Use of CYBER 203 and CYBER 205 computers for three-dimensional transonic flow calculations

Experiences are discussed for modifying two three-dimensional transonic flow computer programs (FLO 22 and FLO 27) for use on the CDC CYBER 203 computer system. Both programs were originally written for use on serial machines. Several methods were attempted to optimize the execution of the two programs on the vector machine: leaving the program in a scalar form (i.e., serial computation) with compiler software used to optimize and vectorize the program, vectorizing parts of the existing algorithm in the program, and incorporating a vectorizable algorithm (ZEBRA I or ZEBRA II) in the program. Comparison runs of the programs were made on CDC CYBER 175. CYBER 203, and two pipe CDC CYBER 205 computer systems

TAWFIVE: A user's guide

The Transonic Analysis of a Wing and Fuselage with Interacted Viscous Effects (TAWFIVE) was developed. A finite volume full potential method is used to model the outer inviscid flow field. First-order viscous effects are modeled by a three dimensional integral boundary layer method. Both turbulent and laminar boundary layers are treated. Wake thickness and curvature effects are modeled using a two dimensional strip method. A very brief discussion of the engineering aspects of the program is given. The input and use of the program are covered in great detail

A title-gap flow model for use in aerodynamic loads assessment of space shuttle thermal protection system: Parallel gap faces

The problem of predicting aerodynamic loads on the insulating tiles of the space shuttle thermal protection system (TPS) is discussed and seen to require a method for predicting pressure and mass flux in the gaps between tiles. A mathematical model of the tile-gap flow is developed, based upon a slow viscous (Stokes) flow analysis, and is verified against experimental data. The tile-gap pressure field is derived from a solution of the two-dimensional Laplace equation; the mass-flux vector is then calculated from the pressure gradient. The means for incorporating this model into a lumped-parameter network analogy for porous-media flow is given. The means for incorporating this model into a lumped-parameter network analogy for porous-media flow is given. The flow model shows tile-gap mass flux to be very sensitive to the gap width indicating a need for coupling the TPS flow and tile displacement calculation. Analytical and experimental work to improve TPS flow predictions and a possible shuttle TPS hardware modification are recommended

Vectorizable multigrid algorithms for transonic flow calculations

The analysis and incorporation into a multigrid scheme of several vectorizable algorithms are discussed. Von Neumann analyses of vertical line, horizontal line, and alternating direction ZEBRA algorithms were performed; and the results were used to predict their multigrid damping rates. The algorithms were then successfully implemented in a transonic conservative full-potential computer program. The convergence acceleration effect of multiple grids is shown and the convergence rates of the vectorizable algorithms are compared to the convergence rates of standard successive line overrelaxation (SLOR) algorithms

Convergence Acceleration of the Harmonic Balance Method using a Time-Level Preconditioner

The Harmonic Balance method is nowadays widely applied for numerically solving problems that are known to possess time-periodic solutions. Key reasons for its success are its wide range of applicability, relative ease of implementation, and computational efficiency compared to time-accurate approaches. The computational efficiency of the Harmonic Balance method is partly derived from the fact that it searches directly for a periodic solution, instead of integrating the governing equations in time until a periodic solution is reached. Convergence acceleration techniques such as multigrid, implicit residual smoothing and local time stepping may also be used to improve the efficiency of the Harmonic Balance method. This paper considers another option for accelerating convergence, namely a novel time-level preconditioner that can be applied to the Harmonic Balance residual locally in each computational cell. This preconditioner is derived from a rigorous stability analysis of the Harmonic Balance equations and is shown to give a speed-up factor of 2 when applied to simulations of laminar vortex shedding behind a circular cylinder

Time-accurate Navier-Stokes calculations with multigrid acceleration

A numerical scheme to solve the unsteady Navier-Stokes equations is described. The scheme is implemented by modifying the multigrid-multiblock version of the steady Navier-Stokes equations solver, TLNS3D. The scheme is fully implicit in time and uses TLNS3D to iteratively invert the equations at each physical time step. The design objective of the scheme is unconditional stability (at least for first- and second-order discretizations of the physical time derivatives). With unconditional stability, the choice of the time step is based on the physical phenomena to be resolved rather than limited by numerical stability which is especially important for high Reynolds number viscous flows, where the spatial variation of grid cell size can be as much as six orders of magnitude. An analysis of the iterative procedure and the implementation of this procedure in TLNS3D are discussed. Numerical results are presented to show both the capabilities of the scheme and its speed up relative to the use of global minimum time stepping. Reductions in computational times of an order of magnitude are demonstrated

Nitrogen uptake and distribution in annual ryegrass

Last updated: 6/9/200

Leaf, shoot, and root fractions of annual ryegrass influenced by nitrogen rate and season

Last updated: 6/9/200

Finite voltage shot noise in normal-metal - superconductor junctions

We express the low-frequency shot noise in a disordered normal-metal - superconductor (NS) junction at finite (subgap) voltage in terms of the normal scattering amplitudes and the Andreev reflection amplitude. In the multichannel limit, the conductance exhibits resonances which are accompanied by an enhancement of the (differential) shot noise. In the study of multichannel single and double barrier junctions we discuss the noise properties of coherent transport at low versus high voltage with respect to the Andreev level spacing.Comment: 6 pages, Latex, 2 eps-figures, to be published in PRB, Appendix on Bogoliubov equation