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At least 667 records · Page 37

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NASA NTRS1974

Aligned magnetohydrodynamic solution for solar wind flow past the earth's magnetosphere

Exact numerical solutions of the MHD equations for a perfect dissipationless gas with aligned magnetic field are given for conditions representative of steady supersonic solar wind flow past an axisymmetric model of the earth's magnetosphere. The solution is based on use of a transformation that relates without approximation the equations of magnetohydrodynamics to those of gasdynamics of a pseudogas that has an unusual equation of state. The results confirm the applicability of the previously existing gasdynamic solutions for the typically modest intensities of the interplanetary magnetic field that lead to Alfven Mach numbers of about 10 or greater. For smaller values, however, significant effects are indicated with the flanks of the bow wave moving away from the earth and the nose moving toward the earth. The results are consistent with direct observations in space.

Spreiter, J. R.↗

NASA NTRS1975

Solutions for incompressible separated boundary layers including viscous-inviscid interaction

Numerical solutions are presented for the laminar and turbulent boundary-layer equations for incompressible flows with separation and reattachment. The separation angularity is avoided by using an inverse technique in which the displacement thickness is prescribed and the pressure is deduced from the resulting solution. The turbulent results appear qualitatively correct despite the use of a two-layer eddy-viscosity model which is generally assumed appropriate only for mild-pressure-gradient flows. A new viscous-inviscid interaction technique is presented in which the inviscid flow is solved inversely by prescribing the pressure from the boundary-layer solution and deducing the new displacement thickness from the solution of a Cauchy integral. Calculations are presented using this interaction procedure for a laminar flow in which separation and reattachment occur on a solid surface.

Carter, J. E.↗

NASA NTRS1975

Inverse solutions for laminar boundary-layer flows with separation and reattachment

Numerical solutions of the laminar, incompressible boundary layer equations are presented for flows involving separation and reattachment. Regular solutions are obtained with an inverse approach in which either the displacement thickness or the skin friction is specified; the pressure is deduced from the solution. A vorticity-stream-function formulation of the boundary layer equations is used to eliminate the unknown pressure. Solutions of the resulting finite difference equations, in which the flow direction is taken into account, are obtained by several global iteration schemes which are stable and have unconditional diagonal dominance. Results are compared with Klineberg and Steger's separated boundary layer calculations, and with Briley's solution of Navier-Stokes equations for a separated region. In addition, an approximate technique is presented in which the streamwise convection of vorticity is set equal to zero in the reversed flow region; such a technique results in a quick forward marching procedure for separated flows.

Carter, J. E.↗

NASA NTRS1981

Multigrid solution of the Navier-Stokes equations on nonuniform grids

The numerical solution of the Navier-Stokes equations in general two dimensional domains is considered. A proper finite difference approximation to the governing equations, on nonstaggered grids, in a transformed plane is formulated. Several aspects of a multigrid method for the solution of the finite difference equations are described. The efficiency of some relaxation schemes and the transfer among the grids which are nonuniform in the physical plane are emphasized.

Fuchs, L.↗

NASA NTRS1981

Application of adaptive grids to fluid-flow problems with asymptotic solutions

Coordinate system selection is an important consideration in the asymptotic numerical solution of any fluid-flow or heat transfer problem. This paper uses a new technique that provides a simple way of moving the mesh points in physical space in order to reduce the error in the computed asymptotic solution relative to that obtained using a fixed mesh. Applications to fluid-flow problems are presented, including boundary layer flow and inviscid supersonic flow over cylinders, and wedges with associated detached shocks. The treatment of curved boundaries, stationary and nonstationary boundaries, and systems of PDE's is discussed. Significant error reductions are demonstrated.

Rai, M. M.↗

NASA NTRS1992

Navier-Stokes solutions with surface catalysis for Martian atmospheric entry

In this study numerical solutions have been obtained for two-dimensional axisymmetric hypersonic nonequilibrium CO2 flow over a high angle blunt cone with appropriate surface boundary conditions to account for energy and mass conservation at the body surface. The flowfield is described by the Navier-Stokes equations and multicomponent conservation laws which account for both translational and internal vibrational nonequilibrium effects. Complete forebody solutions have been obtained for the peak heating point of the Mars entry trajectory specified in the proposed NASA MESUR (Mars Environmental Survey) project. In these solutions, radiative equilibrium wall temperature and surface heating distributions are determined over the MESUR aeroshell forebody for entry velocity equal to 7 km/sec with varying degrees of surface catalysis. The effects of gas kinetics, surface catalysis, transport properties, and vibrational relaxation times on the surface heating are examined. The results identify some important issues in the prediction of surface heating for flows in thermochemical nonequilibrium and show that the Navier-Stokes code used herein is effective for thermal protection system design and materials selection.

Chen, Y.-K.↗

NASA NTRS1993

Least-squares finite element solutions for three-dimensional backward-facing step flow

Comprehensive numerical solutions of the steady state incompressible viscous flow over a three-dimensional backward-facing step up to Re equals 800 are presented. The results are obtained by the least-squares finite element method (LSFEM) which is based on the velocity-pressure-vorticity formulation. The computed model is of the same size as that of Armaly's experiment. Three-dimensional phenomena are observed even at low Reynolds number. The calculated values of the primary reattachment length are in good agreement with experimental results.

Jiang, Bo-Nan↗

DOE OSTI2020

Laser cooling limits in fields with a polarisation gradient of atoms with different recoil energies

Based on the numerical solution of the quantum kinetic equation for the atomic density matrix, which makes it possible to accurately take into account the recoil effects in the interaction of atoms with field photons, we have studied the limits of laser cooling of atoms using closed optical transitions characterised by different recoil parameters (the ratio of the recoil energy to the natural linewidth). It is shown that for optical transitions with an insufficiently small recoil parameter, the polarisation effects, which lead to the possibility of sub-Doppler laser cooling, lose their efficiency and do not ensure an attainment of the temperature below the Doppler limit. The analysis performed allows one to outline the boundaries of the sub-Doppler theory of laser cooling of atoms. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1980

An adaptive computation mesh for the solution of singular perturbation problems

In singular perturbation problems, control of zone size variation can affect the effort required to obtain accurate, numerical solutions of finite difference equations. The mesh is generated by the solution of potential equations. Numerical results for a singular perturbation problem in two dimensions are presented. The mesh was used in calculations of resistive magnetohydrodynamic flow in two dimensions.

Brackbill, J. U.↗

NASA NTRS1981

Dynamic crack propagation and arrest in orthotropic DCB fiber composite specimens

An orthotropic double cantilever beam (DCB) model is used to study dynamic crack propagation and arrest in 90 deg unidirectional Hercules AS/3501-6 graphite fiber epoxy composites. The dynamic fracture toughness of the composite is determined from tests performed on the long-strip specimen and DCB crack arrest experiments are conducted. By using the dynamic fracture toughness in a finite-difference solution of the DCB governing partial differential equations, a numerical solution of the crack propagation and arrest events is computed. Excellent agreement between the experimental and numerical crack arrest results are obtained.

Williams, J. H., Jr.↗

DOE OSTI2021

Vibration-Based Sensor Design: A Grey-Box Approach

Knowledge of the internal structure of an object or device under investigation proceeds from the basic idea of constructing its dynamic behavioral relations governed by a set of differential/algebraic equations that characterize its response. These equations can be partial differential equations leading to finite element or finite difference relations requiring a complex numerical solution on a super computer or ordinary differential equations requiring sophisticated numerical integration techniques to obtain the desired solution. Discrete dynamic systems evolving from digitized data acquisition are typically captured by sampled-data (continuous-to-discrete) representations characterized by a set of difference equations specifying the underlying system dynamics. In any case, with a mathematical description in hand, Grey-Box modeling techniques have evolved, concerned with the estimation of model parameters embedded in a prescribed set of equations (the system) governing its behavior, while capturing the underlying physical phenomenology of the problem at hand.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1976

Numerical and approximate solution of the high Reynolds number small separation problem

Several possible methods of solving the small separation problem at high Reynolds number are investigated. In addition to using analytical methods, there are several numerical approaches which are used. High Reynolds number laminar two dimensional problems are used for simplicity. A brief discussion is given of the finite difference methods since these methods are discussed in detail. Most of the emphasis is placed on developing an approximate integral method. As a model problem the supersonic compression ramp problem is chosen since several numerical solutions along with experimental data are available. The techniques discussed are modified and applied to other similar type wall geometries.

Davis, R. T.↗

NASA NTRS1992

Essentially nonoscillatory postprocessing filtering methods

High order accurate centered flux approximations used in the computation of numerical solutions to nonlinear partial differential equations produce large oscillations in regions of sharp transitions. Here, we present a new class of filtering methods denoted by Essentially Nonoscillatory Least Squares (ENOLS), which constructs an upgraded filtered solution that is close to the physically correct weak solution of the original evolution equation. Our method relies on the evaluation of a least squares polynomial approximation to oscillatory data using a set of points which is determined via the ENO network. Numerical results are given in one and two space dimensions for both scalar and systems of hyperbolic conservation laws. Computational running time, efficiency, and robustness of method are illustrated in various examples such as Riemann initial data for both Burgers' and Euler's equations of gas dynamics. In all standard cases, the filtered solution appears to converge numerically to the correct solution of the original problem. Some interesting results based on nonstandard central difference schemes, which exactly preserve entropy, and have been recently shown generally not to be weakly convergent to a solution of the conservation law, are also obtained using our filters.

Lafon, F.↗

DOE OSTI2020

Coordinate parameterisation and spectral method optimisation for Beltrami field solver in stellarator geometry

The numerical solution of the stepped pressure equilibrium (Hudson et al 2012 Phys. Plasmas 19 112502) requires a fast and robust solver to obtain the Beltrami field in three-dimensional geometry such as stellarators. The spectral method implemented in the stepped pressure equilibrium code (SPEC) is efficient when the domain is a hollow torus, but ill-conditioning of the discretised linear equations occurs in the (solid) toroid due to the artificially singular coordinate parameterisation near the axis. Here, we propose an improved choice for the reference axis to prevent coordinates surfaces from overlapping. Then, we examine the parity and asymptotics of the magnetic vector potential near the axis and suggest the use of recombined and rescaled Zernike radial basis functions. The maximum relative error in the magnetic field of the Wendelstein 7-X geometry is shown to reach 10 –9 at high resolution in a series of convergence tests and benchmarks against the boundary integral equation solver for Taylor states. The new method is also reported to significantly improve the accuracy of multi-volume SPEC calculations. A comparison between free-boundary SPEC and the analytical Dommaschk potential is presented with higher-than-usual Fourier resolution. It is illustrated that we are able to resolve low amplitude current sheets when an interface is placed where there is no flux surface in the analytic solution. This was previously concealed because of insufficient numerical resolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1972

IBM system/360 assembly language interval arithmetic software

Computer software designed to perform interval arithmetic is described. An interval is defined as the set of all real numbers between two given numbers including or excluding one or both endpoints. Interval arithmetic consists of the various elementary arithmetic operations defined on the set of all intervals, such as interval addition, subtraction, union, etc. One of the main applications of interval arithmetic is in the area of error analysis of computer calculations. For example, it has been used sucessfully to compute bounds on sounding errors in the solution of linear algebraic systems, error bounds in numerical solutions of ordinary differential equations, as well as integral equations and boundary value problems. The described software enables users to implement algorithms of the type described in references efficiently on the IBM 360 system.

Phillips, E. J.↗

NASA NTRS1982

Boundary-layer effects in composite laminates. I - Free-edge stress singularities. II - Free-edge stress solutions and basic characteristics

The fundamental nature of the boundary-layer effect in fiber-reinforced composite laminates is formulated in terms of the theory of anisotropic elasticity. The basic structure of the boundary-layer field solution is obtained by using Lekhnitskii's stress potentials (1963). The boundary-layer stress field is found to be singular at composite laminate edges, and the exact order or strength of the boundary layer stress singularity is determined using an eigenfunction expansion method. A complete solution to the boundary-layer problem is then derived, and the convergence and accuracy of the solution are analyzed, comparing results with existing approximate numerical solutions. The solution method is demonstrated for a symmetric graphite-epoxy composite.

Wang, S. S.↗

NASA NTRS1983

N-person differential games. Part 2: The penalty method

The equilibrium strategy for N-person differential games can be found by studying a min-max problem subject to differential systems constraints. The differential constraints are penalized and finite elements are used to compute numerical solutions. Convergence proof and error estimates are given. Numerical results are also included and compared with those obtained by the dual method.

Chen, G.↗

NASA NTRS1984

Spectral methods for exterior elliptic problems

Spectral approximations for exterior elliptic problems in two dimensions are discussed. As in the conventional finite difference or finite element methods, the accuracy of the numerical solutions is limited by the order of the numerical farfield conditions. A spectral boundary treatment is introduced at infinity which is compatible with the infinite order interior spectral scheme. Computational results are presented to demonstrate the spectral accuracy attainable. Although a simple Laplace problem is examined, the analysis covers more complex and general cases.

Canuto, C.↗