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At least 397 records · Page 22

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NASA NTRS1981

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. I - Nonstiff strongly dynamic problems

An implicit finite difference method of fourth order accuracy in space and time is introduced for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The basic form of the method is a two-level scheme which is unconditionally stable and nondissipative. The scheme uses only three mesh points at level t and three mesh points at level t + delta t. The dissipative version of the basic method given is conditionally stable under the CFL (Courant-Friedrichs-Lewy) condition. This version is particularly useful for the numerical solution of problems with strong but nonstiff dynamic features, where the CFL restriction is reasonable on accuracy grounds. Numerical results are provided to illustrate properties of the proposed method.

Harten, A.↗

NASA NTRS1982

Application of two-point difference schemes to the conservative Euler equations for one-dimensional flows

An implicit finite difference method is presented for obtaining steady state solutions to the time dependent, conservative Euler equations for flows containing shocks. The method used the two-point differencing approach of Keller with dissipation added at supersonic points via the retarded density concept. Application of the method to the one-dimensional nozzle flow equations for various combinations of subsonic and supersonic boundary conditions shows the method to be very efficient. Residuals are typically reduced to machine zero in approximately 35 time steps for 50 mesh points. It is shown that the scheme offers certain advantages over the more widely used three-point schemes, especially in regard to application of boundary conditions.

Wornom, S. F.↗

NASA NTRS1982

Three-dimensional flow calculations including boundary layer effects for supersonic inlets at angle of attack

An analysis is presented for calculating the steady three-dimensional flow field in supersonic mixed-compression inlets at incidence. A zonal modeling approach is employed to obtain the solution. The supersonic core flow is computed using a second-order pentahedral bicharacteristic algorithm. The bow shock wave and the reflected internal shock train are determined using a three-dimensional discrete shock fitting procedure. The boundary layer flow adjacent to both the centerbody and the cowl is computed using a second-order implicit finite difference method. The flow in a shock wave-boundary layer interaction region is computed using an integral formulation. The culmination of the present research effort is the development of a production-type computer program capable of analyzing flow in a variety of mixed-compression aircraft inlets. Numerical results and experimental correlations are presented to illustrate application of the analysis.

Vadyak, J.↗

NASA NTRS1983

Induced mass and wave motions in the lower solar atmosphere. I - Effects of shear motion of flux tubes

Observations indicate that various dynamic solar phenomena lead to enhanced emission of electromagnetic waves from radio to X-ray wavelengths which can be traced to magnetic activity in the photospheric level. A number of previous investigations have ignored the dynamic responses in the solar atmosphere. On the other hand, Nakagawa et al. (1978, 1981) have studied the atmospheric responses in the frame of MHD in the supersonic super-Alfvenic region. Studies of the slowly varying dynamic response (subsonic) have been unsuccessful because of the requirements of high accuracy in the numerical scheme in which a rigorous mathematical treatment of the boundary conditions is necessary. Recently, a numerical MHD model was constructed by using the full implicit continuous eulerian method. The present investigation makes use of a method which is written in a more convenient numerical code. A two-dimensional, time-dependent, nonplanar MHD model is used to investigate the induced mass and wave motions in the lower solar atmosphere due to the shear motion of flux tubes.

Wu, S. T.↗

NASA NTRS1984

Optical systolic solutions of linear algebraic equations

The philosophy and data encoding possible in systolic array optical processor (SAOP) were reviewed. The multitude of linear algebraic operations achievable on this architecture is examined. These operations include such linear algebraic algorithms as: matrix-decomposition, direct and indirect solutions, implicit and explicit methods for partial differential equations, eigenvalue and eigenvector calculations, and singular value decomposition. This architecture can be utilized to realize general techniques for solving matrix linear and nonlinear algebraic equations, least mean square error solutions, FIR filters, and nested-loop algorithms for control engineering applications. The data flow and pipelining of operations, design of parallel algorithms and flexible architectures, application of these architectures to computationally intensive physical problems, error source modeling of optical processors, and matching of the computational needs of practical engineering problems to the capabilities of optical processors are emphasized.

Neuman, C. P.↗

NASA NTRS1985

Free-form Design in Solid Modelling

Solid modelling is developed as a means of representing the shapes of components used in the less specialized mechanical engineering industries. Solids can now be modelled with free form surfaces. In some cases parametric geometry is used exclusively, while in others here is mixed use of parametric and implicit geometry. A method is suggested and discussed for free form solids modelling. The method has several advantages, one of which is that it avoids the use of detached surfaces, Boolean operations and surface intersection computations. It involves only minor topological changes to the model and is therefore computationally efficient.

Pratt, M. J.↗

NASA NTRS1985

Use of a hyperbolic grid generation scheme in simulating supersonic viscous flow about three-dimensional winged configuration

The present paper describes a numerical mesh generation technique to be used with an implicit finite difference method for simulating visous supersonic flow about low-aspect-ratio wing body configurations using a single grid strategy. The computational domain is segmented into multiple regions, with borders located in supersonic areas to avoid the otherwise costly interfacing procedure between adjacent segments. The numerical procedure is applied to calculate the turbulent flow around the shuttle orbiter and a canard projectile at supersonic free stream Mach number.

Rizk, Y. M.↗

NASA NTRS1985

CAG12 - A CSCM based procedure for flow of an equilibrium chemically reacting gas

The Conservative Supra Characteristic Method (CSCM), an implicit upwind Navier-Stokes algorithm, is extended to the numerical simulation of flows in chemical equilibrium. The resulting computer code known as Chemistry and Gasdynamics Implicit - Version 2 (CAG12) is described. First-order accurate results are presented for inviscid and viscous Mach 20 flows of air past a hemisphere-cylinder. The solution procedure captures the bow shock in a chemically reacting gas, a technique that is needed for simulating high altitude, rarefied flows. In an initial effort to validate the code, the inviscid results are compared with published gasdynamic and chemistry solutions and satisfactorily agreement is obtained.

Green, M. J.↗

NASA NTRS1986

Navier-Stokes computations for circulation controlled airfoils

Navier-Stokes computations of subsonic to transonic flow past airfoils with augmented lift due to rearward jet blowing over a curved trailing edge are presented. The approach uses a spiral grid topology. Solutions are obtained using a Navier-Stokes code which employs an implicit finite difference method, an algebraic turbulence model, and developments which improve stability, convergence, and accuracy. Results are compared against experiments for no jet blowing and moderate jet pressures and demonstrate the capability to compute these complicated flows.

Pulliam, T. H.↗

NASA NTRS1986

Wall reflection of a viscous vortex ring

The behavior of a viscous axisymmetric vortex ring being reflected from a wall is investigated. The incompressible Navier-Stokes equations formulated in terms of the vorticity function and vector potential are numerically integrated by implicit finite difference methods. To specify the vector potential at a far boundary from the wall, the existing integral method used so far only for an unbounded domain is modified by a kind of image method. The trajectory of the vortex ring calcualted as a result closely resembles that observable from the experiment.

Sa, J. Y.↗

NASA NTRS1986

Hierarchial implicit dynamic least-square solution algorithm

This paper develops an implicit type transient solution strategy which possesses hierarchial levels of application. In particular, due to the manner of formulation, stiffness updating, assembly inversion, solution constraint, as well as iteration are all performed at a localized level. The level of iterative calculations depends on the type of hierarchial partitioning employed, namely degree of freedom, nodal, elemental, material/nonlinear group, substructural, and so on. Since the iterative solution process and application of constraints are applied at a local level, the resulting so-called hierarchial implicit solution algorithm possesses very stable and efficient numerical properties and is highly storage efficient. To demonstrate the scheme, the results of several benchmark examples are presented. These enable comparisons with the Newton-Raphson solved implicit transient solution method. Overall the comparisons illustrate the superior stability and efficiency of the hierarchial scheme.

Padovan, J.↗

NASA NTRS1986

Implicit time-marching solution of the Navier-Stokes equations for thrust reversing and thrust vectoring nozzle flows

An implicit finite volume method is investigated for the solution of the compressible Navier-Stokes equations for flows within thrust reversing and thrust vectoring nozzles. Thrust reversing nozzles typically have sharp corners, and the rapid expansion and large turning angles near these corners are shown to cause unacceptable time step restrictions when conventional approximate factorization methods are used. In this investigation these limitations are overcome by using second-order upwind differencing and line Gauss-Siedel relaxation. This method is implemented with a zonal mesh so that flows through complex nozzle geometries may be efficiently calculated. Results are presented for five nozzle configurations including two with time varying geometries. Three cases are compared with available experimental data and the results are generally acceptable.

Imlay, S. T.↗

NASA NTRS1987

Development of upwind schemes for the Euler equations

Described are many algorithmic and computational aspects of upwind schemes and their second-order accurate formulations based on Total-Variation-Diminishing (TVD) approaches. An operational unification of the underlying first-order scheme is first presented encompassing Godunov's, Roe's, Osher's, and Split-Flux methods. For higher order versions, the preprocessing and postprocessing approaches to constructing TVD discretizations are considered. TVD formulations can be used to construct relaxation methods for unfactored implicit upwind schemes, which in turn can be exploited to construct space-marching procedures for even the unsteady Euler equations. A major part of the report describes time- and space-marching procedures for solving the Euler equations in 2-D, 3-D, Cartesian, and curvilinear coordinates. Along with many illustrative examples, several results of efficient computations on 3-D supersonic flows with subsonic pockets are presented.

Chakravarthy, Sukumar R.↗

NASA NTRS1987

Navier-Stokes computations for circulation control airfoils

Pulliam, Thomas H.↗

NASA NTRS1988

Liquid sprays and flow studies in the direct-injection diesel engine under motored conditions

A two dimensional, implicit finite difference method of the control volume variety, a two equation model of turbulence, and a discrete droplet model were used to study the flow field, turbulence levels, fuel penetration, vaporization, and mixing in diesel engine environments. The model was also used to study the effects of engine speed, injection angle, spray cone angle, droplet distribution, and intake swirl angle on the flow field, spray penetration and vaporization, and turbulence in motored two-stroke diesel engines. It is shown that there are optimum conditions for injection, which depend on droplet distribution, swirl, spray cone angle, and injection angle. The optimum conditions result in good spray penetration and vaporization and in good fuel mixing. The calculation presented clearly indicates that internal combustion engine models can be used to assess, at least qualitatively, the effects of injection characteristics and engine operating conditions on the flow field and on the spray penetration and vaporization in diesel engines.

Nguyen, Hung Lee↗

NASA NTRS1988

An algorithm for unsteady flows with strong convection

An implicit ADI numerical method for the calculation of 2-D unsteady flows with strong convection effects is described. The method is based on the conventional Crank-Nicholson approach for parabolic equations but an upwind-downwind differencing is used for the first order spatial derivatives associated with convection. The differencing is carried out in the current and previous time plane in such a way that the algorithm is second order accurate in both space and time. The difference equations are factored into sequential operators, one in each independent spatial variable; the solution at each time step may then be computed as a sequence of tridiagonal matrix problems. The method may be used in a noniterative manner although iteration at each time step is recommended in situations where the effects of convection are strong.

Peridier, Vallorie↗

NASA NTRS1989

Unsteady Navier-Stokes computations over airfoils using both fixed and dynamic meshes

A finite volume implicit approximate factorization method which solves the thin layer Navier-Stokes equations was used to predict unsteady turbulent flow airfoil behavior. At a constant angle of attack of 16 deg, the NACA 0012 airfoil exhibits an unsteady periodic flow field with the lift coefficient oscillating between 0.89 and 1.60. The Strouhal number is 0.028. Results are similar at 18 deg, with a Strouhal number of 0.033. A leading edge vortex is shed periodically near maximum lift. Dynamic mesh solutions for unstalled airfoil flows show general agreement with experimental pressure coefficients. However, moment coefficients and the maximum lift value are underpredicted. The deep stall case shows some agreement with experiment for increasing angle of attack, but is only qualitatively comparable past stall and for decreasing angle of attack.

Rumsey, Christopher L.↗

NASA NTRS1989

Numerical investigation of the control of the secondary instability process in boundary layers

A numerical model has been developed for investigating boundary layer transition control for a flat plate boundary layer. Active control of a periodically forced boundary layer in an incompressible fluid is studied using surface heating techniques. The spatially evolving boundary layer is simulated. The Navier-Stokes and energy equations are integrated using a fully implicit finite difference/spectral method. Temperature perturbations are introduced locally along finite heater strips to directly attenuate the instability waves in the flow. A feedback control loop is employed in which a downstream sensor is used to monitor wall shear stress fluctuations. Active control of small amplitude two-dimensional and three-dimensional disturbances is numerically simulated. With proper phase control, in-phase reinforcement and out-of-phase attenuation are demonstrated. A receptivity study of the localized temperature perturbations is made. It is shown that narrow heater strips are more receptive in that they maximize the amplitude level of the disturbances in the flow. Active control of the early stages of the fundamental breakdown process is also numerically simulated. Control is achieved with either two-dimensional or three-dimensional control inputs.

Kral, L. D.↗