHD flows has been constructed. Several variants of the filter approach that cater to different flow types are proposed. These filters provide a natural and efficient way for the minimization of the divergence of the magnetic field [divergence of B] numerical error in the sense that no standard divergence cleaning is required. For certain 2-D MHD test problems, divergence free preservation of the magnetic fields of these filter schemes has been achieved.

Yee, H. C.↗
NASA NTRS1979

A vector-continuous loading concept for aerodynamic panel methods

An approach to the reduction of discretization errors in aerodynamic panel methods is presented. The approach is based on preventing the occurence of induced velocity singularities at panel slope discontinuities by maintaining continuity of the velocity jump vector across the panels. The approach was implemented in a two-dimensional incompressible panel method formulation and evaluated by application to several external and internal flow problems. The method is shown to exhibit a second order accuracy trend and to produce smaller errors with velocity component boundary conditions imposed on the real flow than with equipotential boundary conditions imposed on the imaginary flow behind the panels. For flows around airfoil sections with either sharp or blunt trailing edges, the method gives excellent agreement with results from a well developed finite difference method. The method is well behaved and is insensitive to irregularities in panel size distribution.

Kemp, W. B., Jr.↗