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At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Parallel iterative methods for sparse linear and nonlinear equations

As three-dimensional models are gaining importance, iterative methods will become almost mandatory. Among these, preconditioned Krylov subspace methods have been viewed as the most efficient and reliable, when solving linear as well as nonlinear systems of equations. There has been several different approaches taken to adapt iterative methods for supercomputers. Some of these approaches are discussed and the methods that deal more specifically with general unstructured sparse matrices, such as those arising from finite element methods, are emphasized.

Saad, Youcef↗
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

Shock interference studies on a circular cylinder at Mach 16

This paper presents the results of a computational study on the shock interference problems on a cylindrical body typical of an engine inlet cowl leading edge at a nominal Mach number of 16. The two-dimensional Navier-Stokes equations are solved assuming the flow to be in chemical and thermal equilibrium and using a finite element method. The algorithm employs a cell-centered fully implicit upwind scheme. Adaptively generated unstructured meshes of triangles and quadrilaterals are employed. Under certain conditions the finite element code resulted in oscillatory solutions for shock interference at Mach 16. Some of the causes of the unsteady behavior are identified, and to the extent possible, such situations are avoided in the present application. Two shock interference conditions involving a Type IV (supersonic jet) and a Type III (attaching shear layer) are solved. The results are compared with available experimental data and reasonable agreement is observed. A semi-empirical method is also used to estimate the maximum surface heat flux and static pressure.

Prabhu, Ramadas K.↗
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

Adaptive remeshing method for finite-element thermal analysis

A finite-element remeshing approach that makes use of quadrilateral and triangular elements is described. The approach uses the solution on a previous mesh to create a new mesh. Meshes are completely unstructured with highly refined elements in regions of steep gradients and larger elements where gradients are smaller. Studies of convergence rates for heat conduction problems with exact solutions show that for problems with highly localized solution variations, the remeshing approach gives smaller solution errors with fewer unknowns than refinement of uniform, structured meshes.

Thornton, Earl A.↗
NASA NTRS1989

Unsteady aerodynamics methods for transonic aeroelastic analysis

The paper describes the current status of methods development for transonic aeroelastic analysis within the Unsteady Aerodynamics Branch at NASA Langley. The paper first highlights the development of an approximate factorization (AF) algorithm for solution of the unsteady transonic small-distribution (TSD) equation. The AF algorithm has been used as the basis for a three-dimensional TSD code for complete aircraft applications. The paper also describes the development of solution algorithms for the unsteady Euler equations based on the use of unstructured meshes. These Euler methods contain a dynamic mesh algorithm, which is a general procedure to move or deform the mesh so that it continuously conforms to the instantaneous shape of the aeroelastically deformed vehicle.

Batina, John T.↗
NASA NTRS1990

Adaptive grid embedding for the two-dimensional Euler equations

A numerical algorithm is presented for solving the two-dimensional flux-split Euler equations using a multigrid method with adaptive grid embedding. The method uses an unstructured data set along with a system of pointers for communication on the irregularly shaped grid topologies. An explicit two-stage time advancement scheme is implemented. A multigrid algorithm is used to provide grid level communication and to accelerate the convergence of the solution to steady state. Results are presented for an NACA 0012 airfoil in a freestream with Mach numbers of 0.95 and 1.054. Excellent resolution of the shock structures is obtained with the adaptive grid embedding method with significantly fewer grid points than the comparable structured grid.

Warren, Gary P.↗
NASA NTRS1990

Grid generation for computational CFD of full aerodynamic configurations

It is now possible to compute flow about very complex three-dimensional aerodynamic configurations. Grid generation is an essential part of such computations and a basic capability has been demonstrated. The present problems are: (1) choosing among the competing approaches (structured, unstructured or rectangular); (2) automating and packaging software for grid generation; (3) assessing and assuring grid quality; (4) solid boundary-surface representation and grid generation on solid boundaries; (5) automated domain decomposition (structured grids); (6) grid adaption during the flow solution process. This paper discusses some of the capabilities in the computation of complex three-dimensional grids and addresses some of he current challenges.

Smith, Robert E.↗
NASA NTRS1989

Grid generation for the solution of partial differential equations

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.

Eiseman, Peter R.↗
NASA NTRS1990

A manual for PARTI runtime primitives

Primitives are presented that are designed to help users efficiently program irregular problems (e.g., unstructured mesh sweeps, sparse matrix codes, adaptive mesh partial differential equations solvers) on distributed memory machines. These primitives are also designed for use in compilers for distributed memory multiprocessors. Communications patterns are captured at runtime, and the appropriate send and receive messages are automatically generated.

Berryman, Harry↗
NASA NTRS1989

TranAir: Recent advances and applications

TranAir is a computer code which solves the full-potential equation for transonic flow about very general and complex configurations. Piecewise flat surface panels are used to describe the surface geometry. This paneled definition is then embedded in an unstructured cartesian flow field grid. Finite elements are used in the discretization of the flow field grid in a manner which is fully conservative and second-order accurate. Since geometries may be defined with relative ease, and since the user is not involved in the generation of the flow field grid, computational results may be generated rather quickly for a wide range of geometries. For transonic cases in the cruise angle-of-attack range, TranAir has generated results which are in generally good agreement with both Euler results and wind tunnel data. A typical transonic case runs in 1 to 2 CPU hours on a Cray X-MP. For subcritical cases, the code runs in 15 to 30 CPU minutes, even for geometries in which several thousand surface panels are used in the definition. This ability to rapidly and accurately provide both subsonic and transonic predictions about very complex aircraft configurations gives TranAir the potential of being a very powerful and widely used design tool.

Madson, Michael D.↗
NASA NTRS1990

Conical Euler simulation and active suppression of delta wing rocking motion

A conical Euler code was developed to study unsteady vortex-dominated flows about rolling highly-swept delta wings, undergoing either forced or free-to-roll motions including active roll suppression. The flow solver of the code involves a multistage Runge-Kutta time-stepping scheme which uses a finite volume spatial discretization of the Euler equations on an unstructured grid of triangles. The code allows for the additional analysis of the free-to-roll case, by including the rigid-body equation of motion for its simultaneous time integration with the governing flow equations. Results are presented for a 75 deg swept sharp leading edge delta wing at a freestream Mach number of 1.2 and at alpha equal to 10 and 30 deg angle of attack. A forced harmonic analysis indicates that the rolling moment coefficient provides: (1) a positive damping at the lower angle of attack equal to 10 deg, which is verified in a free-to-roll calculation; (2) a negative damping at the higher angle of attack equal to 30 deg at the small roll amplitudes. A free-to-roll calculation for the latter case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation. The wing rocking motion may be actively suppressed, however, through the use of a rate-feedback control law and antisymmetrically deflected leading edge flaps. The descriptions of the conical Euler flow solver and the free-to-roll analysis are presented. Results are also presented which give insight into the flow physics associated with unsteady vortical flows about forced and free-to-roll delta wings, including the active roll suppression of this wing-rock phenomenon.

Lee, Elizabeth M.↗
NASA NTRS1990

CFD code evaluation for internal flow modeling

Research on the computational fluid dynamics (CFD) code evaluation with emphasis on supercomputing in reacting flows is discussed. Advantages of unstructured grids, multigrids, adaptive methods, improved flow solvers, vector processing, parallel processing, and reduction of memory requirements are discussed. As examples, researchers include applications of supercomputing to reacting flow Navier-Stokes equations including shock waves and turbulence and combustion instability problems associated with solid and liquid propellants. Evaluation of codes developed by other organizations are not included. Instead, the basic criteria for accuracy and efficiency have been established, and some applications on rocket combustion have been made. Research toward an ultimate goal, the most accurate and efficient CFD code, is in progress and will continue for years to come.

Chung, T. J.↗
NASA NTRS1991

Distributed memory compiler design for sparse problems

A compiler and runtime support mechanism is described and demonstrated. The methods presented are capable of solving a wide range of sparse and unstructured problems in scientific computing. The compiler takes as input a FORTRAN 77 program enhanced with specifications for distributing data, and the compiler outputs a message passing program that runs on a distributed memory computer. The runtime support for this compiler is a library of primitives designed to efficiently support irregular patterns of distributed array accesses and irregular distributed array partitions. A variety of Intel iPSC/860 performance results obtained through the use of this compiler are presented.

Wu, Janet↗
NASA NTRS1991

Thoughts on the chimera method of simulation of three-dimensional viscous flow

The chimera overset grid is reviewed and discussed relative to other procedures for simulating flow about complex configurations. It is argued that while more refinement of the technique is needed, current schemes are competitive to unstructured grid schemes and should ultimately prove more useful.

Steger, Joseph L.↗
NASA NTRS1990

Finite element methods of analysis for 3D inviscid compressible flows

The applicants have developed a finite element based approach for the solution of three-dimensional compressible flows. The procedure enables flow solutions to be obtained on tetrahedral discretizations of computational domains of complex form. A further development was the incorporation of a solution adaptive mesh strategy in which the adaptivity is achieved by complete remeshing of the solution domain. During the previous year, the applicants were working with the Advanced Aerodynamics Concepts Branch at NASA Ames Research Center with an implementation of the basic meshing and solution procedure. The objective of the work to be performed over this twelve month period was the transfer of the adaptive mesh technology and also the undertaking of basic research into alternative flow algorithms for the Euler equations on unstructured meshes.

Peraire, Jaime↗
NASA NTRS1991

Performance effects of irregular communications patterns on massively parallel multiprocessors

A detailed study of the performance effects of irregular communications patterns on the CM-2 was conducted. The communications capabilities of the CM-2 were characterized under a variety of controlled conditions. In the process of carrying out the performance evaluation, extensive use was made of a parameterized synthetic mesh. In addition, timings with unstructured meshes generated for aerodynamic codes and a set of sparse matrices with banded patterns on non-zeroes were performed. This benchmarking suite stresses the communications capabilities of the CM-2 in a range of different ways. Benchmark results demonstrate that it is possible to make effective use of much of the massive concurrency available in the communications network.

Saltz, Joel↗
NASA NTRS1991

A manual for PARTI runtime primitives, revision 1

Primitives are presented that are designed to help users efficiently program irregular problems (e.g., unstructured mesh sweeps, sparse matrix codes, adaptive mesh partial differential equations solvers) on distributed memory machines. These primitives are also designed for use in compilers for distributed memory multiprocessors. Communications patterns are captured at runtime, and the appropriate send and receive messages are automatically generated.

Das, Raja↗