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Rudy, D. H.

Publications and source records attributed to Rudy, D. H..

At least 19 records

Compute as Fast as the Engineers Can Think! ULTRAFAST COMPUTING TEAM FINAL REPORT

This report documents findings and recommendations by the Ultrafast Computing Team (UCT). In the period 10-12/98, UCT reviewed design case scenarios for a supersonic transport and a reusable launch vehicle to derive computing requirements necessary for support of a design process with efficiency so radically improved that human thought rather than the computer paces the process. Assessment of the present computing capability against the above requirements indicated a need for further improvement in computing speed by several orders of magnitude to reduce time to solution from tens of hours to seconds in major applications. Evaluation of the trends in computer technology revealed a potential to attain the postulated improvement by further increases of single processor performance combined with massively parallel processing in a heterogeneous environment. However, utilization of massively parallel processing to its full capability will require redevelopment of the engineering analysis and optimization methods, including invention of new paradigms. To that end UCT recommends initiation of a new activity at LaRC called Computational Engineering for development of new methods and tools geared to the new computer architectures in disciplines, their coordination, and validation and benefit demonstration through applications.

Biedron, R. T.

Patched-grid computations of high-speed inlet flows

Two implicit algorithms for the compressible Navier-Stokes equations are applied to the computation of high-speed inlet flows typical of those which are encountered on propulsion systems of advanced hypersonic vehicles. A patched grid formulation is used to treat accurately the blunt cowl interaction with the forebody compression field and efficiently treat variations in inlet geometry downstream of the inlet entrance. Results from the two algorithms, each based on an upwind-biased spatial differencing approach for the convective and pressure terms within a flux-difference-splitting framework, are compared with experimental results for both inlets, and reasonable agreement is found.

Thomas, J. L.

Computation of subsonic base flow on a vector processor

Two-dimensional subsonic laminar compressible base flow has been studied using numerical solutions of the time-dependent Navier-Stokes equations. These solutions were obtained using an explicit finite-difference scheme which is highly efficient on a vector processor. The organization of the code for a CDC CYBER-205 computer is described. Solutions were obtained for Mach 0.4 and 0.6 flows past a slender blunt-based model at moderately high Reynolds numbers. The flow in the wake is unsteady with periodic shedding of vortices from the trailing edge. The computed shedding frequency was found to increase with increasing Reynolds number.

Rudy, D. H.

Computation and analysis of a cylinder wake flow

The Karman vortex wake of a circular cylinder at low Reynolds number was computed by a time-accurate, two-dimensional compressible Navier-Stokes equation solver which uses the MacCormack predictor-corrector finite-difference scheme and a nonreflecting boundary condition on the outer flow boundary. The results from a large number of time steps were analyzed using Fast Fourier Transform techniques to identify the important frequency components for comparison with published experimental data. A strong low-frequency component was found below the vortex shedding frequency and not harmonically related to it. The experimentally discovered low-frequency fluctuations in the cylinder wake are considered possibly to be precursors to transition from laminar to turbulent flow conditions. The present finding of similar frequencies in a computed wake tends to confirm their existence as a real wake phenomenon. This computational work provides a complementary means to experimental investigations of wake phenomena.

Townsend, J. C.

Upwind relaxation algorithms for Euler/Navier-Stokes equations

A description of and results from a solution algorithm for the compressible Navier-Stokes equations are presented. The main features of the algorithm are second or third order accurate upwind discretization of the convection and pressure derivatives and a relaxation scheme for the unfactored implicit backward Euler time method, implemented in a finite-volume formulation. Upwind methods were successfully used to obtain solutions to the Euler equations for flows with strong shock waves. The particular upwind method being used is based on the flux vector splitting technique developed by Van Leer and both second and third order accurate discretizations were developed. Currently, the most widely used implicit solution technique for the Navier-Stokes equations use approximate factorization (AF) methods to treat multidimensional problems. The time integration scheme being used in the present algorithm corresponds to a line Gauss-Seidel relaxation method. This method produces good convergence rates for steady-state flows, and most of the algorithm was vectorized on the NASA Langley VPS 32 computer. The Navier-Stokes algorithm was tested for several two-dimensional flow problems. Solutions for the problems gave excellent results. The presented effort is directed toward the extension of the scheme to the full three-dimensional Navier-Stokes equations.

Thomas, J. L.

Separated flow

A brief overview of flow separation phenomena is provided. Langley has many active research programs in flow separation related areas. Three cases are presented which describe specific examples of flow separation research. In each example, a description of the fundamental fluid physics and the complexity of the flow field is presented along with a method of either reducing or controlling the extent of separation. The following examples are discussed: flow over a smooth surface with an adverse pressure gradient; flow over a surface with a geometric discontinuity; and flow with shock-boundary layer interactions. These results will show that improvements are being made in the understanding of flow separation and its control.

Sellers, W. L., III

Navier-Stokes solutions for two-dimensional subsonic base flow

Methods for determining the effects of mass injection from the trailing edge of a bluff body at low speeds and in transonic flow were numerically studied along with an unmodified blunt-based body to gain insight into the effects of vortex shedding on the base drag. The methodology used to obtain finite-difference solutions to the Navier-Stokes equations for subsonic compressible two-dimensional near-wake flows is presented. The effectiveness of an introduced outflow boundary condition which minimizes reflections back into the computational domain was demonstrated with the solution of a model vortex problem. Calculations of the near-wake flow past a circular cylinder were in excellent agreement with experimental data. Laminar-flow solutions for a blunt-based model with and without a base cavity and with mass injection into the wake agreed qualitatively with experimental observations. The drag reduction capability provided by such base modifications was demonstrated.

Rudy, D. H.

Experiences with explicit finite-difference schemes for complex fluid dynamics problems on STAR-100 and CYBER-203 computers

Several two- and three-dimensional external and internal flow problems solved on the STAR-100 and CYBER-203 vector processing computers are described. The flow field was described by the full Navier-Stokes equations which were then solved by explicit finite-difference algorithms. Problem results and computer system requirements are presented. Program organization and data base structure for three-dimensional computer codes which will eliminate or improve on page faulting, are discussed. Storage requirements for three-dimensional codes are reduced by calculating transformation metric data in each step. As a result, in-core grid points were increased in number by 50% to 150,000, with a 10% execution time increase. An assessment of current and future machine requirements shows that even on the CYBER-205 computer only a few problems can be solved realistically. Estimates reveal that the present situation is more storage limited than compute rate limited, but advancements in both storage and speed are essential to realistically calculate three-dimensional flow.

Kumar, A.

Boundary conditions for subsonic compressible Navier-Stokes calculations

A systematic study of inflow and outflow boundary conditions for the numerical solution of the compressible Navier-Stokes equations is presented. Combinations of several representative inflow and outflow boundary conditions are applied in the solution of subsonic flow over a flat plate in a finite computational domain. These boundary conditions are evaluated in terms of their effect on the accuracy of the solution and the rate of convergence to a steady state. It is shown that errors in the data specified at the inflow boundary can produce significant errors in the computed flow field. It is also shown that a non-reflecting outflow boundary condition can significantly reduce the total computational time required.

Rudy, D. H.

A nonreflecting outflow boundary condition for subsonic Navier-Stokes calculations

A nonreflecting boundary condition is presented for the numerical solution of the time-dependent compressible Navier-Stokes equations when these equations are used to obtain a steady state. This boundary condition is shown to be effective in reducing reflections at a subsonic outflow boundary. Numerical calculations using a model problem were made to compare this boundary condition with other outflow boundary conditions. The nonreflecting boundary condition contains a parameter whose optimal value is estimated using the analysis of a simplified set of equations.

Rudy, D. H.

Time-asymptotic solutions of the Navier-Stokes equation for free shear flows using an alternating-direction implicit method

An uncoupled time asymptotic alternating direction implicit method for solving the Navier-Stokes equations was tested on two laminar parallel mixing flows. A constant total temperature was assumed in order to eliminate the need to solve the full energy equation; consequently, static temperature was evaluated by using algebraic relationship. For the mixing of two supersonic streams at a Reynolds number of 1,000, convergent solutions were obtained for a time step 5 times the maximum allowable size for an explicit method. The solution diverged for a time step 10 times the explicit limit. Improved convergence was obtained when upwind differencing was used for convective terms. Larger time steps were not possible with either upwind differencing or the diagonally dominant scheme. Artificial viscosity was added to the continuity equation in order to eliminate divergence for the mixing of a subsonic stream with a supersonic stream at a Reynolds number of 1,000.

Rudy, D. H.

Comments on the role of diagonal dominance in implicit difference methods

Numerical tests were made for a model of the Navier-Stokes equations using a second-order accurate implicit scheme which guarantees diagonal dominance. The results suggest that the failure of implicit methods using large marching steps may not always be attributed to the lack of diagonal dominance in the coefficient matrix. In some cases the failure may be caused by a nonlinear instability associated with the solution method.

Rudy, D. H.

Mean flow field and surface heating produced by unequal shock interactions at hypersonic speeds

Mean velocity profiles were measured in a free shear layer produced by the interaction of two unequal strength shock waves at hypersonic free-stream Mach numbers. Measurements were made over a unit Reynolds number range of 3,770,000 per meter to 17,400,000 per meter based on the flow on the high velocity side of the shear layer. The variation in measured spreading parameters with Mach number for the fully developed flows is consistent with the trend of the available zero velocity ratio data when the Mach numbers for the data given in this study are taken to be characteristic Mach numbers based on the velocity difference across the mixing layer. Surface measurements in the shear-layer attachment region of the blunt-body model indicate peak local heating and static pressure consistent with other published data. Transition Reynolds numbers were found to be significantly lower than those found in previous data.

Birch, S. F.

An investigation of several numerical procedures for time-asymptotic compressible Navier-Stokes solutions

The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.

Rudy, D. H.

A rational approach to the use of Prandtl's mixing length model in free turbulent shear flow calculations

Prandtl's basic mixing length model was used to compute 22 test cases on free turbulent shear flows. The calculations employed appropriate algebraic length scale equations and single values of mixing length constant for planar and axisymmetric flows, respectively. Good agreement with data was obtained except for flows, such as supersonic free shear layers, where large sustained sensitivity changes occur. The inability to predict the more gradual mixing in these flows is tentatively ascribed to the presence of a significant turbulence-induced transverse static pressure gradient which is neglected in conventional solution procedures. Some type of an equation for length scale development was found to be necessary for successful computation of highly nonsimilar flow regions such as jet or wake development from thick wall flows.

Rudy, D. H.