Search NASA⌕ Search

SEARCH · Search NASA

Results for “Numerical Methods”

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.

At least 235 records · Page 13

Numerical methods for analyzing electromagnetic scattering

Attenuation properties of the normal modes in an overmoded waveguide coated with a lossy material were analyzed. It is found that the low-order modes, can be significantly attenuated even with a thin layer of coating if the coating material is not too lossy. A thinner layer of coating is required for large attenuation of the low-order modes if the coating material is magnetic rather than dielectric. The Radar Cross Section (RCS) from an uncoated circular guide terminated by a perfect electric conductor was calculated and compared with available experimental data. It is confirmed that the interior irradiation contributes to the RCS. The equivalent-current method based on the geometrical theory of diffraction (GTD) was chosen for the calculation of the contribution from the rim diffraction. The RCS reduction from a coated circular guide terminated by a PEC are planned schemes for the experiments are included. The waveguide coated with a lossy magnetic material is suggested as a substitute for the corrugated waveguide.

Lee, S. W.↗

Evaluation of 3 numerical methods for propulsion integration studies on transonic transport configurations

An effort has been undertaken at the NASA Langley Research Center to assess the capabilities of available computational methods for use in propulsion integration design studies of transonic transport aircraft, particularly of pylon/nacelle combinations which exhibit essentially no interference drag. The three computer codes selected represent state-of-the-art computational methods for analyzing complex configurations at subsonic and transonic flight conditions. These are: EULER, a finitie volume solution of the Euler equation; VSAERO, a panel solution of the Laplace equation; and PPW, a finite difference solution of the small disturbance transonic equations. In general, all three codes have certain capabilities that allow them to be of some value in predicting the flows about transport configurations, but all have limitations. Until more accurate methods are available, careful application and interpretation of the results of these codes are needed.

Yaros, S. F.↗

Numerical methods and a computer program for subsonic and supersonic aerodynamic design and analysis of wings with attainable thrust considerations

This paper describes methodology and an associated computer program for the design of wing lifting surfaces with attainable thrust taken into consideration. The approach is based on the determination of an optimum combination of a series of candidate surfaces rather than the more commonly used candidate loadings. Special leading-edge surfaces are selected to provide distributed leading-edge thrust forces which compensate for any failure to achieve the full theoretical leading-edge thrust, and a second series of general candidate surfaces is selected to minimize drag subject to constraints on the lift coefficient and, if desired, on the pitching moment coefficient. A primary purpose of the design approach is the introduction of attainable leading-edge thrust considerations so that relatively mild camber surfaces may be employed in the achievement of aerodynamic efficiencies comparable to those attainable if full theoretical leading-edge thrust could be achieved. The program provides an analysis as well as a design capability and is applicable to both subsonic and supersonic flow.

Carlson, H. W.↗

Evaluation of three numerical methods for propulsion integration studies on transonic transport configurations

An effort has been undertaken at the NASA Langley Research Center to assess the capabilities of available computational methods for use in propulsion integration design studies of transonic transport aircraft, particularly of pylon/nacelle combinations which exhibit essentially no interference drag. The three computer codes selected represent state-of-the-art computational methods for analyzing complex configurations at subsonic and transonic flight conditions. These are: EULER, a finite volume solution of the Euler equation; VSAERO, a panel solution of the Laplace equation; and PPW, a finite difference solution of the small disturbance transonic equations. In general, all three codes have certain capabilities that allow them to be of some value in predicting the flows about transport configurations, but all have limitations. Until more accurate methods are available, careful application and interpretation of the results of these codes are needed.

Yaros, Steven F.↗

Improved numerical methods for turbulent viscous recirculating flows

The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This report evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH mode, that has been widely applied to combustor flows, illustrates the substantial gains to be achieved.

Turan, A.↗

An asymptotic induced numerical method for the convection-diffusion-reaction equation

A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method.

Scroggs, Jeffrey S.↗

A numerical method for predicting hypersonic flowfields

The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to react chemically and reach states in thermal nonequilibrium. In this paper, a new procedure based on Gauss-Seidel line relaxation is shown to solve the equations of hypersonic flow fields containing finite reaction rate chemistry and thermal nonequilibrium. The method requires a few hundred time steps and small computer times for axisymmetric flows about simple body shapes. The extension to more complex two-dimensional body geometries appears straightforward.

Maccormack, Robert W.↗

Modelling asteroid brightness variations. I - Numerical methods

A method for generating lightcurves of asteroid models is presented. The effects of the shape of the asteroid and the scattering law of a surface element are distinctly separable, being described by chosen functions that can easily be changed. The shape is specified by means of two functions that yield the length of the radius vector and the normal vector of the surface at a given point. The general shape must be convex, but spherical concavities producing macroscopic shadowing can also be modeled.

Karttunen, H.↗

Numerical methods for hypersonic boundary layer stability

Four different schemes for solving compressible boundary layer stability equations are developed and compared, considering both the temporal and spatial stability for a global eigenvalue spectrum and a local eigenvalue search. The discretizations considered encompass: (1) a second-order-staggered finite-difference scheme; (2) a fourth-order accurate, two-point compact scheme; (3) a single-domain Chebychev spectral collocation scheme; and (4) a multidomain spectral collocation scheme. As Mach number increases, the performance of the single-domain collocation scheme deteriorates due to the outward movement of the critical layer; a multidomain spectral method is accordingly designed to furnish superior resolution of the critical layer.

Malik, M. R.↗

A numerical method for relating two- and three-dimensional pressure distributions on transonic wings

This paper presents a preliminary design method for determining a wing's design pressure distribution and geometry based on airfoil normal Mach numbers and airfoil loading. In this method, the perturbation velocities in supercritical regions are computed from airfoil transonic normal Mach numbers and include the influence of local sweep, taper, and three-dimensional induced velocities, so that the appearance and strength of shocks can be expected to resemble those of the airfoil. The velocities in subcritical wing regions are scaled first with simple sweep theory, and then to achieve the desired load distribution. The method was applied to the design of an oblique flying wing, using a linear potential method. The required wing area could be reduced by 14 percent using this method rather than simple sweep theory.

Kroo, Ilan↗

A comparison of numerical methods for the Rayleigh equation in unbounded domains

A second-order finite difference and two spectral methods, including a Chebyshev tau and a Chebyshev collocation method were implemented to determine the linear hydrodynamic stability of an unbounded shear flow. The velocity profile of the basic flow in the stability analysis mimicks that of a one-stream free mixing layer. Local and global eigenvalue solution methods are used to determine individual eigenvalues and the eigenvalue spectrum, respectively. The calculated eigenvalue spectrum includes a discrete mode, a continuous spectrum associated with the equation singularity and a continuous spectrum associated with the domain unboundedness. The efficiency and the accuracy of these discretization methods in the prediction of the eigensolutions of the discrete mode were evaluated by comparison with a conventional shooting procedure. Their capabilities in mapping out the continuous eigenvalue spectra are also discussed.

Liou, W. W.↗

A numerical method for parameterization of atmospheric chemistry - Computation of tropospheric OH

An efficient and stable computational scheme for parameterization of atmospheric chemistry is described. The 24-hour-average concentration of OH is represented as a set of high-order polynomials in variables such as temperature, densities of H2O, CO, O3, and NO(t) (defined as NO + NO2 + NO3 + 2N2O5 + HNO2 + HNO4) as well as variables determining solar irradiance: cloud cover, density of the overhead ozone column, surface albedo, latitude, and solar declination. This parameterization of OH chemistry was used in the three-dimensional study of global distribution of CH3CCl3. The proposed computational scheme can be used for parameterization of rates of chemical production and loss or of any other output of a full chemical model.

Spivakovsky, C. M.↗

A hybrid numerical method for three-dimensional spatially-developing free-shear flows

The present novel algorithm for 3D incompressible Navier-Stokes equations treats a domain which is (1) infinite in the vertical direction, using a mapped spectral method; (2) finite in the streamwise direction, using a classical Fourier method; and (3) homogeneous in the spanwise direction, using high-order compact finite differencing. A projection method is employed which ensures the exact conservation of mass, as well as the satisfaction of the boundary conditions at infinity. The novel aspects of these methods are noted, and the code they constitute is validated in light of several test cases. Results are presented for two- and three-dimensional mixing layers.

Buell, Jeffrey C.↗

Efficient numerical method for computation of the thermohydrodynamics of laminar lubricating films

The purpose of this paper is to describe an accurate, yet economical, method for computing temperature effects in laminar lubricating films in two dimensions. Because of the marked dependence of lubricant viscosity on temperature, the effect of viscosity variation both across and along a lubricating film can dwarf other deviations from ideal constant-property lubrication. In practice, a thermohydrodynamics program will involve simultaneous solution of the film lubrication problem, together with heat conduction in a solid, complex structure. In pursuit of computational economy, techniques similar to those for Gaussian quadrature are used; it is shown that, for many purposes, the use of just two properly positioned temperatures (Lobatto points) characterizes the transverse temperature distribution.

Elrod, H. G.↗

Numerical methods in Markov chain modeling

Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.

Philippe, Bernard↗

A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting

The present treatment of elliptic regions via hyperbolic flux-splitting and high order methods proposes a flux splitting in which the corresponding Jacobians have real and positive/negative eigenvalues. While resembling the flux splitting used in hyperbolic systems, the present generalization of such splitting to elliptic regions allows the handling of mixed-type systems in a unified and heuristically stable fashion. The van der Waals fluid-dynamics equation is used. Convergence with good resolution to weak solutions for various Riemann problems are observed.

Shu, Chi-Wang↗