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At least 289 records · Page 16

Comparisons of CFD Simulations of Icing Wind Tunnel Clouds with Experiments Conducted at the NASA Propulsions Systems Laboratory

This paper evaluates simulation predictions against experimental test data of icing clouds that were produced during 2018 ice crystal icing physics tests conducted at the NASA Propulsion Systems Laboratory icing wind tunnel. Aero-thermal and cloud parameters are set and known upstream at the tunnel inlet and spray system, but change as the cloud and air thermodynamically interact as the flowing masses reach the tunnel test section. Utilizing the ANSYS Fluent Discrete Phase Model function, 3D computational fluid dynamics (CFD) simulations were performed, capturing the thermodynamic interactions between the test parameters, and providing predictions of the aero thermal and cloud conditions at the tunnel test section. Simulation predictions were compared with test data that were measured at the tunnel exit plane. Evaluations focused on the cloud concentration (total water content), humidity content, and air temperature. CFD simulation predictions showed areas of agreement and disagreement. Simulations showed that cloud concentration profiles at the test section are strongly related to the initial spray nozzle pattern used at the tunnel inlet. Experimental data suggest that greater dispersion of the cloud occurred as the simulated cloud predicted areas of high and low cloud concentration compared to test data profiles. Simulations, however, captured the magnitude and location of the change in humidity content and the change in air temperature due to the presence of the cloud reasonably well, when compared to test data. This result would suggest that while the ANSYS simulation did not fully predict the spreading of the cloud as measured during experiment, it did capture evaporation and the molecular movements of air and vapor relatively well.

CFD↗

An Object Oriented Extensible Architecture for Affordable Aerospace Propulsion Systems

Driven by a need to explore and develop propulsion systems that exceeded current computing capabilities, NASA Glenn embarked on a novel strategy leading to the development of an architecture that enables propulsion simulations never thought possible before. Full engine 3 Dimensional Computational Fluid Dynamic propulsion system simulations were deemed impossible due to the impracticality of the hardware and software computing systems required. However, with a software paradigm shift and an embracing of parallel and distributed processing, an architecture was designed to meet the needs of future propulsion system modeling. The author suggests that the architecture designed at the NASA Glenn Research Center for propulsion system modeling has potential for impacting the direction of development of affordable weapons systems currently under consideration by the Applied Vehicle Technology Panel (AVT). This paper discusses the salient features of the NPSS Architecture including its interface layer, object layer, implementation for accessing legacy codes, numerical zooming infrastructure and its computing layer. The computing layer focuses on the use and deployment of these propulsion simulations on parallel and distributed computing platforms which has been the focus of NASA Ames. Additional features of the object oriented architecture that support MultiDisciplinary (MD) Coupling, computer aided design (CAD) access and MD coupling objects will be discussed. Included will be a discussion of the successes, challenges and benefits of implementing this architecture.

Follen, Gregory J.↗

An Object Oriented Extensible Architecture for Affordable Aerospace Propulsion Systems

Driven by a need to explore and develop propulsion systems that exceeded current computing capabilities, NASA Glenn embarked on a novel strategy leading to the development of an architecture that enables propulsion simulations never thought possible before. Full engine 3 Dimensional Computational Fluid Dynamic propulsion system simulations were deemed impossible due to the impracticality of the hardware and software computing systems required. However, with a software paradigm shift and an embracing of parallel and distributed processing, an architecture was designed to meet the needs of future propulsion system modeling. The author suggests that the architecture designed at the NASA Glenn Research Center for propulsion system modeling has potential for impacting the direction of development of affordable weapons systems currently under consideration by the Applied Vehicle Technology Panel (AVT).

Follen, Gregory J.↗

Fluorescence Visualization of Hypersonic Flow Past Triangular and Rectangular Boundary-layer Trips

Planar laser-induced fluorescence (PLIF) flow visualization has been used to investigate the hypersonic flow of air over surface protrusions that are sized to force laminar-to-turbulent boundary layer transition. These trips were selected to simulate protruding Space Shuttle Orbiter heat shield gap-filler material. Experiments were performed in the NASA Langley Research Center 31-Inch Mach 10 Air Wind Tunnel, which is an electrically-heated, blowdown facility. Two-mm high by 8-mm wide triangular and rectangular trips were attached to a flat plate and were oriented at an angle of 45 degrees with respect to the oncoming flow. Upstream of these trips, nitric oxide (NO) was seeded into the boundary layer. PLIF visualization of this NO allowed observation of both laminar and turbulent boundary layer flow downstream of the trips for varying flow conditions as the flat plate angle of attack was varied. By varying the angle of attack, the Mach number above the boundary layer was varied between 4.2 and 9.8, according to analytical oblique-shock calculations. Computational Fluid Dynamics (CFD) simulations of the flowfield with a laminar boundary layer were also performed to better understand the flow environment. The PLIF images of the tripped boundary layer flow were compared to a case with no trip for which the flow remained laminar over the entire angle-of-attack range studied. Qualitative agreement is found between the present observed transition measurements and a previous experimental roughness-induced transition database determined by other means, which is used by the shuttle return-to-flight program.

Danehy, Paul M.↗

Characterization of Swirl-Venturi Lean Direct Injection Designs for Aviation Gas-Turbine Combustion

Injector geometry, physical mixing, chemical processes, and engine cycle conditions together govern performance, operability and emission characteristics of aviation gas-turbine combustion systems. The present investigation explores swirl-venturi lean direct injection combustor fundamentals, characterizing the influence of key geometric injector parameters on reacting flow physics and emission production trends. In this computational study, a design space exploration was performed using a parameterized swirl-venturi lean direct injector model. From the parametric geometry, 20 three-element lean direct injection combustor sectors were produced and simulated using steady-state, Reynolds-averaged Navier-Stokes reacting computations. Species concentrations were solved directly using a reduced 18-step reaction mechanism for Jet-A. Turbulence closure was obtained using a nonlinear κ-ε model. Results demonstrate sensitivities of the geometric perturbations on axially averaged flow field responses. Output variables include axial velocity, turbulent kinetic energy, static temperature, fuel patternation and minor species mass fractions. Significant trends have been reduced to surrogate model approximations, intended to guide future injector design trade studies and advance aviation gas-turbine combustion research.

Combustion Chamber↗

Rapid Airplane Parametric Input Design (RAPID)

RAPID is a methodology and software system to define a class of airplane configurations and directly evaluate surface grids, volume grids, and grid sensitivity on and about the configurations. A distinguishing characteristic which separates RAPID from other airplane surface modellers is that the output grids and grid sensitivity are directly applicable in CFD analysis. A small set of design parameters and grid control parameters govern the process which is incorporated into interactive software for 'real time' visual analysis and into batch software for the application of optimization technology. The computed surface grids and volume grids are suitable for a wide range of Computational Fluid Dynamics (CFD) simulation. The general airplane configuration has wing, fuselage, horizontal tail, and vertical tail components. The double-delta wing and tail components are manifested by solving a fourth order partial differential equation (PDE) subject to Dirichlet and Neumann boundary conditions. The design parameters are incorporated into the boundary conditions and therefore govern the shapes of the surfaces. The PDE solution yields a smooth transition between boundaries. Surface grids suitable for CFD calculation are created by establishing an H-type topology about the configuration and incorporating grid spacing functions in the PDE equation for the lifting components and the fuselage definition equations. User specified grid parameters govern the location and degree of grid concentration. A two-block volume grid about a configuration is calculated using the Control Point Form (CPF) technique. The interactive software, which runs on Silicon Graphics IRIS workstations, allows design parameters to be continuously varied and the resulting surface grid to be observed in real time. The batch software computes both the surface and volume grids and also computes the sensitivity of the output grid with respect to the input design parameters by applying the precompiler tool ADIFOR to the grid generation program. The output of ADIFOR is a new source code containing the old code plus expressions for derivatives of specified dependent variables (grid coordinates) with respect to specified independent variables (design parameters). The RAPID methodology and software provide a means of rapidly defining numerical prototypes, grids, and grid sensitivity of a class of airplane configurations. This technology and software is highly useful for CFD research for preliminary design and optimization processes.

Smith, Robert E.↗

Comparison of Computed and Measured Vortex Evolution for a UH-60A Rotor in Forward Flight

A Computational Fluid Dynamics (CFD) simulation using the Navier-Stokes equations was performed to determine the evolutionary and dynamical characteristics of the vortex flowfield for a highly flexible aeroelastic UH-60A rotor in forward flight. The experimental wake data were acquired using Particle Image Velocimetry (PIV) during a test of the fullscale UH-60A rotor in the National Full-Scale Aerodynamics Complex 40- by 80-Foot Wind Tunnel. The PIV measurements were made in a stationary cross-flow plane at 90 deg rotor azimuth. The CFD simulation was performed using the OVERFLOW CFD solver loosely coupled with the rotorcraft comprehensive code CAMRAD II. Characteristics of vortices captured in the PIV plane from different blades are compared with CFD calculations. The blade airloads were calculated using two different turbulence models. A limited spatial, temporal, and CFD/comprehensive-code coupling sensitivity analysis was performed in order to verify the unsteady helicopter simulations with a moving rotor grid system.

Evolution↗

Anti-Phase Vortex Reduction Control for Rotor Noise Suppression

An investigation is conducted in 2019 under the NASA Ames Center Innovation Funds (CIF) project entitled “Anti-Phase Vortex Reduction Control for Rotor Noise Suppression“ to experimentally validate an anti-phase rotor noise suppression concept. The first objective of the investigation is to conduct computational fluid dynamics (CFD) simulations to investigate the noise characteristics of several anti-phase rotor designs. The second objective is to conduct a series of acoustic tests of anti-phase rotors in an anechoic chamber at Pennsylvania State University (PSU) to evaluate the merit of the anti-phase rotor concept. The CFD investigation seeks to optimize the anti-phase alternating trailing edge patterns for rotor noise suppression. The design objective is to maximize the noise reduction while maintaining the aerodynamic thrust. The investigation is performed using a three-dimensional (3D) Unsteady Reynolds-Averaged Navier-Stokes (URANS) commercial solver STAR-CCM+ together with the Ffowcs-Williams and Hawkings (FW-H) formula to obtain the aerodynamic thrust and far-field noise level. An acoustic study is conducted for 13 anti-phase design candidates based on a proprietary rotor design. The CAD geometry of the rotor is furnished by PSU. These design candidates include different alternating trailing edge (TE) waveforms, TE segment lengths, TE deflection amplitudes, and transition characteristics. The best design candidate among those explored is an anti-phase rotor that has a four-period TE waveform which results in a reduction in far-field noise level of 2.1 dB in the hover condition and a reduction of 1.1 dB in the forward flight condition at 9.7 m/s. A further acoustic study is conducted for a different rotor manufactured by APC. Five APC rotor design candidates are simulated. The best anti-phase design candidate for the APC rotor results in a reduction in far-field noise level of 4.0 dB in the hover condition. An in-phase design candidate is also studied. This in-phase design provides a noise reduction of 2.5 dB. A series of acoustic experiments in the PSU anechoic chamber have been conducted in July 2019 and October 2019. Both anti-phase and in-phase rotors fabricated for the left-hand and right-hand rotations are tested. In the hover condition, all the rotors do not provide sufficient evidence of improved acoustic performance. However, the experimental data in the hover condition are deemed to be inconclusive due to the flow recirculation in the anechoic chamber caused by the rotor downwash. In the forward flight condition at 9.7 m/s, the anti-phase right-hand rotor produces a noise reduction by as much as 6.5 dB in the frequency range of 2000-4000 Hz, while the in-phase right-hand rotor produces a noise reduction by as much as 5 dB in the same frequency range. Both the anti-phase and in-phase left hand rotors offer no evidence of noise reduction. The difference in the acoustic performance of the left-hand and right-hand rotors could be explained by the location of the microphone array which is placed to the left side of the rotors. This microphone array location could create a bias in the sound pressure level in favor of the right-hand rotor. Using the average noise reduction values, the anti-phase 4H rotor could offer a noise reduction by as much as 3.25 dB while the in-phase 4I rotor could produce up to a 2.5 dB noise reduction. Both the computational and experimental results have provided sufficient evidence to support the noise suppression capability of the proposed anti-phase rotor concepts.

Rotor noise↗

Internal Flow Simulation of Enhanced Performance Solid Rocket Booster for the Space Transportation System

An enhanced performance solid rocket booster concept for the space shuttle system has been proposed. The concept booster will have strong commonality with the existing, proven, reliable four-segment Space Shuttle Reusable Solid Rocket Motors (RSRM) with individual component design (nozzle, insulator, etc.) optimized for a five-segment configuration. Increased performance is desirable to further enhance safety/reliability and/or increase payload capability. Performance increase will be achieved by adding a fifth propellant segment to the current four-segment booster and opening the throat to accommodate the increased mass flow while maintaining current pressure levels. One development concept under consideration is the static test of a "standard" RSRM with a fifth propellant segment inserted and appropriate minimum motor modifications. Feasibility studies are being conducted to assess the potential for any significant departure in component performance/loading from the well-characterized RSRM. An area of concern is the aft motor (submerged nozzle inlet, aft dome, etc.) where the altered internal flow resulting from the performance enhancing features (25% increase in mass flow rate, higher Mach numbers, modified subsonic nozzle contour) may result in increased component erosion and char. To assess this issue and to define the minimum design changes required to successfully static test a fifth segment RSRM engineering test motor, internal flow studies have been initiated. Internal aero-thermal environments were quantified in terms of conventional convective heating and discrete phase alumina particle impact/concentration and accretion calculations via Computational Fluid Dynamics (CFD) simulation. Two sets of comparative CFD simulations of the RSRM and the five-segment (IBM) concept motor were conducted with CFD commercial code FLUENT. The first simulation involved a two-dimensional axi-symmetric model of the full motor, initial grain RSRM. The second set of analyses included three-dimensional models of the RSRM and FSM aft motors with four-degree vectored nozzles.

Ahmad, Rashid A.↗

Noise of Embedded High Aspect Ratio Nozzles

A family of high aspect ratio nozzles were designed to provide a parametric database of canonical embedded propulsion concepts. Nozzle throat geometries with aspect ratios of 2:1, 4:1, and 8:1 were chosen, all with convergent nozzle areas. The transition from the typical round duct to the rectangular nozzle was designed very carefully to produce a flow at the nozzle exit that was uniform and free from swirl. Once the basic rectangular nozzles were designed, external features common to embedded propulsion systems were added: extended lower lip (a.k.a. bevel, aft deck), differing sidewalls, and chevrons. For the latter detailed Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) simulations were made to predict the thrust performance and to optimize parameters such as bevel length, and chevron penetration and azimuthal curvature. Seventeen of these nozzles were fabricated at a scale providing a 2.13 inch diameter equivalent area throat." ! The seventeen nozzles were tested for far-field noise and a few data were presented here on the effect of aspect ratio, bevel length, and chevron count and penetration. The sound field of the 2:1 aspect ratio rectangular jet was very nearly axisymmetric, but the 4:1 and 8:1 were not, the noise on their minor axes being louder than the major axes. Adding bevel length increased the noise of these nozzles, especially on their minor axes, both toward the long and short sides of the beveled nozzle. Chevrons were only added to the 2:1 rectangular jet. Adding 4 chevrons per wide side produced some decrease at aft angles, but increased the high frequency noise at right angles to the jet flow. This trend increased with increasing chevron penetration. Doubling the number of chevrons while maintaining their penetration decreased these effects. Empirical models of the parametric effect of these nozzles were constructed and quantify the trends stated above." Because it is the objective of the Supersonics Project that future design work be done more by physics-based computations and less by experiments, several codes under development were evaluated against these test cases. Preliminary results show that the RANS-based code JeNo predicts the spectral directivity of the low aspect ratio jets well, but has no capability to predict the non-axisymmetry. An effort to address this limitations, used in the RANS-based code of Leib and Goldstein, overpredicted the impact of aspect ratio. The broadband shock noise code RISN, also limited to axisymmetric assumptions, did a good job of predicting the spectral directivity of underexpanded 2:1 cold jet case but was not as successful on high aspect ratio jets, particularly when they are hot. All results are preliminary because the underlying CFD has not been validated yet. An effort using a Large Eddy Simulation code by Stanford University predicted noise that agreed with experiments to within a few dB.

Bridges, James E.↗

Automated Extraction of Flow Features

Computational Fluid Dynamics (CFD) simulations are routinely performed as part of the design process of most fluid handling devices. In order to efficiently and effectively use the results of a CFD simulation, visualization tools are often used. These tools are used in all stages of the CFD simulation including pre-processing, interim-processing, and post-processing, to interpret the results. Each of these stages requires visualization tools that allow one to examine the geometry of the device, as well as the partial or final results of the simulation. An engineer will typically generate a series of contour and vector plots to better understand the physics of how the fluid is interacting with the physical device. Of particular interest are detecting features such as shocks, recirculation zones, and vortices (which will highlight areas of stress and loss). As the demand for CFD analyses continues to increase the need for automated feature extraction capabilities has become vital. In the past, feature extraction and identification were interesting concepts, but not required in understanding the physics of a steady flow field. This is because the results of the more traditional tools like; iso-surface, cuts and streamlines, were more interactive and easily abstracted so they could be represented to the investigator. These tools worked and properly conveyed the collected information at the expense of a great deal of interaction. For unsteady flow-fields, the investigator does not have the luxury of spending time scanning only one "snapshot" of the simulation. Automated assistance is required in pointing out areas of potential interest contained within the flow. This must not require a heavy compute burden (the visualization should not significantly slow down the solution procedure for (co-processing environments). Methods must be developed to abstract the feature of interest and display it in a manner that physically makes sense.

Dorney, Suzanne↗

Automated Extraction of Flow Features

Computational Fluid Dynamics (CFD) simulations are routinely performed as part of the design process of most fluid handling devices. In order to efficiently and effectively use the results of a CFD simulation, visualization tools are often used. These tools are used in all stages of the CFD simulation including pre-processing, interim-processing, and post-processing, to interpret the results. Each of these stages requires visualization tools that allow one to examine the geometry of the device, as well as the partial or final results of the simulation. An engineer will typically generate a series of contour and vector plots to better understand the physics of how the fluid is interacting with the physical device. Of particular interest are detecting features such as shocks, re-circulation zones, and vortices (which will highlight areas of stress and loss). As the demand for CFD analyses continues to increase the need for automated feature extraction capabilities has become vital. In the past, feature extraction and identification were interesting concepts, but not required in understanding the physics of a steady flow field. This is because the results of the more traditional tools like; isc-surface, cuts and streamlines, were more interactive and easily abstracted so they could be represented to the investigator. These tools worked and properly conveyed the collected information at the expense of a great deal of interaction. For unsteady flow-fields, the investigator does not have the luxury of spending time scanning only one "snapshot" of the simulation. Automated assistance is required in pointing out areas of potential interest contained within the flow. This must not require a heavy compute burden (the visualization should not significantly slow down the solution procedure for co-processing environments). Methods must be developed to abstract the feature of interest and display it in a manner that physically makes sense.

Dorney, Suzanne↗

Supersonic flameholding by attached oblique shock waves

The object of this investigation was to explore various regimes of shock-induced combustion that may occur as a result of supersonic flow of a reactive gas mixture past a simple compression ramp or wedge. Attention was confined to combinations of wedge angles, fuel-air mixture ratios and freestream velocities that permit the resulting oblique shock or oblique detonation wave to remain attached. Computational fluid dynamic (CFD) simulations, both inviscid and viscous, were performed and analyzed in order to investigate two modes of compression ramp flameholding; namely, complete oblique detonation wave (ODW) and shock-induced combustion. In addition, the possibility of flame persistence or hysteresis was explored. It was preliminarily concluded that inclusion of viscous effects may be essential to accurately predict the occurrence of the various flameholding modes.

Fort, James A.↗

Integrated flow and structural modeling for rocket engine component test facility propellant systems

A set of PC-based computational Dynamic Fluid Flow Simulation models is presented for modeling facility gas and cryogenic systems. Data obtained provide important information regarding performance envelope parameters for the facility using different engine components; time-dependent valve setting for controlling steady-state, quasi-steady state, and transient profiles; optimum facility pipe and pipe component sizes and parameters; momentum transfer loads; and fluid conditions at critical points. A set of COSMIC NASTRAN-based finite element models is also presented to evaluate the loads and stresses on test facility piping systems from fluid and gaseous effects, thermal chill down, and occasional wind loads. The models are based on Apple Macintosh software which makes it possible to change numerous parameters.

Dequay, L.↗

Aerothermodynamic environment predictions in support of the Aeroassist Flight Experiment

A computational fluid dynamic (CFD) simulation has been made of the flow past an Aeroassist Flight Experiment (AFE) aerobrake model with a payload and sting. The simulation involves solving the complete Navier-Stokes equations in three dimensions. Comparisons with data taken in a Mach 10 wind tunnel test are made and agreement is shown to be very good. Points of comparison include the aerobrake surface pressure and heat transfer rate, the sting surface streamlines, and the sting heat transfer rate. The dependence of the solution on the grid is also explored. Finally, predictions are made for conditions which correspond to a hypersonic shock tunnel force and moment test to be carried out later this year.

Fay, John F.↗

Efficient Parallel Kernel Solvers for Computational Fluid Dynamics Applications

Distributed-memory parallel computers dominate today's parallel computing arena. These machines, such as Intel Paragon, IBM SP2, and Cray Origin2OO, have successfully delivered high performance computing power for solving some of the so-called "grand-challenge" problems. Despite initial success, parallel machines have not been widely accepted in production engineering environments due to the complexity of parallel programming. On a parallel computing system, a task has to be partitioned and distributed appropriately among processors to reduce communication cost and to attain load balance. More importantly, even with careful partitioning and mapping, the performance of an algorithm may still be unsatisfactory, since conventional sequential algorithms may be serial in nature and may not be implemented efficiently on parallel machines. In many cases, new algorithms have to be introduced to increase parallel performance. In order to achieve optimal performance, in addition to partitioning and mapping, a careful performance study should be conducted for a given application to find a good algorithm-machine combination. This process, however, is usually painful and elusive. The goal of this project is to design and develop efficient parallel algorithms for highly accurate Computational Fluid Dynamics (CFD) simulations and other engineering applications. The work plan is 1) developing highly accurate parallel numerical algorithms, 2) conduct preliminary testing to verify the effectiveness and potential of these algorithms, 3) incorporate newly developed algorithms into actual simulation packages. The work plan has well achieved. Two highly accurate, efficient Poisson solvers have been developed and tested based on two different approaches: (1) Adopting a mathematical geometry which has a better capacity to describe the fluid, (2) Using compact scheme to gain high order accuracy in numerical discretization. The previously developed Parallel Diagonal Dominant (PDD) algorithm and Reduced Parallel Diagonal Dominant (RPDD) algorithm have been carefully studied on different parallel platforms for different applications, and a NASA simulation code developed by Man M. Rai and his colleagues has been parallelized and implemented based on data dependency analysis. These achievements are addressed in detail in the paper.

Sun, Xian-He↗

Plane Smoothers for Multiblock Grids: Computational Aspects

Standard multigrid methods are not well suited for problems with anisotropic discrete operators, which can occur, for example, on grids that are stretched in order to resolve a boundary layer. One of the most efficient approaches to yield robust methods is the combination of standard coarsening with alternating-direction plane relaxation in the three dimensions. However, this approach may be difficult to implement in codes with multiblock structured grids because there may be no natural definition of global lines or planes. This inherent obstacle limits the range of an implicit smoother to only the portion of the computational domain in the current block. This report studies in detail, both numerically and analytically, the behavior of blockwise plane smoothers in order to provide guidance to engineers who use block-structured grids. The results obtained so far show alternating-direction plane smoothers to be very robust, even on multiblock grids. In common computational fluid dynamics multiblock simulations, where the number of subdomains crossed by the line of a strong anisotropy is low (up to four), textbook multigrid convergence rates can be obtained with a small overlap of cells between neighboring blocks.

Llorente, Ignacio M.↗

ICEG2D: An Integrated Software Package for Automated Prediction of Flow Fields for Single-Element Airfoils with Ice Accretion

An integrated software package, ICEG2D, was developed to automate computational fluid dynamics (CFD) simulations for single-element airfoils with ice accretion. ICEG2D is designed to automatically perform three primary functions: (1) generating a grid-ready, surface definition based on the geometrical characteristics of the iced airfoil surface, (2) generating a high-quality grid using the generated surface point distribution, and (3) generating the input and restart files needed to run the general purpose CFD solver NPARC. ICEG2D can be executed in batch mode using a script file or in an interactive mode by entering directives from a command line. This report summarizes activities completed in the first year of a three-year research and development program to address issues related to CFD simulations for aircraft components with ice accretion. Specifically, this document describes the technology employed in the software, the installation procedure, and a description of the operation of the software package. Validation of the geometry and grid generation modules of ICEG2D is also discussed.

Thompson, David S.↗