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In anticipation of future supercomputers, finite difference codes are rapidly being extended to simulate three-dimensional compressible flow about complex configurations. Some of these developments are reviewed. The importance of computational flow visualization and diagnostic methods to three-dimensional flow simulation is also briefly discussed.
The problem of solving banded linear systems by direct (non-iterative) techniques on the Vector Processor System (VPS) 32 supercomputer is considered. Two efficient direct methods for solving banded linear systems on the VPS 32 are described. The vector cyclic reduction (VCR) algorithm is discussed in detail. The performance of the VCR on a three parameter model problem is also illustrated. The VCR is an adaptation of the conventional point cyclic reduction algorithm. The second direct method is the Customized Reduction of Augmented Triangles' (CRAT). CRAT has the dominant characteristics of an efficient VPS 32 algorithm. CRAT is tailored to the pipeline architecture of the VPS 32 and as a consequence the algorithm is implicitly vectorizable.
In anticipation of future supercomputers, finite difference codes are rapidly being extended to simulate three-dimensional compressible flow about complex configurations. Some of these developments are reviewed. The importance of computational flow visualization and diagnostic methods to three-dimensional flow simulation is also briefly discussed.
Overview descriptions of on-line environmental data systems, supercomputer facilities, and networks are presented. Each description addresses the concepts of content, capability, and user access relevant to the point of view of potential utilization by the Earth and environmental science community. The information on similar systems or facilities is presented in parallel fashion to encourage and facilitate intercomparison. In addition, summary sheets are given for each description, and a summary table precedes each section.
Topics addressed include: numerical aerodynamic simulation; computational mechanics; supercomputers; aerospace propulsion systems; computational modeling in ballistics; turbulence modeling; computational chemistry; computational fluid dynamics; and computational astrophysics.
The accurate calculation of three-dimensional internal flowfields for application towards aerospace propulsion systems requires computational resources available only on supercomputers. A survey is presented of three-dimensional calculations of hypersonic, transonic, and subsonic internal flowfields conducted at the Lewis Research Center. A steady state Parabolized Navier-Stokes (PNS) solution of flow in a Mach 5.0, mixed compression inlet, a Navier-Stokes solution of flow in the vicinity of a terminal shock, and a PNS solution of flow in a diffusing S-bend with vortex generators are presented and discussed. All of these calculations were performed on either the NAS Cray-2 or the Lewis Research Center Cray XMP.
The complexity of codes for solutions of real aerodynamic problems has progressed from simple two-dimensional models to three-dimensional inviscid and viscous models. As the algorithms used in the codes increased in accuracy, speed and robustness, the codes were steadily incorporated into standard design processes. The highly sophisticated codes, which provide solutions to the truly complex flows, require computers with large memory and high computational speed. The advent of high-speed supercomputers, such that the solutions of these complex flows become more practical, permits the introduction of the codes into the design system at an earlier stage. The results of several codes which either were already introduced into the design process or are rapidly in the process of becoming so, are presented. The codes fall into the area of turbomachinery aerodynamics and hypersonic propulsion. In the former category, results are presented for three-dimensional inviscid and viscous flows through nozzle and unducted fan bladerows. In the latter category, results are presented for two-dimensional inviscid and viscous flows for hypersonic vehicle forebodies and engine inlets.
The exploitation of special features of the current generation of supercomputers is discussed with particular reference to computational quantum chemistry. Modification of algorithms in the light of the very large memory available on the CRAY 2 is described, and multi-processing of programs is considered for both the CRAY XMP and CRAY 2. The overhead in multi-processing can be reduced to a small percentage even for steps that perform extensive IO.
The General Interpolants Method (GIM) is a 3-D, time-dependent, hybrid procedure for generating numerical analogs of the conservation laws. This study is directed toward the development and application of the GIM computer code for fluid dynamic research applications as implemented for the Cyber 200 series of supercomputers. An elliptic and quasi-parabolic version of the GIM code are discussed. Turbulence models, algebraic and differential equations, were added to the basic viscous code. An equilibrium reacting chemistry model and an implicit finite difference scheme are also included.
A short survey of recent research on Krylov subspace methods with emphasis on implementation on vector and parallel computers is presented. Conjugate gradient methods have proven very useful on traditional scalar computers, and their popularity is likely to increase as three-dimensional models gain importance. A conservative approach to derive effective iterative techniques for supercomputers has been to find efficient parallel/vector implementations of the standard algorithms. The main source of difficulty in the incomplete factorization preconditionings is in the solution of the triangular systems at each step. A few approaches consisting of implementing efficient forward and backward triangular solutions are described in detail. Polynomial preconditioning as an alternative to standard incomplete factorization techniques is also discussed. Another efficient approach is to reorder the equations so as to improve the structure of the matrix to achieve better parallelism or vectorization. An overview of these and other ideas and their effectiveness or potential for different types of architectures is given.
An important problem in scientific computing consists in finding a few eigenvalues and corresponding eigenvectors of a very large and sparse matrix. The most popular methods to solve these problems are based on projection techniques on appropriate subspaces. The main attraction of these methods is that they only require the use of the matrix in the form of matrix by vector multiplications. The implementations on supercomputers of two such methods for symmetric matrices, namely Lanczos' method and Davidson's method are compared. Since one of the most important operations in these two methods is the multiplication of vectors by the sparse matrix, methods of performing this operation efficiently are discussed. The advantages and the disadvantages of each method are compared and implementation aspects are discussed. Numerical experiments on a one processor CRAY 2 and CRAY X-MP are reported. Possible parallel implementations are also discussed.
A direct linear equation solution method based on the Choleski factorization procedure is presented which exploits both parallel and vector features of supercomputers. The new equation solver is described, and its performance is evaluated by solving structural analysis problems on three high-performance computers. The method has been implemented using Force, a generic parallel FORTRAN language.
Speed and memory requirements placed on supercomputers by five different disciplines important to aerospace are discussed and compared with the capabilities of various existing computers and those projected to be available before the end of this century. The disciplines chosen for consideration are turbulence physics, aerodynamics, aerothermodynamics, chemistry, and human vision modeling. Example results for problems illustrative of those currently being solved in each of the disciplines are presented and discussed. Limitations imposed on physical modeling and geometrical complexity by the need to obtain solutions in practical amounts of time are identified. Computational challenges for the future, for which either some or all of the current limitations are removed, are described. Meeting some of the challenges will require computer speeds in excess of exaflop/s (10 to the 18th flop/s) and memories in excess of petawords (10 to the 15th words).
Very little use is made of multiple processors available on current supercomputers (computers with a theoretical peak performance capability equal to 100 MFLOPs or more) in computational aerodynamics to significantly improve turnaround time. The productivity of a computer user is directly related to this turnaround time. In a time-sharing environment, the improvement in this speed is achieved when multiple processors are used efficiently to execute an algorithm. The concept of multiple instructions and multiple data (MIMD) through multi-tasking is applied via a strategy which requires relatively minor modifications to an existing code for a single processor. Essentially, this approach maps the available memory to multiple processors, exploiting the C-FORTRAN-Unix interface. The existing single processor code is mapped without the need for developing a new algorithm. The procedure for building a code utilizing this approach is automated with the Unix stream editor. As a demonstration of this approach, a Multiple Processor Multiple Grid (MPMG) code is developed. It is capable of using nine processors, and can be easily extended to a larger number of processors. This code solves the three-dimensional, Reynolds averaged, thin-layer and slender-layer Navier-Stokes equations with an implicit, approximately factored and diagonalized method. The solver is applied to generic oblique-wing aircraft problem on a four processor Cray-2 computer. A tricubic interpolation scheme is developed to increase the accuracy of coupling of overlapped grids. For the oblique-wing aircraft problem, a speedup of two in elapsed (turnaround) time is observed in a saturated time-sharing environment.
The author critiques some security mechanisms in most versions of the Unix operating system and suggests more effective tools that either have working prototypes or have been implemented, for example in secure Unix systems. Although no computer (not even a secure one) is impenetrable, breaking into systems with these alternate mechanisms will cost more, require more skill, and be more easily detected than penetrations of systems without these mechanisms. The mechanisms described fall into four classes (with considerable overlap). User authentication at the local host affirms the identity of the person using the computer. The principle of least privilege dictates that properly authenticated users should have rights precisely sufficient to perform their tasks, and system administration functions should be compartmentalized; to this end, access control lists or capabilities should either replace or augment the default Unix protection system, and mandatory access controls implementing multilevel security models and integrity mechanisms should be available. Since most users access supercomputing environments using networks, the third class of mechanisms augments authentication (where feasible). As no security is perfect, the fourth class of mechanism logs events that may indicate possible security violations; this will allow the reconstruction of a successful penetration (if discovered), or possibly the detection of an attempted penetration.
The field of computational fluid dynamics (CFD) using large-scale supercomputer applications is discussed. Formulational and computational requirements for the various governing equations, including the Euler and Navier-tokes approaches, are examined for typical problems including the viscous flow field solution about a complete aerospace vehicle. Recent computed results and experimental comparisons are given to highlight the presentation. The future of CFD associated with three-dimensional applications is found to be rapidly expanding across a broad front, including internal and external flows and flows across the entire speed regime.
Little use is made of multiple processors available on current supercomputers (computers with a theoretical peak performance capability equal to 100 MFLOPS or more) to improve turnaround time in computational aerodynamics. The productivity of a computer user is directly related to this turnaround time. In a time-sharing environment, such improvement in this speed is achieved when multiple processors are used efficiently to execute an algorithm. The concept of multiple instructions and multiple data (MIMD) is applied through multitasking via a strategy that requires relatively minor modifications to an existing code for a single processor. This approach maps the available memory to multiple processors, exploiting the C-Fortran-Unix interface. The existing code is mapped without the need for developing a new algorithm. The procedure for building a code utilizing this approach is automated with the Unix stream editor.
The design of the processing element of GASP, a GaAs supercomputer with a 500-MHz instruction issue rate and 1-GHz subsystem clocks, is presented. The novel, functionally modular, block data flow architecture of GASP is described. The architecture and design of a GASP processing element is then presented. The processing element (PE) is implemented in a hybrid semiconductor module with 152 custom GaAs ICs of eight different types. The effects of the implementation technology on both the system-level architecture and the PE design are discussed. SPICE simulations indicate that parts of the PE are capable of being clocked at 1 GHz, while the rest of the PE uses a 500-MHz clock. The architecture utilizes data flow techniques at a program block level, which allows efficient execution of parallel programs while maintaining reasonably good performance on sequential programs. A simulation study of the architecture indicates that an instruction execution rate of over 30,000 MIPS can be attained with 65 PEs.