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Articles 151 - 180 of 183

Full-Text Articles in Aerodynamics and Fluid Mechanics

Flow Control Of Airfoil At Post-Stall Conditions By Multiple Frequency Applied Saado Jets, A. Şamil Demirsöz Oct 2006

Flow Control Of Airfoil At Post-Stall Conditions By Multiple Frequency Applied Saado Jets, A. Şamil Demirsöz

Mechanical & Aerospace Engineering Theses & Dissertations

Flow separation over lifting aerodynamic components, such as airfoils and wings, occurs during stall conditions which are caused by adverse changes (i.e.; high angle of attack, inflow conditions, etc.) in the operating conditions of aerodynamic components. During stall conditions, the flow over airfoil loses its momentum, creating high pressure zones on the upper surface of the airfoil and even a small increase in pressure causes the fluid particles to stop and separate to a low pressure zone. In order to eliminate the flow separation, the low momentum flow should be removed in order to maintain the high momentum and low …


Characterizing A Co-Flow Nozzle For Use In A Filtered Rayleigh Scattering System, David S. Miceli Jun 2006

Characterizing A Co-Flow Nozzle For Use In A Filtered Rayleigh Scattering System, David S. Miceli

Theses and Dissertations

Research was conducted on the flow field exiting a co-annular flow nozzle for use in filtered Rayleigh scattering flow visualizations. More specifically, the flow visualizations were of the flow field exiting a coflow nozzle and illuminated by a tunable, nominal 4.2 watt narrow line width Argon laser operating at 514.5nm. ND:YAG lasers are typically used in this application, but some of the properties of a tunable Argon laser make it an attractive alternative. Before generating flow visualizations, the coflow nozzle was characterized both experimentally and computationally. Due to a flow asymmetry in the outer annulus flow field, the nozzle was …


Spatially-Resolved Temperature Diagnostic For Supersonic Flow Using Cross-Beam Doppler-Limited Laser Saturation Spectroscopy, Grady T. Phillips Mar 2006

Spatially-Resolved Temperature Diagnostic For Supersonic Flow Using Cross-Beam Doppler-Limited Laser Saturation Spectroscopy, Grady T. Phillips

Theses and Dissertations

Optical techniques for measuring the temperature in three-dimensional supersonic reactive flows have typically depended on lineshape measurements using single-beam laser absorption spectroscopy. However, absorption over extended path lengths in flows with symmetric, turbulent eddies can lead to systematically high extracted temperatures due to Doppler shifts resulting from flow along the absorption path. To eliminate these problems, Cross-Beam Saturation Absorption Spectroscopy (CBSAS) and Cross-Beam Inter-Modulated Fluorescence (CBIMF) have been developed which utilize two crossed and nearly copropogating laser beams.to record the spectral signal of an I2 ro-vibrational line in a small three-dimensional volume using a tunable CW dye laser. Temperature …


Macroscopic Computational Model Of Dielectric Barrier Discharge Plasma Actuators, Timothy R. Klein Feb 2006

Macroscopic Computational Model Of Dielectric Barrier Discharge Plasma Actuators, Timothy R. Klein

Theses and Dissertations

Recent progress in the generation and sustainment of gas discharges at atmospheric pressure has energized research in the field of plasma-aerodynamics. Plasma actuators are promising devices that achieve flow control with no moving parts, do not alter the airfoil shape and place no parts in the flow. The operation of a plasma actuator is examined using a macroscopic (force and power addition) computational fluid dynamic model of a dielectric barrier discharge, DBD, in Fluent. A parametric approach is adopted to survey the range of requisite magnitudes of momentum and energy delivered to the flow field and to identify the effects …


Response To "Comment On Variational Approach To The Volume Viscosity Of Fluids" [Phys. Fluids 18, 109101 (2006)], Allen J. Zuckerwar, Robert L. Ash Jan 2006

Response To "Comment On Variational Approach To The Volume Viscosity Of Fluids" [Phys. Fluids 18, 109101 (2006)], Allen J. Zuckerwar, Robert L. Ash

Mechanical & Aerospace Engineering Faculty Publications

We respond to the Comment of Markus Scholle and therewith revise our material entropy constraint to account for the production of entropy. (c) 2006 American Institute of Physics.


Variational Approach To The Volume Viscosity Of Fluids, Allan J. Zuckerwar, Robert L. Ash Jan 2006

Variational Approach To The Volume Viscosity Of Fluids, Allan J. Zuckerwar, Robert L. Ash

Mechanical & Aerospace Engineering Faculty Publications

The variational principle of Hamilton is applied to develop an analytical formulation to describe the volume viscosity in fluids. The procedure described here differs from those used in the past in that a dissipative process is represented by the chemical affinity and progress variable (sometimes called "order parameter") of a reacting species. These state variables appear in the variational integral in two places: first, in the expression for the internal energy, and second, in a subsidiary condition accounting for the conservation of the reacting species. As a result of the variational procedure, two dissipative terms appear in the Navier-Stokes equation. …


Quantifying Initial Condition And Parametric Uncertainties In A Nonlinear Aeroelastic System With An Efficient Stochastic Algorithm, Daniel R. Millman Sep 2004

Quantifying Initial Condition And Parametric Uncertainties In A Nonlinear Aeroelastic System With An Efficient Stochastic Algorithm, Daniel R. Millman

Theses and Dissertations

There is a growing interest in understanding how uncertainties in flight conditions and structural parameters affect the character of a limit cycle oscillation (LCO) response, leading to failure of an aeroelastic system. Uncertainty quantification of a stochastic system (parametric uncertainty) with stochastic inputs (initial condition uncertainty) has traditionally been analyzed with Monte Carlo simulations (MCS). Probability density functions (PDF) of the LCO response are obtained from the MCS to estimate the probability of failure. A candidate approach to efficiently estimate the PDF of an LCO response is the stochastic projection method. The objective of this research is to extend the …


Adaptive Harmonic Balance Method For Unsteady, Nonlinear, One-Dimensional Periodic Flows, Raymond C. Maple Sep 2002

Adaptive Harmonic Balance Method For Unsteady, Nonlinear, One-Dimensional Periodic Flows, Raymond C. Maple

Theses and Dissertations

A new adaptive split-domain harmonic balance computational fluid dynamics (CFD) method is developed to solve highly nonlinear time-periodic flows such as those found in turbomachinery. The basic harmonic balance CFD method transforms an unsteady time-periodic problem into a steady-state problem by assuming a solution in the form of a Fourier series in time. The new method employs a unique multi-domain split-operator solution technique to remove a large-series stability restriction present in previous harmonic balance CFD approaches. In addition, the new method adapts the frequency content to the flow, starting with a small number of Fourier frequencies and augmenting the frequency …


Computational Aerodynamic Analysis Of The Flow Field About A Hypervelocity Test Sled, Andrew J. Lofthouse Mar 2002

Computational Aerodynamic Analysis Of The Flow Field About A Hypervelocity Test Sled, Andrew J. Lofthouse

Theses and Dissertations

The flow field about the nose section of a hypervelocity test sled is computed using computational fluid dynamics. The numerical model of the test sled corresponds to the Nike O/U narrow gage sled used in the upgrade program at the High Speed Test Track facility, Holloman Air Force Base, New Mexico. The high temperatures and pressures resulting from the aerodynamic heating and loading affect the sled structure and the performance of the vehicle. The sled transitions from an air environment to a helium environment at a speed of approximately 3,300 feet per second (Mach 3 in air, Mach 1.02 in …


Atmospheric Turbulence Conditions Leading To Focused And Folded Sonic Boom Wave Fronts, Andrew A. Piacsek Jan 2002

Atmospheric Turbulence Conditions Leading To Focused And Folded Sonic Boom Wave Fronts, Andrew A. Piacsek

All Faculty Scholarship for the College of the Sciences

The propagation and subsequent distortion of sonic booms with rippled wave fronts are investigated theoretically using a nonlinear time-domain finite-difference scheme. This work seeks to validate the rippled wave front approach as a method for explaining the significant effects of turbulence on sonic booms [A. S. Pierce and D. J. Maglieri, J. Acoust. Soc. Am. 51, 702–721 (1971)]. A very simple description of turbulence is employed in which velocity perturbations within a shallow layer of the atmosphere form strings of vortices characterized by their size and speed. Passage of a steady-state plane shock front through such a vortex layer …


Reduced Order Modeling For High Speed Flows With Moving Shocks, David J. Lucia Dec 2001

Reduced Order Modeling For High Speed Flows With Moving Shocks, David J. Lucia

Theses and Dissertations

The use of Proper Orthogonal Decomposition (POD) for reduced order modeling (ROM) of fluid problems is extended to high-speed compressible fluid flows. The challenge in using POD for high-speed flows is presented by the presence of moving discontinuities in the flow field. To overcome these difficulties, a domain decomposition approach is developed that isolates the region containing the moving shock wave for special treatment. The domain decomposition implementation produces internal boundaries between the various domain sections. The domains are linked using optimization-based solvers which employ constraints to ensure smoothness in overlapping portions of the internal boundary. This approach is applied …


Computational Fluid Dynamic Study Of A Nascar Winston Cup Series Race Car, Terry L. Meek Jr. Oct 2001

Computational Fluid Dynamic Study Of A Nascar Winston Cup Series Race Car, Terry L. Meek Jr.

Mechanical & Aerospace Engineering Theses & Dissertations

Since the goal of NASCAR racing is to win and since drag is a force the vehicle must overcome, a thorough understanding of the drag generating airflow around and through the automobile is greatly desired. The external airflow contributes to most of the drag that a car experiences and most of the downforce the vehicle produces. Therefore, an estimate of the vehicle's performance may be evaluated using a computational aerodynamics model. This thesis presents a computational fluid dynamic (CFD) analysis of a NASCAR Winston Cup series race car to investigate the salient flow characteristics.

Before a computational analysis could be …


Development And Application Of Adaptive Dynamic Grids For Wake Vortex/Ground Interaction, Ilker Emin Türkgeldi Jul 1999

Development And Application Of Adaptive Dynamic Grids For Wake Vortex/Ground Interaction, Ilker Emin Türkgeldi

Mechanical & Aerospace Engineering Theses & Dissertations

An adaptive and dynamic grid approach is developed for the numerical computations of wake vortex flow problems with ground interaction. The unnecessary grid points at the far field of the original, large, single zone grid are removed for computational efficiency. Next, the grid is modified into an adaptive one, where the fine core region keeps track of the vortices and can be split into two regions when the vortex separation distance exceeds a specified limit length. In the final step a multi zonal feature is added to this grid by means of two embedded grids placed at the vortex centers …


Efficient Dynamic Unstructured Methods And Applications For Transonic Flows And Hypersonic Stage Separation, Xiaobing Luo Jan 1999

Efficient Dynamic Unstructured Methods And Applications For Transonic Flows And Hypersonic Stage Separation, Xiaobing Luo

Mechanical & Aerospace Engineering Theses & Dissertations

Relative-moving boundary problems have a wide variety of applications. They appear in staging during a launch process, store separation from a military aircraft, rotor-stator interaction in turbomachinery, and dynamic aeroelasticity.

The dynamic unstructured technology (DUT) is potentially a strong approach to simulate unsteady flows around relative-moving bodies, by solving time-dependent governing equations. The dual-time stepping scheme is implemented to improve its efficiency while not compromising the accuracy of solutions. The validation of the implicit scheme is performed on a pitching NACA0012 airfoil and a rectangular wing with low reduced frequencies in transonic flows. All the matured accelerating techniques, including the …


Vortex Wake And Exhaust Plume Interaction, Including Ground Effect, Ihab Gaber Adam Jul 1998

Vortex Wake And Exhaust Plume Interaction, Including Ground Effect, Ihab Gaber Adam

Mechanical & Aerospace Engineering Theses & Dissertations

Computational modeling and studies of the near-field wake-vortex turbulent flows, far-field turbulent wake-vortex/exhaust-plume interaction for subsonic and High Speed Civil Transport (HSCT) airplane, and wake-vortex/exhaust-plume interaction with the ground are carried out. The three-dimensional, compressible Reynolds-Averaged Navier-Stokes (RANS) equations are solved using the implicit, upwind, Roe-flux-differencing, finite-volume scheme. The turbulence models of Baldwin and Lomax, one-equation model of Spalart and Allmaras and two-equation shear stress transport model of Menter are implemented with the RANS solver for turbulent-flow modeling.

For the near-field study, computations are carried out on a fine grid for a rectangular wing with a NACA-0012 airfoil section and …


Three-Dimensional Aerodynamic Design Optimization Using Discrete Sensitivity Analysis And Parallel Computing, Amidu Olawale Oloso Apr 1997

Three-Dimensional Aerodynamic Design Optimization Using Discrete Sensitivity Analysis And Parallel Computing, Amidu Olawale Oloso

Mechanical & Aerospace Engineering Theses & Dissertations

A hybrid automatic differentiation/incremental iterative method was implemented in the general purpose advanced computational fluid dynamics code (CFL3D Version 4.1) to yield a new code (CFL3D.ADII) that is capable of computing consistently discrete first order sensitivity derivatives for complex geometries. With the exception of unsteady problems, the new code retains all the useful features and capabilities of the original CFL3D flow analysis code. The superiority of the new code over a carefully applied method of finite-differences is demonstrated.

A coarse grain, scalable, distributed-memory, parallel version of CFL3D.ADII was developed based on "derivative stripmining". In this data-parallel approach, an identical copy …


A Study Of The Numerical Implementation Of Multidisciplinary Design Optimization Strategies, Rodney A. Taylor Jul 1996

A Study Of The Numerical Implementation Of Multidisciplinary Design Optimization Strategies, Rodney A. Taylor

Mechanical & Aerospace Engineering Theses & Dissertations

Design optimization provides an organized, systematic, and efficient method for obtaining design improvements based upon a specified measure of design performance. In the multidisciplinary design optimization (MDO) environment efficient optimization techniques allow complex designs to be improved by managing conflicting disciplinary design goals so as to improve the global design. This thesis studies the implementation issues surrounding MDO techniques and strategies. To facilitate this investigation two testbed problems have been selected for study. These problems consider two approaches to the conceptual design of an aeroelastic wing. The first approach is based on an idealized, two-dimensional representation of an airfoil under …


Wing-Section Optimization For Supersonic Viscous Flow, Cem Cihan Item Apr 1995

Wing-Section Optimization For Supersonic Viscous Flow, Cem Cihan Item

Mechanical & Aerospace Engineering Theses & Dissertations

The recent interest in the High Speed Civil Transport (HSCT) has resulted in renewed research studies of optimized supersonic cruise transport configurations. Incorporation of flow viscosity effects in the design process of such a supersonic wing is currently under investigation. This may lead to more accurate problem formulations and, in tum, greater aerodynamic efficiency than can be obtained by the traditional, inviscid, linear theories. In this context, for a design code to be a candidate for a complex optimization problem, such as three-dimensional viscous supersonic wing design, it should be validated using simpler building-block shapes.

To optimize the shape of …


Flow Visualization Of A Turbulent Shear Flow Using An Optical Wavefront Sensor, Daniel W. Jewell Dec 1994

Flow Visualization Of A Turbulent Shear Flow Using An Optical Wavefront Sensor, Daniel W. Jewell

Theses and Dissertations

The research reported here investigated the use of a shearing interferometer (SI) wavefront sensor to determine the effects of shear-layer turbulence on an optical wavefront. A collimated helium-neon laser beam was propagated through a plane shear-layer produced by mixing helium and nitrogen at different velocities. Since the gases have different indices of refraction, the optical wavefront was distorted by different amounts by each gas. The SI measured the wavefront slope across the sampled area of the wavefront. The shear-layer was viewed from two orthogonal directions. This document contains shadow graphs, interference patterns imaged by each of the SI's six cameras, …


A Numerical Analysis Of Smoothed Particle Hydrodynamics, David A. Fulk Sep 1994

A Numerical Analysis Of Smoothed Particle Hydrodynamics, David A. Fulk

Theses and Dissertations

This dissertation studies the numerical method of Smoothed Particle Hydrodynamics SPH as a technique for solving systems of conservation equations. The research starts with a detailed consistency analysis of the method. Higher dimensions and non-smooth functions are considered in addition to the smooth one dimensional case. A stability analysis is then performed. Using a linear technique, an instability is found. Solutions are proposed to resolve the instability. Also a total variation stability analysis is performed leading to a monotone form of SPH. The concepts of consistency and stability are then used in a convergence proof. This proof uses lemmas derived …


Implementation Of A Multiblock Sensitivity Analysis Method In Numerical Aerodynamic Shape Optimization, James Matthew Lacasse Apr 1994

Implementation Of A Multiblock Sensitivity Analysis Method In Numerical Aerodynamic Shape Optimization, James Matthew Lacasse

Mechanical & Aerospace Engineering Theses & Dissertations

A multiblock sensitivity analysis method is applied in a numerical aerodynamic shape optimization technique. The Sensitivity Analysis Domain Decomposition (SADD) scheme which is implemented in this study was developed to reduce the computer memory requirements resulting from the aerodynamic sensitivity analysis equations, Discrete sensitivity analysis offers the ability to compute quasi-analytical derivatives in a more efficient manner than traditional finite-difference methods, which tend to be computationally expensive and prone to inaccuracies.

The direct optimization procedure couples CFD analysis based on the two-dimensional thin-layer Navier-Stokes equations with a gradient-based numerical optimization technique. The linking mechanism is the sensitivity equation derived from …


A Numerical Study Of High-Speed Missile Configurations Using A Block- Structured Parallel Algorithm, Douglas C. Blake Dec 1993

A Numerical Study Of High-Speed Missile Configurations Using A Block- Structured Parallel Algorithm, Douglas C. Blake

Theses and Dissertations

A numerical analysis of the aerodynamic phenomena associated with the high-speed flight of a sharp-nosed, four-finned, high-fineness ratio missile using a block-structured, parallel computer algorithm is presented. The algorithm, PANS-3EM, utilizes a second-order-accurate, shock-capturing, Total Variation Diminishing scheme and incorporates a Baldwin-Lomax turbulence model. PANS-3EM allows for extreme flexibility in the choice of computational domain decomposition and computing machine of implementation. Developmental work consists of conceptualization and verification of the algorithm as well as parallel performance and scalability studies conducted on a variety of computing platforms. Using PANS-3EM, the aerodynamic characteristics of the missile are investigated. Drag and pitching moment …


Simulation Of Vertical Tail Buffet In Internal Vortex Breakdown Flows, Mark William Flanagan Oct 1993

Simulation Of Vertical Tail Buffet In Internal Vortex Breakdown Flows, Mark William Flanagan

Mechanical & Aerospace Engineering Theses & Dissertations

Computational simulation of vertical tail buffet in an internal vortex breakdown flow is considered. The fiuid-flow problem is formulated using the full, compressible, unsteady Navier-Stokes equations which are solved using an implicit, flux-difference splitting, finite volume scheme. The fluid-flow problem is solved in a configured circular duct using quasi-axisymmetric assumptions to simplify the flow equations. A plate is placed transverse to the incoming flow. Solution of the flow in the duct is performed with and without a rigid plate, and with and without an elastic plate. The elastic response of the plate is calculated assuming that it is a cantilever …


Application Of Sensitivity Analysis To The Euler Equations, Vamshi Mohan Korivi Jul 1991

Application Of Sensitivity Analysis To The Euler Equations, Vamshi Mohan Korivi

Mechanical & Aerospace Engineering Theses & Dissertations

An approximation method is presented for efficiently predicting the changes which occur in a steady-state numerical solution of the Euler equations as a consequence of a small change in the geometric shape of the domain. The method is extended to develop a general procedure for calculating aerodynamic sensitivity derivatives with respect to variations of geometric shape. The techniques are implemented using an upwind cell centered finite volume formulation, and are applied to two test cases, (1) a subsonic nozzle (M∞ = 0.85), and (2) a supersonic inlet (M∞ = 2.0). Conventional numerical solutions are first obtained for flow …


Effect Of Passive Flow-Control Devices On The Drug Of A Tractor-Trailer Model, Jagjit K. Ahuja Jan 1991

Effect Of Passive Flow-Control Devices On The Drug Of A Tractor-Trailer Model, Jagjit K. Ahuja

Mechanical & Aerospace Engineering Theses & Dissertations

The aerodynamic drag of tractor trailers is responsible for approximately half of the fuel consumption at highway speeds (55m.p.h.). Thus, it is important that vehicle drag be reduced in order to reduce operating costs and to conserve fuel. The purpose of the subject research conducted in the Old Dominion University Low-Speed Wind Tunnel was to determine the effect of various add-on flow-control devices, such as a cab-mounted flow deflector and gap seals between the tractor and the trailer. In addition, the effect of trailer rear-edge shaping has been studied. This was accomplished by contouring the trailer's rear end. It has …


Navier-Stokes Analysis Of Cold Gas Scramjet Nozzle-Afterbody Flowfields, Walter C. Engelund Oct 1989

Navier-Stokes Analysis Of Cold Gas Scramjet Nozzle-Afterbody Flowfields, Walter C. Engelund

Mechanical & Aerospace Engineering Theses & Dissertations

The recent renewal of interest in hypersonic aerodynamics, brought about largely in part due to the development of the National Aerospace Plane (NASP), is resulting in an increased reliance on computational fluid dynamics for flowfield data in this flight regime. The design of the nozzle-afterbody section for a hypersonic transport such as the NASP is currently underway, and is being conducted using both computational fluid dynamics and cold, non-reacting, simulant gas experimental models. In this study, a computational analysis is conducted for the flow through a scramjet nozzle-afterbody test section.

Computations have been performed for a cold gas simulation of …


Domain Decomposition For Multigrid, Finite Volume Flow Solvers, Victor Robert Lessard Oct 1989

Domain Decomposition For Multigrid, Finite Volume Flow Solvers, Victor Robert Lessard

Mechanical & Aerospace Engineering Theses & Dissertations

Computing the flow fields about three-dimensional complex configurations accurately becomes a difficult task, if it is attempted to generate a single, body fitted grid with proper clustering. The domain decomposition methods, which divide the computational domain into less complex subdomains, are extensively used to decrease the grid generation workload. A domain decomposition technique also allows the use of different solution methods for different subdomains. The objective of this work is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multigrid, finite volume solution algorithms. A computer code, given the name MaGGiE, …


Evaluation Of Equilibrium Turbulence For A Hypersonic Boundary Layer At Nonadiabatic Wall Conditions, Cindy W. Albertson Jul 1989

Evaluation Of Equilibrium Turbulence For A Hypersonic Boundary Layer At Nonadiabatic Wall Conditions, Cindy W. Albertson

Mechanical & Aerospace Engineering Theses & Dissertations

This paper presents an experimental study to characterize the compressible turbulent boundary layer produced along a flat plate in the NASA Langley 8-Foot High Temperature Tunnel and determine the test conditions necessary to achieve equilibrium turbulence. In addition, the present study extends the data base for equilibrium compressible turbulent boundary layers over quasi-isothermal walls which are far from the adiabatic wall temperature. The measurements consist of pilot pressure, static pressure, and total temperature distributions in the boundary layer. A flat plate measuring 9.7 feet long and 4.3, feet wide was used for the study to provide a naturally turbulent boundary …


Calculations Of Three-Dimensional Transonic Flows Using The Implicit Formulation Of The Isenthalpic Euler Equations With Flux Vector Splitting, Frank E. Cannizzaro Jul 1988

Calculations Of Three-Dimensional Transonic Flows Using The Implicit Formulation Of The Isenthalpic Euler Equations With Flux Vector Splitting, Frank E. Cannizzaro

Mechanical & Aerospace Engineering Theses & Dissertations

A numerical method for solving three-dimensional transonic flows using the isenthalpic formulation of the Euler equations is developed. The method uses van Leer's flux vector splitting to solve the implicit formulation of the governing equations, which are applied to a cell centered finite-volume scheme. A three factor spatial approximate factorization is implemented in solving the implicit part of the governing equations. Time marching to a steady state solution requires short computational times due to the relative efficiency of the basic method. Computational times are further reduced by the implementation of the multigrid acceleration technique, which provided converged solutions in approximately …


An Evaluation Of A Taylor-Galerkin Algorithm For High Speed Inviscid Flows Using Quadrilateral And Triangular Elements, Kim S. Bey Apr 1986

An Evaluation Of A Taylor-Galerkin Algorithm For High Speed Inviscid Flows Using Quadrilateral And Triangular Elements, Kim S. Bey

Mechanical & Aerospace Engineering Theses & Dissertations

The Taylor-Galerkin finite element algorithm is used to obtain solutions to the two-dimensional compressible Euler equations. The mathematical formulation of the algorithm is presented for a typical scalar equation. The derivation results in element equations which are assembled over the entire solution domain to obtain the system of equations that are solved explicitly. The algorithm has the unique feature that the finite element matrices can be evaluated in closed form, avoiding expensive numerical integration. Aspects of vector programming strategies and mesh generation important to an effective analysis procedure are also described. Solutions to supersonic flow problems with exact solutions are …