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At least 163 records · Page 9

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NASA NTRS1988

Study of three-dimensional effects on vortex breakdown

The incompressible axisymmetric steady Navier-Stokes equations in primitive variables are used to simulate vortex breakdown. The equations, discretized using a second-order, central-difference scheme, are linearized and then solved using an exact LU decomposition, Gaussian elimination, and Newton iteration. Solutions are presented for Reynolds numbers, based on vortex-core radius, as high as 1500. An attempt to study the stability of the axisymmetric solutions against three-dimensional perturbations is discussed.

Salas, M. D.↗

NASA NTRS1988

Three dimensional simulation of an underexpanded jet interacting with a supersonic cross flow

A new three-dimensional computational fluid dynamics (CFD) code has been developed to simulate the flow fields of an underexpanded jet transversely injected into supersonic air stream inside the combustors of ramjets and scramjets. The code employs an implicit finite volume, lower-upper (LU) time marching method to solve the complete three-dimensional Navier-Stokes equations in a fully-coupled and very efficient manner. Results clearly depict the flow characteristics, including the shock structure, separated flow regions around the injector, and the wake flow in the lee of the injector.

Yu, Sheng-Tao↗

NASA NTRS1989

Vortex breakdown simulation - A circumspect study of the steady, laminar, axisymmetric model

The incompressible axisymmetric steady Navier-Stokes equations are written using the streamfunction-vorticity formulation. The resulting equations are discretized using a second-order central-difference scheme. The discretized equations are linearized and then solved using an exact LU decomposition, Gaussian elimination, and Newton iteration. Solutions are presented for Reynolds numbers (based on vortex core radius) 100-1800 and swirl parameter 0.9-1.1. The effects of inflow boundary conditions, the location of farfield and outflow boundaries, and mesh refinement are examined. Finally, the stability of the steady solutions is investigated by solving the time-dependent equations.

Salas, M. D.↗

NASA NTRS1988

Extensions of the CSCM methodology for nonequilibrium reacting gas flows

The paper describes the extension of the CSCM flux difference splitting to produce conservative unconditionally stable implicit upwind methods for the extended equation set. The CSCM-S single data level relaxation algorithm is argued to be particularly advantageous for efficiently solving the set of equations. Attention is given to issues of alternative state variable representations and to complementary thermodynamic relations that parameterize and need to be effectively coupled with the solution procedure for the partial differential equations. Within the framework of iteration, consideration is given to more efficient approximate solution procedures than the full block coupled LU decomposition. Results of early numerical experiments are given to illustrate the developments.

Lombard, C. K.↗

NASA NTRS1988

Optical matrix-vector processing for computational fluid dynamics

An optical processor to solve partial differential equations for computational fluid dynamics applications is considered. This application is new and original for optical processors. The algorithms that are used are optical realizations of the Newton-Raphson method for nonlinear equations and a new optical LU direct decomposition and Gauss-Seidel iterative solution to the resultant linear algebraic equations. These algorithms are used to solve Burger's equation (a specific form of the momentum equation in fluid dynamics). The nonlinear equations provide 1-D velocity data at each time step. Simulation results of optical processing with these algorithms on computational fluid dynamics data is included.

Perlee, Caroline J.↗

NASA NTRS1988

General linear codes for fault-tolerant matrix operations on processor arrays

Various checksum codes have been suggested for fault-tolerant matrix computations on processor arrays. Use of these codes is limited due to potential roundoff and overflow errors. Numerical errors may also be misconstrued as errors due to physical faults in the system. In this a set of linear codes is identified which can be used for fault-tolerant matrix operations such as matrix addition, multiplication, transposition, and LU-decomposition, with minimum numerical error. Encoding schemes are given for some of the example codes which fall under the general set of codes. With the help of experiments, a rule of thumb for the selection of a particular code for a given application is derived.

Nair, V. S. S.↗

NASA NTRS1989

A numerical study of chemically reacting flow in nozzles

The Space Station uses small rocket motors, called thrusters, for orientation control. Because of the lack of viable design tools for small rockets, the initial thruster design was basically a very small version of a large rocket motor. Thrust measurements of the initial design were lower than predicted. To improve predictions it was decided to develop a version of the RPLUS2D reacting flow code for thruster calculations. RPLUS2D employs an implicit finite volume, lower-upper symmetric successive overrelaxation (LU-SSOR) scheme for solving the complete two-dimensional Navier-Stokes equations and species transport equations in a coupled and very efficient manner. The combustion processes are modeled by a 9-species, 18 step finite-rate chemistry model, and the turbulence is simulated by a Baldwin-Lomax algebraic model. The code is extended to handle multiple subsonic inlet conditions where the total mass flow is governed by conditions calculated at the thruster-throat. Results are shown for a thruster design where the overall mixture ratio is hydrogen rich. A calculation of a large area ratio divergent nozzle is also presented.

Vanoverbeke, Thomas J.↗

NASA NTRS1989

A block-corrected subdomain solution procedure for recirculating flow calculations

This paper describes a robust and efficient subdomain solution procedure for two-dimensional recirculating flows. The solution domain is divided into a number of overlapping subdomains, and a direct fully coupled solution is obtained for each subdomain using a sparse matrix form of LU decomposition. An effective parabolic block correction procedure, which calculates global corrections to the tentative solution by a marching technique similar to that used for boundary layer flows, is used to accelerate the convergence of the basic procedure. The use of effective block correction is found to be essential for the success of the subdomain approach on strongly recirculating flows. In a number of laminar two-dimensional flows, the new block-corrected method performed extremely well, rivaling the best direct methods in execution time, while requiring substantially less computer storage. The new method proved to be from two to ten times faster than conventional iterative methods, while requiring only a moderate increase in storage.

Braaten, M. E.↗

NASA NTRS1990

Extension of a streamwise upwind algorithm to a moving grid system

A new streamwise upwind algorithm was derived to compute unsteady flow fields with the use of a moving-grid system. The temporally nonconservative LU-ADI (lower-upper-factored, alternating-direction-implicit) method was applied for time marching computations. A comparison of the temporally nonconservative method with a time-conservative implicit upwind method indicates that the solutions are insensitive to the conservative properties of the implicit solvers when practical time steps are used. Using this new method, computations were made for an oscillating wing at a transonic Mach number. The computed results confirm that the present upwind scheme captures the shock motion better than the central-difference scheme based on the beam-warming algorithm. The new upwind option of the code allows larger time-steps and thus is more efficient, even though it requires slightly more computational time per time step than the central-difference option.

Obayashi, Shigeru↗

NASA NTRS1989

A nearly-linear computational-cost scheme for the forward dynamics of an N-body pendulum

The dynamic equations of motion of an n-body pendulum with spherical joints are derived to be a mixed system of differential and algebraic equations (DAE's). The DAE's are kept in implicit form to save arithmetic and preserve the sparsity of the system and are solved by the robust implicit integration method. At each solution point, the predicted solution is corrected to its exact solution within given tolerance using Newton's iterative method. For each iteration, a linear system of the form J delta X = E has to be solved. The computational cost for solving this linear system directly by LU factorization is O(n exp 3), and it can be reduced significantly by exploring the structure of J. It is shown that by recognizing the recursive patterns and exploiting the sparsity of the system the multiplicative and additive computational costs for solving J delta X = E are O(n) and O(n exp 2), respectively. The formulation and solution method for an n-body pendulum is presented. The computational cost is shown to be nearly linearly proportional to the number of bodies.

Chou, Jack C. K.↗

NASA NTRS1990

Counterrotating prop-fan simulations which feature a relative-motion multiblock grid decomposition enabling arbitrary time-steps

Improvements are presented of a computer algorithm developed for the time-accurate flow analysis of rotating machines. The flow model is a finite volume method utilizing a high-resolution approximate Riemann solver for interface flux definitions. The numerical scheme is a block LU implicit iterative-refinement method which possesses apparent unconditional stability. Multiblock composite gridding is used to orderly partition the field into a specified arrangement of blocks exhibiting varying degrees of similarity. Block-block relative motion is achieved using local grid distortion to reduce grid skewness and accommodate arbitrary time step selection. A general high-order numerical scheme is applied to satisfy the geometric conservation law. An even-blade-count counterrotating unducted fan configuration is chosen for a computational study comparing solutions resulting from altering parameters such as time step size and iteration count. The solutions are compared with measured data.

Janus, J. Mark↗

NASA NTRS1990

Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations

The compressible Navier-Stokes equations are solved for a variety of two-dimensional inviscid and viscous problems by preconditioned conjugate gradient-like algorithms. Roe's flux difference splitting technique is used to discretize the inviscid fluxes. The viscous terms are discretized by using central differences. An algebraic turbulence model is also incorporated. The system of linear equations which arises out of the linearization of a fully implicit scheme is solved iteratively by the well known methods of GMRES (Generalized Minimum Residual technique) and Chebyschev iteration. Incomplete LU factorization and block diagonal factorization are used as preconditioners. The resulting algorithm is competitive with the best current schemes, but has wide applications in parallel computing and unstructured mesh computations.

Venkatakrishnan, V.↗

NASA NTRS1990

An interactive adaptive remeshing algorithm for the two-dimensional Euler equations

An interactive adaptive remeshing algorithm utilizing a frontal grid generator and a variety of time integration schemes for the two-dimensional Euler equations on unstructured meshes is presented. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. The time integration methods available include: an explicit four stage Runge-Kutta and a fully implicit LU decomposition. A cell-centered finite volume upwind scheme utilizing Roe's approximate Riemann solver is developed. To obtain higher order accurate results a monotone linear reconstruction procedure proposed by Barth is utilized. Results for flow over a transonic circular arc and flow through a supersonic nozzle are examined.

Slack, David C.↗

NASA NTRS1990

Characteristic-based algorithms for flows in thermo-chemical nonequilibrium

A generalized finite-rate chemistry algorithm with Steger-Warming, Van Leer, and Roe characteristic-based flux splittings is presented in three-dimensional generalized coordinates for the Navier-Stokes equations. Attention is placed on convergence to steady-state solutions with fully coupled chemistry. Time integration schemes including explicit m-stage Runge-Kutta, implicit approximate-factorization, relaxation and LU decomposition are investigated and compared in terms of residual reduction per unit of CPU time. Practical issues such as code vectorization and memory usage on modern supercomputers are discussed.

Walters, Robert W.↗

NASA NTRS1988

Interactive grid generation for turbomachinery flow field simulations

The control point form of algebraic grid generation presented provides the means that are needed to generate well structured grids of turbomachinery flow simulations. It uses a sparse collection of control points distributed over the flow domain. The shape and position of coordinate curves can be adjusted from these control points while the grid conforms precisely to all boundaries. An interactive program called TURBO, which uses the control point form, is being developed. Basic features of the code are discussed and sample grids are presented. A finite volume LU implicit scheme is used to simulate flow in a turbine cascade on the grid generated by the program.

Choo, Yung K.↗

NASA NTRS1990

Real-number codes for fault-tolerant matrix operations on processor arrays

A generalization of existing real number codes is proposed. It is proven that linearity is a necessary and sufficient condition for codes used for fault-tolerant matrix operations such as matrix addition, multiplication, transposition, and LU decomposition. It is also proven that for every linear code defined over a finite field, there exists a corresponding linear real-number code with similar error detecting capabilities. Encoding schemes are given for some of the example codes which fall under the general set of real-number codes. With the help of experiments, a rule is derived for the selection of a particular code for a given application. The performance overhead of fault tolerance schemes using the generalized encoding schemes is shown to be very low, and this is substantiated through simulation experiments.

Nair, V. S. S.↗

NASA NTRS1991

Simulation Of Flow In A Turbine Cascade

Report discusses application of lower-upper (LU) implicit numerical-integration scheme, together with interactive grid-generation method, to simulation of inviscid, compressible flow in two-dimensional model of turbine cascade. Study part of continuing effort to develop techniques for computation of complicated three-dimensional flows in turbomachinery.

Choo, Yung K.↗

NASA NTRS1991

Navier-Stokes Simulation Of Wind-Tunnel Flow

Report describes three-dimensional Navier-Stokes simulation of transonic flow past model wing in wind tunnel and in free air. Numerical integration performed by LU-ADI factorization algorithm. Simulation shows effects of walls of tunnel.

Obayashi, S.↗