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NASA NTRS1993

Multi-resolution analysis for ENO schemes

Given a function u(x) which is represented by its cell-averages in cells which are formed by some unstructured grid, we show how to decompose the function into various scales of variation. This is done by considering a set of nested grids in which the given grid is the finest, and identifying in each locality the coarsest grid in the set from which u(x) can be recovered to a prescribed accuracy. We apply this multi-resolution analysis to Essentially Non-oscillatory Schemes (ENO) schemes in order to reduce the number of numerical flux computations which is needed in order to advance the solution by one time-step. This is accomplished by decomposing the numerical solution at the beginning of each time-step into levels of resolution, and performing the computation in each locality at the appropriate coarser grid. We present an efficient algorithm for implementing this program in the one-dimensional case; this algorithm can be extended to the multi-dimensional case with cartesian grids.

Harten, Ami↗

NASA NTRS1996

Segmentation of Unstructured Datasets

Datasets generated by computer simulations and experiments in Computational Fluid Dynamics tend to be extremely large and complex. It is difficult to visualize these datasets using standard techniques like Volume Rendering and Ray Casting. Object Segmentation provides a technique to extract and quantify regions of interest within these massive datasets. This thesis explores basic algorithms to extract coherent amorphous regions from two-dimensional and three-dimensional scalar unstructured grids. The techniques are applied to datasets from Computational Fluid Dynamics and from Finite Element Analysis.

Bhat, Smitha↗

NASA NTRS1996

Global Load Balancing with Parallel Mesh Adaption on Distributed-Memory Systems

Dynamic mesh adaption on unstructured grids is a powerful tool for efficiently computing unsteady problems to resolve solution features of interest. Unfortunately, this causes load imbalance among processors on a parallel machine. This paper describes the parallel implementation of a tetrahedral mesh adaption scheme and a new global load balancing method. A heuristic remapping algorithm is presented that assigns partitions to processors such that the redistribution cost is minimized. Results indicate that the parallel performance of the mesh adaption code depends on the nature of the adaption region and show a 35.5X speedup on 64 processors of an SP2 when 35% of the mesh is randomly adapted. For large-scale scientific computations, our load balancing strategy gives almost a sixfold reduction in solver execution times over non-balanced loads. Furthermore, our heuristic remapper yields processor assignments that are less than 3% off the optimal solutions but requires only 1% of the computational time.

Biswas, Rupak↗

NASA NTRS1996

Subsonic Analysis of 0.04-Scale F-16XL Models Using an Unstructured Euler Code

The subsonic flow field about an F-16XL airplane model configuration was investigated with an inviscid unstructured grid technique. The computed surface pressures were compared to wind-tunnel test results at Mach 0.148 for a range of angles of attack from 0 deg to 20 deg. To evaluate the effect of grid dependency on the solution, a grid study was performed in which fine, medium, and coarse grid meshes were generated. The off-surface vortical flow field was locally adapted and showed improved correlation to the wind-tunnel data when compared to the nonadapted flow field. Computational results are also compared to experimental five-hole pressure probe data. A detailed analysis of the off-body computed pressure contours, velocity vectors, and particle traces are presented and discussed.

Lessard, Wendy B.↗

NASA NTRS1996

Global Load Balancing with Parallel Mesh Adaption on Distributed-Memory Systems

Dynamic mesh adaptation on unstructured grids is a powerful tool for efficiently computing unsteady problems to resolve solution features of interest. Unfortunately, this causes load inbalances among processors on a parallel machine. This paper described the parallel implementation of a tetrahedral mesh adaption scheme and a new global load balancing method. A heuristic remapping algorithm is presented that assigns partitions to processors such that the redistribution coast is minimized. Results indicate that the parallel performance of the mesh adaption code depends on the nature of the adaption region and show a 35.5X speedup on 64 processors of an SP2 when 35 percent of the mesh is randomly adapted. For large scale scientific computations, our load balancing strategy gives an almost sixfold reduction in solver execution times over non-balanced loads. Furthermore, our heuristic remappier yields processor assignments that are less than 3 percent of the optimal solutions, but requires only 1 percent of the computational time.

Biswas, Rupak↗

NASA NTRS1996

Flows in Pinned Arrays Simulating Brush Seals

Flows through idealized pin arrays were investigated using an unstructured grid finite difference model and the simplified Ergun model to predict leakage flows and pressure drops in brush seals. The models are in good agreement in the laminar region with departures in the laminar-turbulent transition region defined by the simplified Ergun model. No local disturbances in the velocity or pressure fields, symptomatic of turbulence were found in the numerical results. The simplified model failed to predict the pressure drop of a 32-pin anisotropic array. Transitional and anisotropic behavior requires

Hendricks, R.C.↗

NASA NTRS1996

Annual Research Briefs - 1996, Center for Turbulence Research

Partial contents include: (1) Simulation of jet impingement heat transfer with the k-e-V2 model; (2) A new methodology for turbulence modelers using Direct Numerical Simulation (DNS) database analysis; (3) A particle representation model for the deformation of homogeneous turbulence; (4) Modeling of inhomogeneous compressible turbulence using a two-scale statistical theory; (5) Lewis number effects on partially premixed flames; (6) Conditional moment closure of mixing and reaction in turbulent non-premixed combustion; (7) Dynamic models for LES of turbulent front propagation with a spectral method; (8) Jet noise using large eddy simulation; (9) Towards numerical simulations of trailing-edge aeroacoustics; (10) A model for the onset of vortex breakdown; (11) Compressing an elliptic vortex: transition to turbulence by tumble breakdown; (12) A new method for the adaptive control of vortex-wall interactions; (13) Symmetries in turbulent boundary layer flows; (14) Near-wall models in large eddy simulations of flow behind a backward-facing step; (15) Assessment of the subgrid-scale models at low and high Reynolds numbers; (16) Large-eddy simulations of flow around a NACA 4412 airfoil using unstructured grids; (17) Progress on LES of flow past a circular cylinder; (18) Experimental investigation of flow through an asymmetric plane diffuser; (19) Progress in the large-eddy simulation of an asymmetric plane diffuser; (20) A numerical study of self-similarity in a turbulent plane wake using large-eddy simulation; (21) On the generation of turbulent inflow conditions for boundary layer simulations, and (22) A new class of finite difference schemes.

COMPUTATIONAL FLUID DYNAMICS↗

NASA NTRS1996

A Least-Squares Finite Element Method for Electromagnetic Scattering Problems

The least-squares finite element method (LSFEM) is applied to electromagnetic scattering and radar cross section (RCS) calculations. In contrast to most existing numerical approaches, in which divergence-free constraints are omitted, the LSFF-M directly incorporates two divergence equations in the discretization process. The importance of including the divergence equations is demonstrated by showing that otherwise spurious solutions with large divergence occur near the scatterers. The LSFEM is based on unstructured grids and possesses full flexibility in handling complex geometry and local refinement Moreover, the LSFEM does not require any special handling, such as upwinding, staggered grids, artificial dissipation, flux-differencing, etc. Implicit time discretization is used and the scheme is unconditionally stable. By using a matrix-free iterative method, the computational cost and memory requirement for the present scheme is competitive with other approaches. The accuracy of the LSFEM is verified by several benchmark test problems.

Wu, Jie↗

NASA NTRS1996

Research in Computational Aeroscience Applications Implemented on Advanced Parallel Computing Systems

Improving the numerical linear algebra routines for use in new Navier-Stokes codes, specifically Tim Barth's unstructured grid code, with spin-offs to TRANAIR is reported. A fast distance calculation routine for Navier-Stokes codes using the new one-equation turbulence models is written. The primary focus of this work was devoted to improving matrix-iterative methods. New algorithms have been developed which activate the full potential of classical Cray-class computers as well as distributed-memory parallel computers.

Wigton, Larry↗

NASA NTRS1998

Assessment of an Euler-Interacting Boundary Layer Method Using High Reynolds Number Transonic Flight Data

Flight-measured high Reynolds number turbulent-flow pressure distributions on a transport wing in transonic flow are compared to unstructured-grid calculations to assess the predictive ability of a three-dimensional Euler code (USM3D) coupled to an interacting boundary layer module. The two experimental pressure distributions selected for comparative analysis with the calculations are complex and turbulent but typical of an advanced technology laminar flow wing. An advancing front method (VGRID) was used to generate several tetrahedral grids for each test case. Initial calculations left considerable room for improvement in accuracy. Studies were then made of experimental errors, transition location, viscous effects, nacelle flow modeling, number and placement of spanwise boundary layer stations, and grid resolution. The most significant improvements in the accuracy of the calculations were gained by improvement of the nacelle flow model and by refinement of the computational grid. Final calculations yield results in close agreement with the experiment. Indications are that further grid refinement would produce additional improvement but would require more computer memory than is available. The appendix data compare the experimental attachment line location with calculations for different grid sizes. Good agreement is obtained between the experimental and calculated attachment line locations.

Bonhaus, Daryl L.↗

NASA NTRS1998

Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations

A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the U.S. for solving the Euler and Navier-Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier-Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.

Frink, Neal T.↗

NASA NTRS1998

On Convergence Acceleration Techniques for Unstructured Meshes

A discussion of convergence acceleration techniques as they relate to computational fluid dynamics problems on unstructured meshes is given. Rather than providing a detailed description of particular methods, the various different building blocks of current solution techniques are discussed and examples of solution strategies using one or several of these ideas are given. Issues relating to unstructured grid CFD problems are given additional consideration, including suitability of algorithms to current hardware trends, memory and cpu tradeoffs, treatment of non-linearities, and the development of efficient strategies for handling anisotropy-induced stiffness. The outlook for future potential improvements is also discussed.

Mavriplis, Dimitri J.↗

NASA NTRS1996

A New Axisymmetric MHD Model of the Interaction of the Solar Wind with Venus

A new two-dimensional axisymmetric MHD model is used to study the interaction of the solar wind with Venus under conditions where the interplanetary field is approximately aligned with the solar wind velocity. This numerical model solves the MHD transport equations for density, velocity, pressure, and magnetic field on an adaptively refined, unstructured grid system. This use of an adaptive grid allows high spatial resolution in regions of large density/velocity gradients and yet can be run on a workstation. The actual grid sizes vary from about 0.06 R(sub v) near the bowshock to 2 R(sub v) in the unperturbed solar wind. The results of the calculations are compared with observed magnetic field values obtained from the magnetometer on the Pioneer Venus Orbiter, at a time when the angle between the solar wind velocity vector and the interplanetary magnetic field (IMF) was only 7.6 deg. Good qualitative agreement between the observed and calculated field behavior is found. The overall results suggest that the induced magnetotail disappears when the IMF is radial for an extended time period and implies that it weakens when the field rotated through a near-radial orientation.

DeZeeuw, Darren L.↗

NASA NTRS1999

Forced Mixer Nozzle Optimization

Computational fluid dynamic (CFD) and computational acoustic analyses (CAA) were performed for a TFE731-40 compound nozzle, a TFE731-60 mixer nozzle and an Energy Efficient Engine (E(sup 3)) mixer nozzle for comparison with available data. The CFD analyses were performed with a three dimensional, Navier-Stokes solution of the flowfield on an unstructured grid using the RAMPANT program. The CAA analyses were performed with the NASA Glenn MGB program using a structured grid. A successful aerodynamic solution for the TFE731-40 compound nozzle operating statically was obtained, simulating an engine operating on a test stand. Analysis of the CFD results of the TFE731-40 with the MGB program produced predicted sound power levels that agree quite well with the measured data front full-scale static engine tests. Comparison of the predicted sound pressure with the data show good agreement near the jet axis, but the noise levels are overpredicted at angles closer to the inlet. The predicted sound power level for the TFE731-60 did not agree as well with measured static engine data as the TFE731-40. Although a reduction in the predicted noise level due to the mixed flow was observed, the reduction was not as significant as the measured data. The analysis of the V2 mixer from the E(sup 3) study showed that peak temperatures predicted in the mixer exit flowfield were within 5 percent of the values measured by the exit probes. The noise predictions of the V2 mixer nozzle tended to be 3-5 dB higher in peak noise level than the measurements. In addition, the maximum frequency of the noise was also overpredicted. An analysis of the 3 candidate mixer nozzle configurations demonstrated the feasibility of using centerbody lobes and porosity to improve mixing efficiency. A final configuration was designed with a predicted thermal mixing efficiency that was 5 percent higher than the 3 candidate mixers. The results of the MGB noise calculations show that the final design will exceed the design goal of a 3 dB reduction in noise as compared to the baseline TFE731-40.

Sheoran, Yogi↗

NASA NTRS1999

Parallel Implementation of the Discontinuous Galerkin Method

This paper describes a parallel implementation of the discontinuous Galerkin method. Discontinuous Galerkin is a spatially compact method that retains its accuracy and robustness on non-smooth unstructured grids and is well suited for time dependent simulations. Several parallelization approaches are studied and evaluated. The most natural and symmetric of the approaches has been implemented in all object-oriented code used to simulate aeroacoustic scattering. The parallel implementation is MPI-based and has been tested on various parallel platforms such as the SGI Origin, IBM SP2, and clusters of SGI and Sun workstations. The scalability results presented for the SGI Origin show slightly superlinear speedup on a fixed-size problem due to cache effects.

Baggag, Abdalkader↗

NASA NTRS1999

Parallel Visualization of Large-Scale Aerodynamics Calculations: A Case Study on the Cray T3E

This paper reports the performance of a parallel volume rendering algorithm for visualizing a large-scale, unstructured-grid dataset produced by a three-dimensional aerodynamics simulation. This dataset, containing over 18 million tetrahedra, allows us to extend our performance results to a problem which is more than 30 times larger than the one we examined previously. This high resolution dataset also allows us to see fine, three-dimensional features in the flow field. All our tests were performed on the Silicon Graphics Inc. (SGI)/Cray T3E operated by NASA's Goddard Space Flight Center. Using 511 processors, a rendering rate of almost 9 million tetrahedra/second was achieved with a parallel overhead of 26%.

Ma, Kwan-Liu↗

NASA NTRS1999

CFD Predictions of Sonic-Boom Characteristics for Unmodified and Modified SR-71 Configurations

Shaped sonic-boom signatures refer to signatures that look something other than the typical N-waves. Shaped sonic-boom signatures such as "flat-top," "ramp-type," or "hybrid-type" waveforms have been shown to reduce the subjective loudness without requiring reductions in overpressure peaks. The shaping of sonic-boom signatures requires increasing the shock rise time and changes in frequency spectra. So far, a flat-top waveform was shown to be achievable in wind tunnels; however, the influence of long propagation distance and real atmosphere on shaped signatures should be addressed using flight tests. Two different approaches have been proposed for sonic-boom minimization flight tests. The first approach, proposed by Eagle Aerospace, is for a flight test using a modified BQM-34 "FIREBEE" remotely piloted vehicle. The 30-foot long FIREBEE has a steady state flight condition at the Mach number and altitude of interest, and it can be recovered by helicopter from the water. As an alternative approach, a modified SR-71 vehicle has been proposed by the McDonnell Douglas Corporation. Benefits of the SR-71 include its variable geometry supersonic inlets, small cockpit bulge, higher Mach number capabilities, slender design, and longer length (105 foot). The present investigation addresses the sonic-boom analysis for the second vehicle.The objective of the current investigation is to assess the feasibility of a modified SR-71 configuration, with McDonnell Douglas-designed fuselage modifications, intended to produce shaped sonic-boom signatures on the ground. The present study describes the use of a higher-order computational fluid dynamics (CFD) method to predict the sonic-boom characteristics for both unmodified and modified SR-71 configurations. An Euler unstructured grid methodology is used to predict the near-field, three-dimensional pressure patterns generated by both SR-71 models. The computed near-field pressure signatures are extrapolated to specified distances below the aircraft down to impingement on the ground using the code MDBOOM. Comparisons of the near-field pressure signatures with available flight-test data are presented in the current paper.

Fouladi, Kamran↗

NASA NTRS1999

Unstructured Navier-Stokes Analysis of Full TCA Configuration

This paper presents an Unstructured Navier-Stokes Analysis of Full TCA (Technology Concept Airplane) Configuration. The topics include: 1) Motivation; 2) Milestone and approach; 3) Overview of the unstructured-grid system; 4) Results on full TCA W/B/N/D/E configuration; 5) Concluding remarks; and 6) Future directions.

Frink, Neal T.↗