Jet-shock interactions.
Finite difference scheme from method of characteristics to investigate flow field and intersecting exhaust plumes from nozzles
Mourer, J.↗
SEARCH · Search NASA
Results for “finite difference method”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Numerical methods for the solution of the degenerate nonlinear elliptic equations arising in optimal stochastic control theory.
Optimal control problems for Markov chains solved by iterative method, using nonlinear finite difference equations to approximate degenerate elliptic functions
Kleinman, A. J.↗
Flow field analysis of aircraft configurations using a numerical solution to the three-dimensional unified supersonic/hypersonic small disturbance equations, part 1
The unified small disturbance equations are numerically solved using the well-known Lax-Wendroff finite difference technique. The method allows complete determination of the inviscid flow field and surface properties as long as the flow remains supersonic. Shock waves and other discontinuities are accounted for implicity in the numerical method. This technique was programed for general application to the three-dimensional case. The validity of the method is demonstrated by calculations on cones, axisymmetric bodies, lifting bodies, delta wings, and a conical wing/body combination. Part 1 contains the discussion of problem development and results of the study. Part 2 contains flow charts, subroutine descriptions, and a listing of the computer program.
Gunness, R. C., Jr.↗
View factor computer program (program view) user's manual
The purpose of program VIEW is to compute view factors between specified surfaces and to be compatible with level 15.5 of the NASTRAN structural analysis program. Program VIEW is a modification of a (finite element) view factor computation program called RAVFAC. VIEW is designed to run on an IBM System/360 operating under OS (operating system), with a minimum region size of 110 K bytes. The actual computation of view factors is still performed exactly as it was in the original version of RAVFAC. In developing VIEW, RAVFAC was modified to satisfy the following compatibility requirements: (1) accept finite element input which can also be used as input to NASTRAN, (2) produce output (view factors) in a format which can be used as input to NASTRAN, and (3) follow NASTRAN program design so that in the future VIEW can be incorporated into NASTRAN as a subroutine. The VIEW program permits computation of the view factors between surfaces, taking into account the presence of any intermediate surfaces. VIEW also computes these view factors either by contour integration or by finite difference (double summation) methods.
Puccinelli, E. F.↗
A Computer Program for Calculating Three-Dimensional Compressible Laminar and Turbulent Boundary Layers on Arbitrary Wings
A computer program for calculating three dimensional compressible laminar and turbulent boundary layers on arbitrary wings is described and presented. The computer program consists of three separate programs, namely, a geometry program to represent the wing analytically, a velocity program to compute the external velocity components from a given experimental pressure distribution and a finite difference boundary layer method to solve the governing equations for compressible flows. To illustrate the usage of the computer program, three different test cases are presented and the preparation of the input data as well as the computed output data is discussed in some detail.
Cebeci, T.↗
A split-recoupled-semidirect computational technique applied to transonic flow over lifting airfoils
A new version of the semidirect iterative method eliminates significant restrictions of previous versions of the method. A semidirect method solves finite-difference equations by a rapid globally implicit iterative process driven by a fast direct elliptic solver. The new approach can treat complex systems of equations in an efficient 'correction form', and allows the use of general, nonorthogonal, boundary-fitted coordinate transformations. These features are expected to lead to significant practical applications with conservation-equation systems in either two or three dimensions. The present application to the full potential equations for steady transonic flow over an airfoil at angle of attack illustrates the utility of the technique.
Martin, E. D.↗
Recent sidewall boundary-layer investigations with suction in the Langley 0.3-m Transonic Cryogenic Tunnel
An experimental and theoretical study of the Langley 0.3-m Transonic Cryogenic Tunnel (TCT) sidewall boundary-layer with and without suction, has been made. Without suction, the boundary-layer displacement thickness at a station ahead of the model varied from about 1.6 mm to 1.3 mm over a Reynolds number range of 20 million to 200 million per m at Mach numbers from 0.30 to 0.76. Measured velocity profiles were correlated using the defect law of Hama. The boundary-layer displacement thickness decreased when suction was applied; however, after suction of about 2 percent of test section mass flow, the change in the thickness was small. A comparison of the measured suction effectiveness with finite difference and integral methods of boundary-layer calculation showed that both methods predicted the right trend over the range of suction velocities (up to a suction to free-stream velocity ratio of -0.02).
Murthy, A. V.↗
Studies of sidewall boundary layer in the Langley 0.3 meter transonic cryogenic tunnel with and without suction
Boundary layer measurements on the sidewalls of the Langley 0.3 Meter Transonic Cryogenic Tunnel were made to determine the effectiveness of the passive boundary layer bleed system over a Reynolds number range from 20 to 200 x 10 to the sixth power per meter at Mach numbers from 0.30 to 0.76. The tunnel sidewall boundary layer displacement thickness was about 2 percent of the width of the test section without the boundary layer bleed. Measured velocity profiles correlated well with the defect law of Hama. With the boundary layer bleed equivalent to about 2 percent of the test section mass flow, the boundary layer displacement thickness reduced to about 1 percent of the test section width, which is generally considered acceptable for testing airfoils. It was also noticed that effectiveness of the bleed was nearly independent of the Mach number and Reynolds number over the range of conditions tested. A comparison of the measured suction effectiveness of the bleed with the finite difference and integral methods of boundary layer calculation showed good agreement.
Murthy, A. V.↗
Surface deformation and geoid anomalies over single and double-layered convective systems
Using a primitive variable formulation of the finite-element method, the differences in the surface observables, such as topography and geoid, produced by single- and double-layered thermal convection, were compared. Both constant and depth-dependent viscosities have been considered. For the same Rayleigh number, larger surface perturbations are produced by single-cell convection. For the same Nusselt number, the magnitudes of the surface observables are greater for double-layered convection. For the same surface heat-flux, surface topographies have similar magnitudes, but the relative amplitudes of geoid anomalies depend greatly on the style of viscosity stratification. This difference in the geoid between the two systems increases with greater surface heat-flow, regardless of viscosity structure.
Koch, M.↗
Numerical simulation of excited jet mixing layers
A numerical simulation of unsteady flow in jet mixing layers, both with and without external excitation, has been performed by solving the time-dependent compressible Navier-Stokes equations. Computations were performed on a CRAY X-MP computer using MacCormick's explicit finite difference algorithm. Different excitation methods were investigated and were shown to be very effective in controlling the well organized periodic production, shedding and pairing of large scale vortex structures. It is found that pressure excitation was generally more effective than temperature excitation, and that grid refinement results in substantial improvement in the resolution of unsteady features. The location and orientation, in addition to the frequency, of the excitation source are shown to have a significant influence on the production and interaction of large scale vortex structures in the jet mixing layer.
Scott, J. N.↗
Numerical simulation of the vortical flow over a round-edged double-delta wing
Simulations of three-dimensional vortical flows over a thin double-delta wing with an aspect ratio of 2.05 have been performed. Steady-state solutions to the unsteady incompressible Navier-Stokes equations are obtained using a new implicit upwind-relaxation finite-difference scheme. The method is second-order accurate spatially and naturally dissipative. Numerical results indicate that key features of both vortical interaction and vortex breakdown are successfully simulated. The computed lift coefficients and lateral trajectories of the vortical cores are in good agreement with the experimental data.
Hsu, C.-H.↗
Electromagnetic scattering analysis on a hypercube parallel architecture
The applicability of a parallel architecture to the solution of large electromagnetic scattering problems is demonstrated. Two techniques, finite difference and the method of moments, are used to provide insight into the comparative speedups which can be attained for several algorithms. The flexibility of the hypercube architecture for different analysis algorithms is illustrated.
Patterson, Jean E.↗
Current research in cavitating fluid films
A review of the current research of cavitation in fluid films is presented. Phenomena and experimental observations include gaseous cavitation, vapor cavitation, and gas entrainment. Cavitation in flooded, starved, and dynamically loaded journal bearings, as well as squeeze films are reviewed. Observations of cavitation damage in bearings and the possibility of cavitation between parallel plates with microasperities were discussed. The transcavity fluid transport process, meniscus motion and geometry or form of the film during rupture, and reformation were summarized. Performance effects were related to heat transfer models in the cavitated region and hysteresis influence on rotor dynamics coefficients. A number of cavitation algorithms was presented together with solution procedures using the finite difference and finite element methods. Although Newtonian fluids were assumed in most of the discussions, the effect of non-Newtonian fluids on cavitation was also discussed.
Brewe, D. E.↗
Time-dependent viscous incompressible Navier-Stokes equations - The finite difference Galerkin formulation and streamfunction algorithms
Numerical techniques are developed to solve the Navier-Stokes equations for unsteady incompressible flow. The extension of the finite-difference Galerkin (FDG) method of Stephens et al. (1984) to the continuous-time case in two or three space dimensions is explained, and the numerical implementation of the method is discussed with particular attention to the staggered-MAC-grid primitive-variable discretization, the application of discrete mass balance to avoid problems inherent in FDG schemes, the direct interpretation of the FDG expansion variables as a discrete streamfunction, and a mass-balance approach to two-dimensional problems with throughflow or obstacles. Numerical results are presented graphically for the evolution of asymptotic steady flow in a driven cavity at Reynolds number 400, 1000, or 3200; good agreement with published experimental data is demonstrated, with accurate predictions of secondary-vortex formation from wall bubble recirculations at Reynolds number 1000.
Goodrich, John W.↗
A numerical study of the interaction between unsteady free-stream disturbances and localized variations in surface geometry
A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite-difference and spectral methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T-S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves.
Bodonyi, R. J.↗
Finite difference time domain calculation of transients in antennas with nonlinear loads
In this paper transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.
Luebbers, Raymond J.↗
Pre- and postprocessing techniques for determining goodness of computational meshes
Research in error estimation, mesh conditioning, and solution enhancement for finite element, finite difference, and finite volume methods has been incorporated into AUDITOR, a modern, user-friendly code, which operates on 2D and 3D unstructured neutral files to improve the accuracy and reliability of computational results. Residual error estimation capabilities provide local and global estimates of solution error in the energy norm. Higher order results for derived quantities may be extracted from initial solutions. Within the X-MOTIF graphical user interface, extensive visualization capabilities support critical evaluation of results in linear elasticity, steady state heat transfer, and both compressible and incompressible fluid dynamics.
Oden, J. Tinsley↗
Numerical simulation of laminar-turbulent transition in a spatially-developing flat plate wake
Laminar-turbulent transition of an incompressible flat-plate wake is investigated by direct numerical integration of the Navier-Stokes equations. For the numerical integration, a combination of finite-difference and spectral methods along with an ADI/Crank-Nicolson/Adams-Bashforth time integration scheme is employed. Subject to 2D forcing, the wake exhibited a rapidly-growing fundamental disturbance that quickly saturated. This saturation was due partly to the stabilizing effect of the mean flow distortion. Downstream of the saturation point, disturbance energy was concentrated in the fundamental disturbance, the second harmonic, and the mean flow distortion component. At large amplitude levels, a Karman vortex street formed. Variations in the 2D forcing level did not alter the qualitative behavior of the disturbances. Simulations of 3D breakdown indicates that the presence of large-amplitude, 2D disturbances tends to initially suppress small-amplitude 3D disturbance growth. Following this initial suppression, a resumption of 3D growth is observed that may have been due to a secondary instability mechanism. For high levels of 3D disturbance energy, lambda-shaped vortical structures formed between adjacent Karman vortices.
Dratler, D. I.↗