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At least 1,153 records · Page 64

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NASA NTRS1991

Discretized Newton-relaxation solution of high resolution flux-difference split schemes

A method is presented for the implicit solution of high resolution flux-difference split schemes for which it is impractical to obtain the Jacobian matrix analytically. The method is used frequently in numerical schemes for solving nonlinear systems of equations, but apparently has not been used to date for approximating the Jacobian of the Roe numerical flux vectors. The method consists of obtaining a discretized Jacobian by using simple finite-differences of the flux vectors, and then using this discretized Jacobian in a Newton-relaxation solution method. The method is applied to both compressible and incompressible flows. Numerical results are presented that demonstrate the method works for both inviscid and viscous flows.

Whitfield, David L.↗

NASA NTRS1991

Time-accurate finite difference solutions to the incompressible Navier-Stokes/energy equations

Two new algorithms for solving coupled Navier-Stokes and energy equations are presented. The algorithms are compared with available Navier-Stokes solutions for the model problem of a driven-cavity-flow over a range of Reynolds numbers. It is noted that the algorithms represent two different implementations of the fractional step approach to the solution of the coupled Navier-Stokes and energy equations using the Boussinesq approximation.

Mirfakhraee, Ali↗

NASA NTRS1991

Development of a nonequilibrium radiative heating prediction method for coupled flowfield solutions

A method for predicting radiation in thermochemical nonequilibrium flows has been developed. A summary of the development is presented, with emphasis on its unique features. The optimization of the method to provide efficient solutions allowing coupling to flowfield solvers is discussed. Representative results are obtained and compared to previous solutions and flight data. The method is found to be a useful tool for studies of nonequilibrium flowfields.

Hartung, Lin C.↗

NASA NTRS1991

Solution-adaptive program SADAP3D

A generic solution-adaptive grid program based on an error equi-distribution concept has been developed for use in complex multidimensional flows. The capability of a generic, user-friendly, multidimensional algorithm is demonstrated using several complex 3D flows in high-speed regimes. A simple scheme enforces the continuity of grid spacing along each currently adapted grid line as the computation proceeds. Calculation of normal vectors at each point of a grid plane is enhanced. The grid movement is automatically controlled by reinstating grid-spacing continuity locally in the mainstream of the unidirectional computation. It is concluded that the scheme can be readily coupled with many flow solvers to enhance accuracy and efficiency of solutions.

Djomehri, M. J.↗

NASA NTRS1991

On the explicit versus family solution of the fully diurnal photochemical equations of the stratosphere

The family approach used to solve chemical equations is examined by integrating a heirarchy of versions of a 2D model of stratospheric chemistry and transport on an isentropic surface. Errors of up to 20 percent in radical concentrations can result from the use of a small number of families; the use of more families increases the accuracy of the solutions. The minimum number of families which can be used to provide an accurate solution is discussed, and the parameterization of long-time-scale species is recommended for making the model more efficient. The most pervasive errors are found in calculations of the concentrations of radical species, a problem which can lead to errors in predicting O3 over the long run. Methods for improving the schemes are presented, emphasizing the possibility of producing an improved 3D model.

Austin, John↗

NASA NTRS1991

Solution and shock-induced exsolution of argon in vitreous carbon

To add to the knowledge of noble gas solution and exsolution in carbonaceus material, experiments were performed on vitreous carbon. Ar-rich vitreous carbon samples were prepared under vapor-saturated conditions using argon as the pressurizing medium. Solubility data were obtained for temperatures of 773 to 973 K and pressures of 250 to 1500 bars. Up to 7 wt pct Ar was dissolved in the carbon. The solubility data were compared to a thermodynamic model of argon atoms dissolving into a fixed population of 'holes' in the carbon. Two variations of the model yielded estimates of the enthalpy of solution of Ar in vitreous carbon equal to about -4700 cal/mole. Preliminary shock experiments showed that 28 percent of the total argon was released by driving 4 GPa shocks into the argon-rich carbon. It was demonstrated that shock-induced argon loss is not simply caused by the impact-induced diminution of grain size. The present value of shock pressure required for partial impact devolatilization of Ar from carbon is below the range (5-30 GPa) at which H2O is released from phyllosilicates.

Gazis, Carey↗

NASA NTRS1991

On the discontinuity in kinetic solutions of the collisionless polar wind

The use of a Maxwellian ion velocity distribution in kinetic solutions of the collisionless polar wind regime results in a velocity distribution and associated moments that display sharp discontinuities at the boundary, which quantitatively affects the solution at high altitudes. This paper investigates the causes of this discontinuity, using both analytical and numerical approaches; it is shown that the choice of appropriate boundary conditions will eliminate the discontinuity.

Khoyloo, A.↗

NASA NTRS1992

An Implementation Of The Solution-Adaptive-Grid Method

NASA technical memorandum discusses solution-adaptive-grid method and Self Adaptive Grid Evolution (SAGE) computer code, which implements method. Provides for redistribution of points in grids used to compute flows, especially supersonic and hypersonic flows containing shocks, and other strong gradient regions, discontinuities, and sheer layers. Performed on basis of flow solution obtained on initial grid, then flow recomputed on adapted grid.

Davies, Carol B.↗

NASA NTRS1992

Approximate Solutions Of Equations Of Steady Diffusion

Rigorous analysis yields reliable criteria for "best-fit" functions. Improved "curve-fitting" method yields approximate solutions to differential equations of steady-state diffusion. Method applies to problems in which rates of diffusion depend linearly or nonlinearly on concentrations of diffusants, approximate solutions analytic or numerical, and boundary conditions of Dirichlet type, of Neumann type, or mixture of both types. Applied to equations for diffusion of charge carriers in semiconductors in which mobilities and lifetimes of charge carriers depend on concentrations.

Edmonds, Larry D.↗

NASA NTRS1992

Numerical Asymptotic Solutions Of Differential Equations

Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

Thurston, Gaylen A.↗

NASA NTRS1991

Solution of geometrically nonlinear statics problems by the p-version of the finite element method

This project is concerned with the possibility of using computers for the simulation of structural systems with the same degree of reliability as full scale physical experiments. Reliable numerical simulation will make it possible to reduce the costs of engineering and improve the quality of engineering decisions based on computed information. An error of idealization is an error between the actual physical quantities on which engineering decisions are based (e.g., maximum principal stress, first natural frequency, etc.) and the same data corresponding to the exact solution of the mathematical model. An error of discretization is an error between the quantities of interest corresponding to the exact and approximate solutions of a mathematical model. A high degree of reliability can be achieved in numerical simulation only if both the errors of idealization and errors of discretization can be shown to be small.

Szabo, Barna A.↗

NASA NTRS1992

Development of iterative techniques for the solution of unsteady compressible viscous flows

The development of efficient iterative solution methods for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations is discussed. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. In this work, another approach based on the classical conjugate gradient method, known as the Generalized Minimum Residual (GMRES) algorithm is investigated. The GMRES algorithm has been used in the past by a number of researchers for solving steady viscous and inviscid flow problems. Here, we investigate the suitability of this algorithm for solving the system of non-linear equations that arise in unsteady Navier-Stokes solvers at each time step.

Sankar, Lakshmi N.↗

NASA NTRS1992

A study of solution crystal growth in LOW-g (2-IML-1)

During the International Microgravity Laboratory-1 (IML-1) mission it is planned to grow triglycine sulfate (TGS) crystals from aqueous solution using the modified Fluids Experiment System (FES). A special cooled sting technique will be used for solution crystal growth. The objectives of the experiment are as follows: (1) to grow crystals of TGS using the modified FES; (2) to perform holographic interferometric tomography of the fluid field in three dimensions; (3) to study the fluid motion due to g-jitter by multiple exposure holography of tracer particles; and (4) to study the influence of g-jitter on the growth rate.

Lal, Ravindra B.↗

NASA NTRS1992

Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations

A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.

Soh, Woo Y.↗

NASA NTRS1991

Cell separations and the demixing of aqueous two phase polymer solutions in microgravity

Partition in phase separated aqueous polymer solutions is a cell separation procedure thought to be adversely influenced by gravity. In preparation for performing cell partitioning experiments in space, and to provide general information concerning the demixing of immiscible liquids in low gravity, a series of phase separated aqueous polymer solutions have been flown on two shuttle flights. Fluorocarbon oil and water emulsions were also flown on the second flight. The aqueous polymer emulsions, which in one g demix largely by sedimentation and convection due to the density differences between the phases, demixed more slowly than on the ground and the final disposition of the phases was determined by the wetting of the container wall by the phases. The demixing behavior and kinetics were influenced by the phase volume ratio, physical properties of the systems and chamber wall interaction. The average domain size increased linearly with time as the systems demixed.

Brooks, Donald E.↗

NASA NTRS1991

The solution of radiative transfer problems in molecular bands without the LTE assumption by accelerated lambda iteration methods

An iterative method based on the use of approximate transfer operators, which was designed initially to solve multilevel NLTE line formation problems in stellar atmospheres, is adapted and applied to the solution of the NLTE molecular band radiative transfer in planetary atmospheres. The matrices to be constructed and inverted are much smaller than those used in the traditional Curtis matrix technique, which makes possible the treatment of more realistic problems using relatively small computers. This technique converges much more rapidly than straightforward iteration between the transfer equation and the equations of statistical equilibrium. A test application of this new technique to the solution of NLTE radiative transfer problems for optically thick and thin bands (the 4.3 micron CO2 band in the Venusian atmosphere and the 4.7 and 2.3 micron CO bands in the earth's atmosphere) is described.

Kutepov, A. A.↗

NASA NTRS1992

Optimization and analysis of large chemical kinetic mechanisms using the solution mapping method - Combustion of methane

A method of systematic optimization, solution mapping, as applied to a large-scale dynamic model is presented. The basis of the technique is parameterization of model responses in terms of model parameters by simple algebraic expressions. These expressions are obtained by computer experiments arranged in a factorial design. The developed parameterized responses are then used in a joint multiparameter multidata-set optimization. A brief review of the mathematical background of the technique is given. The concept of active parameters is discussed. The technique is applied to determine an optimum set of parameters for a methane combustion mechanism. Five independent responses - comprising ignition delay times, pre-ignition methyl radical concentration profiles, and laminar premixed flame velocities - were optimized with respect to thirteen reaction rate parameters. The numerical predictions of the optimized model are compared to those computed with several recent literature mechanisms. The utility of the solution mapping technique in situations where the optimum is not unique is also demonstrated.

Frenklach, Michael↗

NASA NTRS1992

Finite difference solution for transient cooling of a radiating-conducting semitransparent layer

Transient solutions were obtained for cooling a semitransparent material by radiation and conduction. The layer is in a vacuum environment so the only means for heat dissipation is by radiation from within the medium leaving through the boundaries. Heat conduction serves only to partially equalize temperatures across the layer. As the optical thickness is increased, steep temperature gradients exist near the boundaries when conduction is relatively small. A solution procedure is required that will provide accurate temperature distributions adjacent to the boundaries, or radiative heat losses will be in error. The approach utilized numerical Gaussian integration to obtain the local radiative source term, and a finite difference procedure with variable space and time increments to solve the transient energy equation.

Siegel, Robert↗