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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

On the Dynamics of Implicit Linear Multistep Methods

Some new guidelines on the usage of implicit linear multistep methods (LMMs) as time-dependent approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) are explored. The commonly used implicit LMMs in CFD belong to the class of superstable time discretizations. It can be shown that the nonlinear asymptotic behavior in terms of bifurcation diagrams and basins of attractions of these schemes can provide an improved range of initial data and time step over the linearized stability limit.

Yee, H. C.↗
NASA NTRS1999

Integrated Modeling Tools for Thermal Analysis and Applications

Integrated modeling of spacecraft systems is a rapidly evolving area in which multidisciplinary models are developed to design and analyze spacecraft configurations. These models are especially important in the early design stages where rapid trades between subsystems can substantially impact design decisions. Integrated modeling is one of the cornerstones of two of NASA's planned missions in the Origins Program -- the Next Generation Space Telescope (NGST) and the Space Interferometry Mission (SIM). Common modeling tools for control design and opto-mechanical analysis have recently emerged and are becoming increasingly widely used. A discipline that has been somewhat less integrated, but is nevertheless of critical concern for high precision optical instruments, is thermal analysis and design. A major factor contributing to this mild estrangement is that the modeling philosophies and objectives for structural and thermal systems typically do not coincide. Consequently the tools that are used in these discplines suffer a degree of incompatibility, each having developed along their own evolutionary path. Although standard thermal tools have worked relatively well in the past. integration with other disciplines requires revisiting modeling assumptions and solution methods. Over the past several years we have been developing a MATLAB based integrated modeling tool called IMOS (Integrated Modeling of Optical Systems) which integrates many aspects of structural, optical, control and dynamical analysis disciplines. Recent efforts have included developing a thermal modeling and analysis capability, which is the subject of this article. Currently, the IMOS thermal suite contains steady state and transient heat equation solvers, and the ability to set up the linear conduction network from an IMOS finite element model. The IMOS code generates linear conduction elements associated with plates and beams/rods of the thermal network directly from the finite element structural model. Conductances for temperature varying materials are accommodated. This capability both streamlines the process of developing the thermal model from the finite element model, and also makes the structural and thermal models compatible in the sense that each structural node is associated with a thermal node. This is particularly useful when the purpose of the analysis is to predict structural deformations due to thermal loads. The steady state solver uses a restricted step size Newton method, and the transient solver is an adaptive step size implicit method applicable to general differential algebraic systems. Temperature dependent conductances and capacitances are accommodated by the solvers. In addition to discussing the modeling and solution methods. applications where the thermal modeling is "in the loop" with sensitivity analysis, optimization and optical performance drawn from our experiences with the Space Interferometry Mission (SIM), and the Next Generation Space Telescope (NGST) are presented.

Milman, Mark H.↗
NASA NTRS1994

Development of advanced Navier-Stokes solver

The objective of research was to develop and validate new computational algorithms for solving the steady and unsteady Euler and Navier-Stokes equations. The end-products are new three-dimensional Euler and Navier-Stokes codes that are faster, more reliable, more accurate, and easier to use. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible/incompressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. Convergence rates and the robustness of the codes are enhanced by the use of an implicit full approximation storage multigrid method.

Yoon, Seokkwan↗
NASA NTRS1985

A factored implicit scheme for numerical weather prediction

An implicit method is proposed to factor the nonlinear partial differential equations governing fast and slow modes of dynamic motion in numerical weather prediction schemes. The method permits separate factorization of the slow and fast modes of the implicit operator. A simple two-dimensional version of the system of three-dimensional equations governing atmospheric dynamics over shallow water was analyzed to assess the accuracy of the proposed method. It is shown that the method has a small error which is comparable to other discretization errors in the overall scheme.

Augenbaum, J. M.↗
NASA NTRS1985

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed.

Ortega, J. M.↗
NASA NTRS1985

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed.

Ortega, J. M.↗
NASA NTRS1987

A barely implicit correction for flux-corrected transport

In virtue of adding one elliptic equation that must be implicitly solved, the 'barely implicit correction' method presented removes the stringent sidestep limit imposed by sound speed in the explicit methods. The barely implicit method is presently combined with a flux-corrected transport algorithm, which has been rendered fourth-order by the appropriate subtraction of corrected fluxes, in order to accurately represent the sharp gradients in subsonic flows. The multigrid MGRID technique (DeVore, 1984) is used to efficiently solve the elliptic pressure equation.

Patnaik, G.↗
NASA NTRS1990

Least-squares finite element methods for compressible Euler equations

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Jiang, Bo-Nan↗
NASA NTRS1994

Spectral Methods for Computational Fluid Dynamics

As a tool for large-scale computations in fluid dynamics, spectral methods were prophesized in 1944, born in 1954, virtually buried in the mid-1960's, resurrected in 1969, evangalized in the 1970's, and catholicized in the 1980's. The use of spectral methods for meteorological problems was proposed by Blinova in 1944 and the first numerical computations were conducted by Silberman (1954). By the early 1960's computers had achieved sufficient power to permit calculations with hundreds of degrees of freedom. For problems of this size the traditional way of computing the nonlinear terms in spectral methods was expensive compared with finite-difference methods. Consequently, spectral methods fell out of favor. The expense of computing nonlinear terms remained a severe drawback until Orszag (1969) and Eliasen, Machenauer, and Rasmussen (1970) developed the transform methods that still form the backbone of many large-scale spectral computations. The original proselytes of spectral methods were meteorologists involved in global weather modeling and fluid dynamicists investigating isotropic turbulence. The converts who were inspired by the successes of these pioneers remained, for the most part, confined to these and closely related fields throughout the 1970's. During that decade spectral methods appeared to be well-suited only for problems governed by ordinary diSerential eqllations or by partial differential equations with periodic boundary conditions. And, of course, the solution itself needed to be smooth. Some of the obstacles to wider application of spectral methods were: (1) poor resolution of discontinuous solutions; (2) inefficient implementation of implicit methods; and (3) drastic geometric constraints. All of these barriers have undergone some erosion during the 1980's, particularly the latter two. As a result, the applicability and appeal of spectral methods for computational fluid dynamics has broadened considerably. The motivation for the use of spectral methods in numerical calculations stems from the attractive approximation properties of orthogonal polynomial expansions.

Zang, T. A.↗
NASA NTRS1990

Application of a streamwise upwind algorithm for unsteady transonic computations over oscillating wings

A new streamwise upwind algorithm has been derived to compute unsteady flows with a moving grid system and applied to compute flows over oscillating wings at transonic Mach numbers. Comparisons have been made between results obtained from this upwind algorithm, using both temporally nonconservative- and conservative-implicit methods, with the results obtained from a central-difference method, and also with experimental data. The results show (1) the efficiency and practicality of the temporally nonconservative implicit solver and (2) the robustness and accuracy of the upwind method for unsteady computations compared to the central-difference method.

Obayashi, Shigeru↗
NASA NTRS1992

Stagnation-point heat-transfer rate predictions at aeroassist flight conditions

The results are presented for the stagnation-point heat-transfer rates used in the design process of the Aeroassist Flight Experiment (AFE) vehicle over its entire aeropass trajectory. The prediction methods used in this investigation demonstrate the application of computational fluid dynamics (CFD) techniques to a wide range of flight conditions and their usefulness in a design process. The heating rates were computed by a viscous-shock-layer (VSL) code at the lower altitudes and by a Navier-Stokes (N-S) code for the higher altitude cases. For both methods, finite-rate chemically reacting gas was considered, and a temperature-dependent wall-catalysis model was used. The wall temperature for each case was assumed to be radiative equilibrium temperature, based on total heating. The radiative heating was estimated by using a correlation equation. Wall slip was included in the N-S calculation method, and this method implicitly accounts for shock slip. The N-S/VSL combination of projection methods was established by comparison with the published benchmark flow-field code LAURA results at lower altitudes, and the direct simulation Monte Carlo results at higher altitude cases. To obtain the design heating rate over the entire forward face of the vehicle, a boundary-layer method (BLIMP code) that employs reacting chemistry and surface catalysis was used. The ratio of the VSL or N-S method prediction to that obtained from the boundary-layer method code at the stagnation point is used to define an adjustment factor, which accounts for the errors involved in using the boundary-layer method.

Gupta, Roop N.↗
NASA NTRS1989

A numerical method for predicting hypersonic flowfields

The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to chemically react and reach states in thermal nonequilibrium. The prediction of hypersonic flowfields requires a numerical method capable of solving the conservation equations of fluid flow, the chemical rate equations for specie formation and dissociation, and the transfer of energy relations between translational and vibrational temperature states. Because the number of equations to be solved is large, the numerical method should also be as efficient as possible. The proposed paper presents a fully implicit method that fully couples the solution of the fluid flow equations with the gas physics and chemistry relations. The method flux splits the inviscid flow terms, central differences of the viscous terms, preserves element conservation in the strong chemistry source terms, and solves the resulting block matrix equation by Gauss Seidel line relaxation.

Maccormack, Robert W.↗
NASA NTRS1984

Relaxation and approximate factorization methods for the unsteady full potential equation

The unsteady form of the full potential equation is solved in conservation form, using implicit methods based on approximate factorization and relaxation schemes. A local time linearization for density is introduced to enable solution to the equation in terms of phi, the velocity potential. A novel flux-biasing technique is applied to generate proper forms of the artificial viscosity, to treat hyperbolic regions with shocks and sonic lines present. The wake is properly modeled by accounting not only for jumps in phi, but also for jumps in higher derivatives of phi obtained from requirements of density continuity. The far field is modeled using the Riemann invariants to simulate nonreflecting boundary conditions. Results are presented for flows over airfoils, cylinders, and spheres. Comparisons are made with available Euler and full potential results.

Shankar, V.↗
NASA NTRS1983

A direct method for the solution of unsteady two-dimensional incompressible Navier-Stokes equations

The unsteady incompressible Navier-Stokes equations are formulated in terms of vorticity and stream function in generalized curvilinear orthogonal coordinates to facilitiate analysis of flow configurations with general geometries. The numerical method developed solves the conservative form of the transport equation using the alternating-direction implicit method, whereas the stream-function equation is solved by direct block Gaussian elimination. The method is applied to a model problem of flow over a back-step in a doubly infinite channel, using clustered conformal coordinates. One-dimensional stretching functions, dependent on the Reynolds number and the asymptotic behavior of the flow, are used to provide suitable grid distribution in the separation and reattachment regions, as well as in the inflow and outflow regions. The optimum grid distribution selected attempts to honor the multiple length scales of the separated-flow model problem. The asymptotic behavior of the finite-differenced transport equation near infinity is examined and the numerical method is carefully developed so as to lead to spatially second-order accurate wiggle-free solutions, i.e., with minimum dispersive error. Results have been obtained in the entire laminar range for the backstep channel and are in good agreement with the available experimental data for this flow problem.

Ghia, K. N.↗
NASA NTRS1994

A Fully Implicit Time Accurate Method for Hypersonic Combustion: Application to Shock-induced Combustion Instability

A new fully implicit, time accurate algorithm suitable for chemically reacting, viscous flows in the transonic-to-hypersonic regime is described. The method is based on a class of Total Variation Diminishing (TVD) schemes and uses successive Gauss-Siedel relaxation sweeps. The inversion of large matrices is avoided by partitioning the system into reacting and nonreacting parts, but still maintaining a fully coupled interaction. As a result, the matrices that have to be inverted are of the same size as those obtained with the commonly used point implicit methods. In this paper we illustrate the applicability of the new algorithm to hypervelocity unsteady combustion applications. We present a series of numerical simulations of the periodic combustion instabilities observed in ballistic-range experiments of blunt projectiles flying at subdetonative speeds through hydrogen-air mixtures. The computed frequencies of oscillation are in excellent agreement with experimental data.

Yungster, Shaye↗
NASA NTRS1995

A deterministic particle method for one-dimensional reaction-diffusion equations

We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.

Mascagni, Michael↗
NASA NTRS1992

Finite element developments for two dimensional multiple-interface phase change problems

Finite element developments for multiple phase change problems in two-dimensional models are presented for the first time. The enthalpy method is used to simulate latent heat release in conjunction with fixed grid techniques. An unconditionally stable implicit method is used for the time integration. The effects of boundary conditions and the different phase regions on the multiple phase front developments are examined for numerous examples. Discussions and conclusions are appropriately addressed.

Ouyang, Tianhong↗