Hereditary optimal control problems - Numerical method based upon a Pade approximation
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Lee, A. Y.↗
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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↗
Modeling supersonic combustion using a fully implicit numerical method
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Wilson, Gregory J.↗
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↗
Numerical methods for the analysis of sampled-data systems and for the computation of system zeros
MARSYAS is a computer-aided control system design package for the simulation and analysis of dynamic systems. In the summer of 1991 MARSYAS was updated to allow for the analysis of sampled-data systems in terms of frequency response, stability, etc. This update was continued during the summer of 1992 in order to extend further MARSYAS commands to the study of sampled-data systems. Further work was done to examine the computation of OPENAT transfer functions, root-locii and w-plane frequency response plots.
Hodel, A. Scottedward↗
A numerical method for the stress analysis of stiffened-shell structures under nonuniform temperature distributions
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LOADS AND STRESSES, STRUCTURAL↗
A numerical method for evaluating wave drag
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Cahn, Maurice S↗
A simple numerical method for the calculation of the laminar boundary layer
An iteration difference method for the calculation of the incompressible laminar boundary layer is described. The method uses Prandtl's boundary layer equation and the boundary conditions directly and permits the attainment of an arbitrary accuracy. The method has been tested successfully in the continuation of the Blasius profile on the flat plate, on the circular cylinder investigated by Heimenz and on an elliptical cylinder of fineness ratio 1:4. The method makes possible the testing of previously developed methods, all of which contain important assumptions.
BOUNDARY LAYER, LAMINAR - CALCULATIONS - SCHRODER ↗
Development of numerical methods for overset grids with applications for the integrated Space Shuttle vehicle
Algorithms and computer code developments were performed for the overset grid approach to solving computational fluid dynamics problems. The techniques developed are applicable to compressible Navier-Stokes flow for any general complex configurations. The computer codes developed were tested on different complex configurations with the Space Shuttle launch vehicle configuration as the primary test bed. General, efficient and user-friendly codes were produced for grid generation, flow solution and force and moment computation.
Chan, William M.↗