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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Bounded motion design in the Earth zonal problem using differential algebra based normal form methods

Establishing long-term relative bounded motion between orbits in perturbed dynamics is a key challenge in astrodynamics to enable cluster flight with minimum propellant expenditure. Herein, we present an approach that allows for the design of long-term relative bounded motion considering a zonal gravitational model. Entire sets of orbits are obtained via high-order Taylor expansions of Poincarè return maps about reference fixed points. The high-order normal form algorithm is used to determine a change in expansion variables of the map into normal form space, in which the phase space behavior is circular and can be easily parameterized by action–angle coordinates. The action–angle representation of the normal form coordinates is then used to parameterize the original Poincarè return map and average it over a full phase space revolution by a path integral along the angle parameterization. As a result, the averaged nodal period and drift in the ascending node are obtained, for which the bounded motion conditions are straightforwardly imposed. Sets of highly accurate bounded orbits are obtained, extending over several thousand kilometers, and valid for decades.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1989

Accurate simulation of vortical flows

Even with recent supercomputers having a large memory, Navier-Stokes simulations for vortical flows do not provide satisfactory results because of the lack of grid resolution to accurately simulate the strength of separation vortices. To overcome this problem, a zonal method is proposed to increase the number of grid points locally. Interface scheme which is critical for an efficient and stable zonal method is based on the Fortified Navier-Stokes concept. Application to both two-dimensional conical and three-dimensional delta wing problems indicates this simple zonal method can improve the accuracy of vortical flow simulations.

Fujii, Kozo↗
NASA NTRS1974

Analytical satellite theories based on a new set of canonical elements

A new analytical satellite theory is presented. Instead of the 6 classical elements of Delaunay, a set of 8 canonical elements is used. Whereas the time is the independent variable in classical theory, the true anomaly is the independent variable in the new theory. The new approach has four features: (1) The amount of formulas in the solution is reduced considerably. (2) The first order results are almost as accurate as second order results in classical theory. (3) The theory is easier to understand from a didactical point of view. (4) The problems connected with the inaccuracy of the mean motion that are typical for classical satellite theory are no longer present. The new elements are applied to analytical solutions of the zonal oblateness problem and to the problem of the 24 hour satellite.

Scheifele, G.↗
NASA NTRS1991

Computation of incompressible viscous flows through artificial heart devices with moving boundaries

The extension of computational fluid dynamics techniques to artificial heart flow simulations is illustrated. Unsteady incompressible Navier-Stokes equations written in 3-D generalized curvilinear coordinates are solved iteratively at each physical time step until the incompressibility condition is satisfied. The solution method is based on the pseudo compressibility approach and uses an implicit upwind differencing scheme together with the Gauss-Seidel line relaxation method. The efficiency and robustness of the time accurate formulation of the algorithm are tested by computing the flow through model geometries. A channel flow with a moving indentation is computed and validated with experimental measurements and other numerical solutions. In order to handle the geometric complexity and the moving boundary problems, a zonal method and an overlapping grid embedding scheme are used, respectively. Steady state solutions for the flow through a tilting disk heart valve was compared against experimental measurements. Good agreement was obtained. The flow computation during the valve opening and closing is carried out to illustrate the moving boundary capability.

Kiris, Cetin↗
NASA NTRS1984

Applications of a conservative zonal scheme to transient and geometrically complex problems

A conservative zoning technique, wherein the flow field for a finite-difference calculation is divided into several regions to simplify grid generation, is discussed and is applied in the solution of a two-dimensional problem of complex topology. Calculations are performed on two zonal, or patched, grid systems for the supersonic flow over a double-airfoil configuration. The solution is smooth and continuous across the zonal interfaces, and shock waves pass through the boundaries without distortion. In addition, the time-accuracy of the zonal-boundary method is verified by a two-zone cyclinder calculation with a stationary inner and a rotating outer mesh.The feasibility of the zonal approach for use in the solution of geometrically complex and unsteady problems is thus demonstrated.

Hessenius, K. A.↗
NASA NTRS1986

Applications of a Conservative Zonal Scheme to Transient and Geometrically Complex Problems

A conservative zoning technique, wherein the flow field for a finite-difference calculation is divided into several regions to simplify grid generation, is discussed and is applied in the solution of a two-dimensional problem of complex topology. Calculations are performed on two zonal, or patched, grid systems for the supersonic flow over a double-airfoil configuration. The solution is smooth and continuous across the zonal interfaces, and shock waves pass through the boundaries without distortion. In addition, the time accuracy of the zonal boundary method is verified by a two-zone cylinder calculation with a stationary inner and a rotating outer mesh. The feasibility of the zonal approach for use in the solution of geometrically complex and unsteady problems is thus demonstrated.

Hessenius, Kristin A.↗
NASA NTRS1975

Temperature fields of an absorptive medium in a radiating system of arbitrary configuration (the spatial problem)

A generalized zonal method based on systems of linear algebraic equations is used to determine the temperature fields in an absorptive grey medium filling a closed radiation system that consists of three boundary zones, of which one is adiabatic and the other two are isothermal. The example calculation considers the case of a solenoidal radiation field of local radiative equilibrium.

Surinov, Y. A.↗
NASA NTRS1989

Zonal multigrid solution of compressible flow problems on unstructured and adaptive meshes

The simultaneous use of adaptive meshing techniques with a multigrid strategy for solving the 2-D Euler equations in the context of unstructured meshes is studied. To obtain optimal efficiency, methods capable of computing locally improved solutions without recourse to global recalculations are pursued. A method for locally refining an existing unstructured mesh, without regenerating a new global mesh is employed, and the domain is automatically partitioned into refined and unrefined regions. Two multigrid strategies are developed. In the first, time-stepping is performed on a global fine mesh covering the entire domain, and convergence acceleration is achieved through the use of zonal coarse grid accelerator meshes, which lie under the adaptively refined regions of the global fine mesh. Both schemes are shown to produce similar convergence rates to each other, and also with respect to a previously developed global multigrid algorithm, which performs time-stepping throughout the entire domain, on each mesh level. However, the present schemes exhibit higher computational efficiency due to the smaller number of operations on each level.

Mavriplis, Dimitri J.↗
DOE OSTI2020

First implementation of gyrokinetic exact linearized Landau collision operator and comparison with models

Gyrokinetic simulations are fundamental to understanding and predicting turbulent transport in magnetically confined fusion plasmas. Previous simulations have used model collision operators with approximate field-particle terms of unknown accuracy and/or have neglected collisional finite Larmor radius (FLR) effects. We have implemented the linearized Fokker–Planck collision operator with exact field-particle terms and full FLR effects in a gyrokinetic code (GENE). The new operator, referred to as “exact” in this paper, allows the accuracy of model collision operators to be assessed. The conservative Landau form is implemented because its symmetry underlies the conservation laws and the H-theorem, and enables numerical methods to preserve this conservation, independent of resolution. The implementation utilizes the finite-volume method recently employed to discretize the Sugama collision model in GENE, allowing direct comparison between the two operators. Results show that the Sugama model appears accurate for the growth rates of trapped electron modes (TEMs) driven only by density gradients, but appreciably underestimates the growth rates as the collisionality and electron temperature gradient increase. The TEM turbulent fluxes near the nonlinear threshold using the exact operator are similar to the Sugama model for the n e = d ln T e /d ln n e = 0 case, but substantially larger than the Sugama model for the n e = 1 case. The FLR effects reduce the growth rates increasingly with wavenumber deepening a “valley” at the intermediate binormal wavenumber as the unstable mode extends from the TEM regime to the electron temperature gradient instability regime. Application to the Hinton–Rosenbluth problem shows that zonal flows decay faster as the radial wavenumber increases and the exact operator yields weaker decay rates.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1983

Barotropic instability of weakly non-parallel zonal flows

Integrations of the linear stability problem, in the present numerical investigation of weakly nonparallel zonal flows barotropic instability having localized intense shear regions, reveal the existence of unstable localized wave packets. The spatial structure and eigenfrequencies of these packets depend on two parameters measuring the degree of supercriticality and the zonal length scale of the shear region. It is found that instability structure is defined by conditions ensuring the decay of the wave packet at infinity, and the transition from long to short waves across a turning point region that is controlled by nonparallel effects.

Merkine, L.-O.↗
NASA NTRS1982

Climate studies with a multi-layer energy balance model. I - Model description and sensitivity to the solar constant. II - The role of feedback mechanisms in the CO2 problem

A nine-layer zonally averaged, steady-state model, based upon thermal energy balance, is developed for use in climate sensitivity studies and includes an accurate treatment of radiative transfer, parameterized meridional and vertical energy transport, and thermodynamic interaction between the surface and the atmosphere. A high degree of nonlinearity is exhibited by the model in a study of sensitivity to changes in the solar constant. The change in the hemispheric mean surface temperature is +3.1 C in response to a 2% increase in the solar constant and -4.3 C in response to a 2% decrease in the solar constant. The sensitivity varies with latitude, and the response of atmospheric temperature varies with height. In addition, the model is used to study the sensitivity of climate to a doubling of the atmospheric CO2 content. It is found that the tropospheric temperature lapse rate decreases at low latitudes but increases at high latitudes in response to a doubled CO2 content. Averaged over the Northern Hemisphere, the change is +2.3 C in the surface temperature and +0.47 C in the earth's brightness temperature. The effects of some feedback mechanisms on the climate sensitivity to a doubled CO2 content show that the sensitivity of surface temperature approximately doubles at all latitudes due to the change in water vapor content.

Peng, L.↗
NASA NTRS1988

Upper-level baroclinic instability

Effects on baroclinic instability of 'partial equilibration' and an Ekman lower boundary condition were examined by considering the linear stability of various zonal wind profiles having, as in the Charney (1947) problem, constant vertical shear and positive meridional gradient of potential vorticity aloft, but with reduced shear and zero or negative potential vorticity gradient at low levels. It is shown that, compared to the Charney problem, the partially equilibrated basic state zonal wind profiles obtained here have instabilities whose growth rates are less sensitive to the presence of an Ekman lower boundary condition.

Snyder, Christopher M.↗
NASA NTRS1991

Predictions of zonal wind and angular momentum by the NMC medium-range forecast model during 1985-89

This paper investigates the quality of weather predictions of the atmosphere's relative angular momentum (M) made by the most recent version of the NMC medium-range forecast model (MRF88) during December 1985-1989. It was found that, compared with older versions of MRF, bias errors in the MRF88 forecasts of M became more prominent, while random errors were not affected. Both types of errors in the M forecasts could be traced to problems with forecasts in the zonal mean zonal wind in the tropics.

Rosen, Richard D.↗
NASA NTRS1997

Application of a Chimera Full Potential Algorithm for Solving Aerodynamic Problems

A numerical scheme utilizing a chimera zonal grid approach for solving the three dimensional full potential equation is described. Special emphasis is placed on describing the spatial differencing algorithm around the chimera interface. Results from two spatial discretization variations are presented; one using a hybrid first-order/second-order-accurate scheme and the second using a fully second-order-accurate scheme. The presentation is highlighted with a number of transonic wing flow field computations.

Holst, Terry L.↗
NASA NTRS1985

A Lagrangian method for the shallow water equations based on a Voronoi mesh - Flows on a rotating sphere

A Lagrangian scheme using the Voronoi mesh is applied to study shallow water flow on a sphere. Discrete approximations to the shallow water equations are obtained for the surfaces of a nonrotating and a rotating sphere, and discrete differential operators are defined for the gradient and the divergence on the sphere. Dissipation is put into the model, when needed, by merging fluid points when they get too close to each other. The full numerical scheme is described and results of numerical computations on various test cases are given, including zonal flow and the Riemann problem.

Augenbaum, J. M.↗
NASA NTRS1988

Application of multiple grids topology to supersonic internal/external flow interactions

For many aerodynamic applications, it is very difficult to construct a smooth body-fitted grid around complex configurations. An approach, called 'multiple grids' or 'zonal grids', which subdivides the entire physical domain into several subdomains, is used to overcome such difficulties. The approach is applied to obtain the solutions to the Euler equations for the supersonic internal/external flow around a fighter-aircraft configuration. Steady-state solutions are presented for Mach 2 at 0, 3.79, 7, and 10 deg angles-of-attack. The problem of conservative treatment at the zonal interfaces is also addressed.

Kathong, M.↗
NASA NTRS1984

Feasibility of using the Massively Parallel Processor for large eddy simulations and other Computational Fluid Dynamics applications

The results of an investigation into the feasibility of using the MPP for direct and large eddy simulations of the Navier-Stokes equations is presented. A major part of this study was devoted to the implementation of two of the standard numerical algorithms for CFD. These implementations were not run on the Massively Parallel Processor (MPP) since the machine delivered to NASA Goddard does not have sufficient capacity. Instead, a detailed implementation plan was designed and from these were derived estimates of the time and space requirements of the algorithms on a suitably configured MPP. In addition, other issues related to the practical implementation of these algorithms on an MPP-like architecture were considered; namely, adaptive grid generation, zonal boundary conditions, the table lookup problem, and the software interface. Performance estimates show that the architectural components of the MPP, the Staging Memory and the Array Unit, appear to be well suited to the numerical algorithms of CFD. This combined with the prospect of building a faster and larger MMP-like machine holds the promise of achieving sustained gigaflop rates that are required for the numerical simulations in CFD.

Bruno, John↗