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At least 55 records · Page 3

Symmetric linear systems - An application of algebraic systems theory

Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.

Hazewinkel, M.

Numerical solution of a coupled pair of elliptic equations from solid state electronics

Iterative methods are considered for the solution of a coupled pair of second order elliptic partial differential equations which arise in the field of solid state electronics. A finite difference scheme is used which retains the conservative form of the differential equations. Numerical solutions are obtained in two ways, by multigrid and dynamic alternating direction implicit methods. Numerical results are presented which show the multigrid method to be an efficient way of solving this problem. Previously announced in STAR as N83-30109

Phillips, T. N.

Enabling Execution of a Legacy CFD Mini Application on Accelerators Using OpenMP

We describe the process and outcome of our efforts to port a legacy Fortran benchmark code to heterogeneous GPU-accelerated computing architectures using OpenMP. The benchmark code is one of the multi-zone NAS Parallel Benchmarks (NPB-MZ) called SP-MZ. This “mini-app” mimics the computation and data movement that is found in popular legacy and modern implicit computational fluid dynamics (CFD)solvers. Our objective was to examine how efficiently legacy Fortran codes can be ported to accelerators by leveraging OpenMP directives. We describe the development and optimization process and demonstrate the performance impact of various code modifications. We show select profiling results from the Nvidia nvvp profiler to help others diagnose and overcome performance issues in their own applications. We present results for two compute systems endowed with Nvidia V100 accelerators.

Ioannis Nompelis

Some numerical and physical aspects of unsteady Navier-Stokes computations over airfoils using dynamic meshes

An upwind-biased implicit approximate factorization algorithm is applied to several unsteady flows on dynamic meshes. The thin-layer form of the compressible Navier-Stokes equations is used to solve both laminar and turbulent flows over airfoils pitching about the quarter chord. Numerical aspects of the solutions are investigated, including grid and time step effects. Two methods for determining fluxes - flux-vector splitting and flux-difference splitting - are compared. Flux-difference splitting predicts results more accurately than flux-vector splitting on a coarse mesh, but both methods agree on a fine mesh. Physical aspects of the computations are also examined. An equilibrium turbulent boundary layer model computes generally better unsteady results in comparison with experiment than a nonequilibrium model for the transonic case analyzed. Also, the size and location of the primary shed vortex for an airfoil pitching up at a constant rate is calculated in good agreement with experiment for two pitch rates.

Rumsey, Christopher L.

Finite element solution techniques for large-scale problems in computational fluid dynamics

Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations.

Liou, J.

Acceleration of convergence by shifting the spectrum of implicit finite difference operators associated with the equations of gas dynamics

Eigensystem analysis techniques are applied to finite difference formulations of the Navier-Stokes equations in one dimension. Spectra of the resulting implicit difference operators are computed. The largest eigenvalues are calculated by using a combination of the Frechet derivative of the operators and Arnoldi's method. The accuracy of Arnoldi's method is tested by comparing the rate of convergence of the iterative method with the dominant eigenvalue of the original iteration matrix. On the basis of the pattern of eigenvalue distributions for various flow configurations, a shifting of the implicit operators in question is devised. This procedure has improved the rates of convergence of CFD codes by 20 - 50 percent.

Cheer, A.

Stable boundary approximations for a class of implicit schemes for the one-dimensional inviscid equations of gas dynamics

The applicability to practical calculations of recent theoretical developments in the stability analysis of difference approximations for initial-boundary-value problems of the hyperbolic type. For the numerical experiments, select the one-dimensional inviscid gas-dynamic equations in conservation-law form is selected. A class of implicit schemes based on linear multistep methods for ordinary differential equations is chosen and the use of space or space-time extrapolations as implicit or explicit boundary schemes is emphasized. Some numerical examples with various inflow-outflow conditions highlight the commonly discussed issues: explicit versus implicit boundary schemes, unconditionally stable schemes, and underspecification or overspecification of boundary conditions.

Yee, H. C.

Transient rotor dynamic rub phenomena - Theory and test

This paper develops an implicit integration scheme for transient rotor dynamic rub prediction and includes a correlation study with actual test results. A Nordsieck-like numerical integration scheme is applied directly to the second-order equations of motion. The assumption that forces and torques on the rotor are functions of the position and velocity at the point of application and its nearest neighbor is made in order to make the computational time proportional to the number of elements in the rotor dynamics model rather than the cube of the number. The test rig consists of a turbine driven, flexible shaft supported by squeeze film dampers. The blade loss event occurs due to collision of a balance bolt on one of the disks with a high speed plunger. The rotor is seen to spiral outward and contact against a stationary assemblage of seal shoes.

Kascak, A. F.

Unsteady Navier-Stokes computations over airfoils using both fixed and dynamic meshes

A finite volume implicit approximate factorization method which solves the thin layer Navier-Stokes equations was used to predict unsteady turbulent flow airfoil behavior. At a constant angle of attack of 16 deg, the NACA 0012 airfoil exhibits an unsteady periodic flow field with the lift coefficient oscillating between 0.89 and 1.60. The Strouhal number is 0.028. Results are similar at 18 deg, with a Strouhal number of 0.033. A leading edge vortex is shed periodically near maximum lift. Dynamic mesh solutions for unstalled airfoil flows show general agreement with experimental pressure coefficients. However, moment coefficients and the maximum lift value are underpredicted. The deep stall case shows some agreement with experiment for increasing angle of attack, but is only qualitatively comparable past stall and for decreasing angle of attack.

Rumsey, Christopher L.

Unsteady transonic airfoil computation using implicit Euler scheme on body-fixed grid

The unsteady Euler equations have been derived for the flow relative motion with respect to a frame of reference that is rigidly attached to the moving airfoil. The grid is generated once by an elliptic solver without a need for dynamic grid computation. An implicit factored finite-volume scheme has been developed and implemented through a fully vectorized computer program. Implicit second-order and explicit second and fourth-order dissipations are added to the scheme. The boundary conditions are explicitly satisfied. The scheme is applied to steady and unsteady transonic airfoil flows and the results are in good agreement with the experimental data. For forced harmonic airfoil motions, periodic solutions are achieved within the third cycle of oscillation.

Kandil, Osama A.

Sensitivity of Age-of-Air Calculations to the Choice of Advection Scheme

The age of air has recently emerged as a diagnostic of atmospheric transport unaffected by chemical parameterizations, and the features in the age distributions computed in models have been interpreted in terms of the models' large-scale circulation field. This study shows, however, that in addition to the simulated large-scale circulation, three-dimensional age calculations can also be affected by the choice of advection scheme employed in solving the tracer continuity equation, Specifically, using the 3.0deg latitude X 3.6deg longitude and 40 vertical level version of the Geophysical Fluid Dynamics Laboratory SKYHI GCM and six online transport schemes ranging from Eulerian through semi-Lagrangian to fully Lagrangian, it will be demonstrated that the oldest ages are obtained using the nondiffusive centered-difference schemes while the youngest ages are computed with a semi-Lagrangian transport (SLT) scheme. The centered- difference schemes are capable of producing ages older than 10 years in the mesosphere, thus eliminating the "young bias" found in previous age-of-air calculations. At this stage, only limited intuitive explanations can be advanced for this sensitivity of age-of-air calculations to the choice of advection scheme, In particular, age distributions computed online with the National Center for Atmospheric Research Community Climate Model (MACCM3) using different varieties of the SLT scheme are substantially older than the SKYHI SLT distribution. The different varieties, including a noninterpolating-in-the-vertical version (which is essentially centered-difference in the vertical), also produce a narrower range of age distributions than the suite of advection schemes employed in the SKYHI model. While additional MACCM3 experiments with a wider range of schemes would be necessary to provide more definitive insights, the older and less variable MACCM3 age distributions can plausibly be interpreted as being due to the semi-implicit semi-Lagrangian dynamics employed in the MACCM3. This type of dynamical core (employed with a 60-min time step) is likely to reduce SLT's interpolation errors that are compounded by the short-term variability characteristic of the explicit centered-difference dynamics employed in the SKYHI model (time step of 3 min). In the extreme case of a very slowly varying circulation, the choice of advection scheme has no effect on two-dimensional (latitude-height) age-of-air calculations, owing to the smooth nature of the transport circulation in 2D models. These results suggest that nondiffusive schemes may be the preferred choice for multiyear simulations of tracers not overly sensitive to the requirement of monotonicity (this category includes many greenhouse gases). At the same time, age-of-air calculations offer a simple quantitative diagnostic of a scheme's long-term diffusive properties and may help in the evaluation of dynamical cores in multiyear integrations. On the other hand, the sensitivity of the computed ages to the model numerics calls for caution in using age of air as a diagnostic of a GCM's large-scale circulation field.

Eluszkiewicz, Janusz

Experimental test of the variability of G using Viking lander ranging data

Results are presented from the analysis of solar-system astrometric data, notably the range data to the Viking landers on Mars. A least-squares fit of the parameters of the solar system model to these data limits a simple time variation in the effective Newtonian gravitational constant to (2 + or - 4) x 10 to the -12th/yr and a rate of drift of atomic clocks relative to the implicit clock of relativistic dynamics to (1 + or - 8) x 10 to the -12th/yr. The error limits quoted are the result of uncertainties in the masses of the asteroids.

Hellings, R. W.

Some design constraints required for the use of generic software in embedded systems: Packages which manage abstract dynamic structures without the need for garbage collection

The embedded systems running real-time applications, for which Ada was designed, require their own mechanisms for the management of dynamically allocated storage. There is a need for packages which manage their own internalo structures to control their deallocation as well, due to the performance implications of garbage collection by the KAPSE. This places a requirement upon the design of generic packages which manage generically structured private types built-up from application-defined input types. These kinds of generic packages should figure greatly in the development of lower-level software such as operating systems, schedulers, controllers, and device driver; and will manage structures such as queues, stacks, link-lists, files, and binary multary (hierarchical) trees. Controlled to prevent inadvertent de-designation of dynamic elements, which is implicit in the assignment operation A study was made of the use of limited private type, in solving the problems of controlling the accumulation of anonymous, detached objects in running systems. The use of deallocator prodecures for run-down of application-defined input types during deallocation operations during satellites.

Johnson, Charles S.

Finite element structural redesign by large admissible perturbations

In structural redesign, two structural states are involved; the baseline (known) State S1 with unacceptable performance, and the objective (unknown) State S2 with given performance specifications. The difference between the two states in performance and design variables may be as high as 100 percent or more depending on the scale of the structure. A Perturbation Approach to Redesign (PAR) is presented to relate any two structural states S1 and S2 that are modeled by the same finite element model and represented by different values of the design variables. General perturbation equations are derived expressing implicitly the natural frequencies, dynamic modes, static deflections, static stresses, Euler buckling loads, and buckling modes of the objective S2 in terms of its performance specifications, and S1 data and Finite Element Analysis (FEA) results. Large Admissible Perturbation (LEAP) algorithms are implemented in code RESTRUCT to define the objective S2 incrementally without trial and error by postprocessing FEA results of S1 with no additional FEAs. Systematic numerical applications in redesign of a 10 element 48 degree of freedom (dof) beam, a 104 element 192 dof offshore tower, a 64 element 216 dof plate, and a 144 element 896 dof cylindrical shell show the accuracy, efficiency, and potential of PAR to find an objective state that may differ 100 percent from the baseline design.

Bernitsas, Michael M.

Three-dimensional aerodynamic shape optimization of supersonic delta wings

A recently developed three-dimensional aerodynamic shape optimization procedure AeSOP(sub 3D) is described. This procedure incorporates some of the most promising concepts from the area of computational aerodynamic analysis and design, specifically, discrete sensitivity analysis, a fully implicit 3D Computational Fluid Dynamics (CFD) methodology, and 3D Bezier-Bernstein surface parameterizations. The new procedure is demonstrated in the preliminary design of supersonic delta wings. Starting from a symmetric clipped delta wing geometry, a Mach 1.62 asymmetric delta wing and two Mach 1. 5 cranked delta wings were designed subject to various aerodynamic and geometric constraints.

Burgreen, Greg W.

Implicit finite-difference simulations of steady and unsteady transonic flows

Implicit methods for several fluid dynamic formulations have been developed and applied to steady-state and low-frequency transonic flows. The basic steps involved in the construction of implicit schemes include: selection of linearly stable accurate implicit difference operators, time-linearization of nonlinear terms, and approximate factorization of the implicit operators into easily solved systems of equations. The proposed schemes are found very efficient for the simpler formulations.

Ballhaus, W. F.

Full Stall Simulations of a Redesigned Ventilation Fan for the ISS

The concept of a stall is studied rigorously in the aerospace industry. From a design standpoint, instabilities such as stall are undesirable– operation in the stall regime has a tremendous impact on aerodynamic performance as well as structural integrity. In extreme cases, operating in stall conditions can cause failure. Further, stall can cause a loss of lift on aircraft wings or a loss of thrust in aircraft engines. In any case, stall continues to be a topic of interest in the aerospace industry. The present work aims to analyze the stall characteristics of a ventilation fan that was recently designed for the International Space Station (ISS). Although the ventilation fan has a rotor-stator design, this paper considers a rotor-only configuration. The FUN3D Computational Fluid Dynamic (CFD) solver developed by NASA Langley Research Center was used to simulate the operational characteristics of the ventilation fan. FUN3D solves the Unsteady Reynolds-Averaged Naiver-Stokes (URANS) equations using implicit time marching and a dynamic overset grid. The FUN3D solver was originally written for exterior flow fields; however, this work represents an extension of the FUN3D solver to turbomachinery or interior flow fields. The FUN3D results for the rotor-only ventilation fan accurately captured the operational characteristics inherent to compressors– the results shared similar performance trends when compared to the experimental results for the rotor-stator case. A peak adiabatic efficiency of 96% occurred at a MFR of 105.2 CFM, the minimum aerodynamically stable point. A computationally stable stall occurred at a mass flow rate of 43.8 CFM where the adiabatic efficiency dropped to 69%.

CFD

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

Batina, John T.