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NASA NTRS2005

Verification, Validation, and Solution Quality in Computational Physics: CFD Methods Applied to Ice Sheet Physics

Procedures and methods for veri.cation of coding algebra and for validations of models and calculations used in the aerospace computational fluid dynamics (CFD) community would be ef.cacious if used by the glacier dynamics modeling community. This paper presents some of those methods, and how they might be applied to uncertainty management supporting code veri.cation and model validation for glacier dynamics. The similarities and differences between their use in CFD analysis and the proposed application of these methods to glacier modeling are discussed. After establishing sources of uncertainty and methods for code veri.cation, the paper looks at a representative sampling of veri.cation and validation efforts that are underway in the glacier modeling community, and establishes a context for these within an overall solution quality assessment. Finally, a vision of a new information architecture and interactive scienti.c interface is introduced and advocated.

Thompson, David E.↗

NASA NTRS2014

Arbitrary Shape Deformation in CFD Design

Sculptor(R) is a commercially available software tool, based on an Arbitrary Shape Design (ASD), which allows the user to perform shape optimization for computational fluid dynamics (CFD) design. The developed software tool provides important advances in the state-of-the-art of automatic CFD shape deformations and optimization software. CFD is an analysis tool that is used by engineering designers to help gain a greater understanding of the fluid flow phenomena involved in the components being designed. The next step in the engineering design process is to then modify, the design to improve the components' performance. This step has traditionally been performed manually via trial and error. Two major problems that have, in the past, hindered the development of an automated CFD shape optimization are (1) inadequate shape parameterization algorithms, and (2) inadequate algorithms for CFD grid modification. The ASD that has been developed as part of the Sculptor(R) software tool is a major advancement in solving these two issues. First, the ASD allows the CFD designer to freely create his own shape parameters, thereby eliminating the restriction of only being able to use the CAD model parameters. Then, the software performs a smooth volumetric deformation, which eliminates the extremely costly process of having to remesh the grid for every shape change (which is how this process had previously been achieved). Sculptor(R) can be used to optimize shapes for aerodynamic and structural design of spacecraft, aircraft, watercraft, ducts, and other objects that affect and are affected by flows of fluids and heat. Sculptor(R) makes it possible to perform, in real time, a design change that would manually take hours or days if remeshing were needed.

Landon, Mark↗

NASA NTRS2016

Predictive Evaluations of Oxygen-Rich Hydrocarbon Combustion Gas-Centered Swirl Coaxial Injectors using a Flamelet-Based 3-D CFD Simulation Approach

NASA Marshall Space Flight Center (MSFC) has embarked upon a joint project with the Air Force to improve the state-of-the-art of space application combustion device design and operational understanding. One goal of the project is to design, build and hot-fire test a 40,000 pound-thrust Oxygen/Rocket Propellant-2 (RP-2) Oxygen-Rich staged engine at MSFC. The overall project goals afford the opportunity to test multiple different injector designs and experimentally evaluate the any effect on the engine performance and combustion dynamics. To maximize the available test resources and benefits, pre-test, combusting flow, Computational Fluid Dynamics (CFD) analysis was performed on the individual injectors to guide the design. The results of the CFD analysis were used to design the injectors for specific, targeted fluid dynamic features and the analysis results also provided some predictive input for acoustic and thermal analysis of the main Thrust Chamber Assembly (TCA). MSFC has developed and demonstrated the ability to utilize a computationally efficient, flamelet-based combustion model to guide the pre-test design of single-element Gas Centered Swirl Coaxial (GCSC) injectors. Previous, Oxygen/RP-2 simulation models utilizing the Loci-STREAM flow solver, were validated using single injector test data from the EC-1 Air Force test facility. The simulation effort herein is an extension of the validated, CFD driven, single-injector design approach applied to single injectors which will be part of a larger engine array. Time-accurate, Three-Dimensional, CFD simulations were performed for five different classes of injector geometries. Simulations were performed to guide the design of the injector to achieve a variety of intended performance goals. For example, two GCSC injectors were designed to achieve stable hydrodynamic behavior of the propellant circuits while providing the largest thermal margin possible within the design envelope. While another injector was designed to purposefully create a hydrodynamic instability in the fuel supply circuit as predicted by the CFD analysis. Future multi-injector analysis and testing will indicate what if any changes occur in the predicted behavior for the single-element injector when the same injector geometry is placed in a multi-element array.

Richardson, Brian R.↗

NASA NTRS2006

An Initial Non-Equilibrium Porous-Media Model for CFD Simulation of Stirling Regenerators

The objective of this paper is to define empirical parameters (or closwre models) for an initial thermai non-equilibrium porous-media model for use in Computational Fluid Dynamics (CFD) codes for simulation of Stirling regenerators. The two CFD codes currently being used at Glenn Research Center (GRC) for Stirling engine modeling are Fluent and CFD-ACE. The porous-media models available in each of these codes are equilibrium models, which assmne that the solid matrix and the fluid are in thermal equilibrium at each spatial location within the porous medium. This is believed to be a poor assumption for the oscillating-flow environment within Stirling regenerators; Stirling 1-D regenerator models, used in Stirling design, we non-equilibrium regenerator models and suggest regenerator matrix and gas average temperatures can differ by several degrees at a given axial location end time during the cycle. A NASA regenerator research grant has been providing experimental and computational results to support definition of various empirical coefficients needed in defining a noa-equilibrium, macroscopic, porous-media model (i.e., to define "closure" relations). The grant effort is being led by Cleveland State University, with subcontractor assistance from the University of Minnesota, Gedeon Associates, and Sunpower, Inc. Friction-factor and heat-transfer correlations based on data taken with the NASAlSunpower oscillating-flow test rig also provide experimentally based correlations that are useful in defining parameters for the porous-media model; these correlations are documented in Gedeon Associates' Sage Stirling-Code Manuals. These sources of experimentally based information were used to define the following terms and parameters needed in the non-equilibrium porous-media model: hydrodynamic dispersion, permeability, inertial coefficient, fluid effective thermal conductivity (including themal dispersion and estimate of tortuosity effects}, and fluid-solid heat transfer coefficient. Solid effective thermal conductivity (including the effect of tortuosity) was also estimated. Determination of the porous-media model parameters was based on planned use in a CFD model of Infinia's Stirling Technology Demonstration Convertor (TDC), which uses a random-fiber regenerator matrix. The non-equilibrium porous-media model presented is considered to be an initial, or "draft," model for possible incorporation in commercial CFD codes, with the expectation that the empirical parameters will likely need to be updated once resulting Stirling CFD model regenerator and engine results have been analyzed. The emphasis of the paper is on use of available data to define empirical parameters (and closure models) needed in a thermal non-equilibrium porous-media model for Stirling regenerator simulation. Such a model has not yet been implemented by the authors or their associates. However, it is anticipated that a thermal non-equilibrium model such as that presented here, when iacorporated in the CFD codes, will improve our ability to accurately model Stirling regenerators with CFD relative to current thermal-equilibrium porous-media models.

Tew, Roy↗

NASA NTRSDate not supplied

Construction of a Fluid Flowfield from Discrete Point Data using Machine Learning

Many verification and validation procedures in aerospace engineering involve the comparison of computational fluid dynamics (CFD) data to experimental results from sources like wind tunnel tests. However, an incongruity exists between the data available from these sources: flow visualization is available by default in computational data, whereas in most experimental setups the available data is far more discrete and far more limited: integrated forces and moments, discrete pressure and temperature probes, etc. When differences exist between quantities of interest like lift and drag coefficients, the lack of full-field flow data from the experiments complicates most attempts to reconcile why the different data sources disagree. To this end, a shallow neural network, constrained by certain fluid flow properties, was trained to approximate flow field snapshots given only discrete data like that available in a wind tunnel test. The constructed snapshots, even for complex incompressible fluid flows, were found to agree at the large scales with the true flow fields. With this tool, researchers can more readily and easily understand why quantities of interest differ between their experimental and computational datasets. This in turn improves the resulting data's uncertainty measures.

Yury Lebedev↗

NASA NTRSDate not supplied

Construction of a Fluid Flowfield from Discrete Point Data using Machine Learning

Yury Lebedev↗

DOE OSTI2022

aphBO-2GP-3B: a budgeted asynchronous parallel multi-acquisition functions for constrained Bayesian optimization on high-performing computing architecture

High-fidelity complex engineering simulations are often predictive, but also computationally expensive and often require substantial computational efforts. The mitigation of computational burden is usually enabled through parallelism in high-performance cluster (HPC) architecture. Optimization problems associated with these applications is a challenging problem due to the high computational cost of the high-fidelity simulations. In this paper, an asynchronous parallel constrained Bayesian optimization method is proposed to efficiently solve the computationally expensive simulation-based optimization problems on the HPC platform, with a budgeted computational resource, where the maximum number of simulations is a constant. The advantage of this method are three-fold. Firstly, the efficiency of the Bayesian optimization is improved, where multiple input locations are evaluated parallel in an asynchronous manner to accelerate the optimization convergence with respect to physical runtime. This efficiency feature is further improved so that when each of the inputs is finished, another input is queried without waiting for the whole batch to complete. Second, the proposed method can handle both known and unknown constraints. Third, the proposed method samples several acquisition functions based on their rewards using a modified GP-Hedge scheme. The proposed framework is termed aphBO-2GP-3B, which means asynchronous parallel hedge Bayesian optimization with two Gaussian processes and three batches. The numerical performance of the proposed framework aphBO-2GP-3B is comprehensively benchmarked using 16 numerical examples, compared against other 6 parallel Bayesian optimization variants and 1 parallel Monte Carlo as a baseline, and demonstrated using two real-world high-fidelity expensive industrial applications. The first engineering application is based on finite element analysis (FEA) and the second one is based on computational fluid dynamics (CFD) simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Model reduction for hypersonic aerodynamics via conservative LSPG projection and hyper-reduction

High-speed aerospace engineering applications rely heavily on computational fluid dynamics (CFD) models for design and analysis due to the expense and difficulty of flight tests and experiments. This reliance on CFD models necessitates performing accurate and reliable uncertainty quantification (UQ) of the CFD models. However, it is very computationally expensive to run CFD for hypersonic flows due to the fine grid resolution required to capture the strong shocks and large gradients that are typically present. Furthermore, UQ approaches are “many-query” problems requiring many runs with a wide range of input parameters. One way to enable computationally expensive models to be used in such many-query problems is to employ projection-based reduced-order models (ROMs) in lieu of the (high-fidelity) full-order model. In particular, the least-squares Petrov–Galerkin (LSPG) ROM (equipped with hyper-reduction) has demonstrated the ability to significantly reduce simulation costs while retaining high levels of accuracy on a range of problems including subsonic CFD applications. This allows computationally inexpensive LSPG ROM simulations to replace the full-order model simulations in UQ studies, which makes this many-query task tractable, even for large-scale CFD models. This work presents the first application of LSPG to a hypersonic CFD application. In particular, we present results for LSPG ROMs of the HIFiRE-1 in a three-dimensional, turbulent Mach 7.1 flow, showcasing the ability of the ROM to significantly reduce computational costs while maintaining high levels of accuracy in computed quantities of interest.

Fluid Dynamics↗

DOE OSTI2025

Accelerating computational fluid dynamics simulation of post-combustion carbon capture modeling with MeshGraphNets

Packed columns are commonly used in post-combustion processes to capture CO 2 emissions by providing enhanced contact area between a CO 2 -laden gas and CO 2 -absorbing solvent. To study and optimize solvent-based post-combustion carbon capture systems (CCSs), computational fluid dynamics (CFD) can be used to model the liquid–gas countercurrent flow hydrodynamics in these columns and derive key determinants of CO 2 -capture efficiency. However, the large design space of these systems hinders the application of CFD for design optimization due to its high computational cost. In contrast, data-driven modeling approaches can produce fast surrogates to study large-scale physics problems. We build our surrogates using MeshGraphNets (MGN), a graph neural network framework that efficiently learns and produces mesh-based simulations. We apply MGN to a random packed column modeled with over 160K graph nodes and a design space consisting of three key input parameters: solvent surface tension, inlet velocity, and contact angle. Our models can adapt to a wide range of these parameters and accurately predict the complex interactions within the system at rates over 1700 times faster than CFD, affirming its practicality in downstream design optimization tasks. This underscores the robustness and versatility of MGN in modeling complex fluid dynamics for large-scale CCS analyses.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

CFD support of NASP design

This paper presents a summary of design studies from the 'open' literature which illustrate the level of effort and the use of computational fluid dynamics (CFD) to support the National Aerospace Plane (NASP) X-30 design. CFD plays a major role in the NASP program, particularly for the very high speed regions (Mach greater than 10) where wind tunnels cannot fully simulate the flow and/or flow-field measurements are difficult to obtain. Full simulation (nose-to-tail analysis) of the NASP flow field, both internal and external, is discussed.

Mcclinton, Charles R.↗

NASA NTRS1990

CFD support of NASP design

This paper presents a summary of design studies from the 'open' literature which illustrate the level of effort and the use of computational fluid dynamics (CFD) to support the National Aerospace Plane (NASP) X-30 design. CFD plays a major role in the NASP program, particularly for the very high speed regions (Mach greater than 10) where wind tunnels cannot fully simulate the flow, and flow field measurements are difficult to obtain. Full simulation (nose-to-tail analysis) of the NASP flow field, both internal and external, is discussed.

Mcclinton, Charles R.↗

NASA NTRS2007

Automatic Conversion of Conceptual Geometry to CFD Geometry for Aircraft Design

Conceptual aircraft design is usually based on simple analysis codes. Its objective is to provide an overall system performance of the developed concept, while preliminary aircraft design uses high-fidelity analysis tools such as computational fluid dynamics (CFD) analysis codes or finite element structural analysis codes. In some applications, such as low-boom supersonic concept development, it is important to be able to explore a variety of drastically different configurations while using CFD analysis to check whether a given configuration can be tailored to have a low-boom ground signature. It poses an extremely challenging problem of integrating CFD analysis in conceptual design. This presentation will discuss a computer code, called iPatch, for automatic conversion of conceptual geometry to CFD geometry. In general, conceptual aircraft geometry is not as well-defined as a CAD geometry model. In particular, a conceptual aircraft geometry model usually does not define the intersection curves for the connecting surfaces. The computer code iPatch eliminates the gap between conceptual geometry and CFD geometry by accomplishing the following three tasks automatically: (1) use bicubic B-splines to extrapolate (if necessary) each surface in a conceptual geometry so that all the independently defined geometry components (such as wing and fuselage) can be intersected to form a watertight CFD geometry, (2) compute the intersection curves of surface patches at any resolution (up to 10-7 accuracy) specified by users, and (3) write the B-spline surface patches and the corresponding boundary points for the watertight CFD geometry in the format that can be directly exported to the meshing tool VGRID in the CFD software TetrUSS. As a result, conceptual designers can get quick feedback on the aerodynamic characteristics of their concepts, which will allow them to understand some subtlety in their concepts and to be able to assess their concepts with a higher degree of confidence. This integration of CFD analysis in conceptual aircraft design will greatly eliminate some uncertainty due to simple analysis codes used to develop the concepts and improve the feasibility/credibility of the final concept. The presentation will highlight the mathematical challenges of accomplishing the aforementioned three tasks and the computational algorithms used by iPatch.

Li, Wu↗

DOE OSTI2024

Developing And Scaling an OpenFOAM Model to Study Turbulent Flow in a HFIR Coolant Channel

Improving the understanding of how computational fluid dynamics (CFD) direct numerical simulations (DNS) of flows in the High Flux Isotope Reactor (HFIR) perform when run in parallel using the high performance computing (HPC) platform Summit at the Oak Ridge Leadership Computing Facility (OLCF) is of particular importance to boost the computational tools used to support HFIR conversion to low enriched fuel (LEU). Evaluation of scaling performance was driven by the increasing importance of graphics processing unit (GPU) usage in HPC, which is becoming the standard for modern supercomputers such as Summit. The desired results are to obtain a strong positive correlation between the computational resources dedicated to a problem and the relative speed-up of the simulation in comparison to a benchmark. This capability will allow substantially improvement in HFIR flow analytical capabilities, specifically when predicting turbulence properties at high Reynolds numbers. The study leverages previous simulation results performed with code PHASTA (finite element) on HPC platforms Cori (NERSC) and Theta (ALCF) [1] with computing options provided in the computing platform OpenFOAM (finite volume) at OLCF. Transitioning from PHASTA to OpenFOAM will (1) eliminate dependence on third-party software for mesh generation and manipulation, (2) reduce resource needs by employing modern architectures, and (3) build expertise for future modeling of HFIR-specific problems like heat transfer in involute geometry, entrance effects, flow structure in channel corners, and so on—all important issues when defining the available thermal margins in the transition to LEU. CPUs and GPUs differ significantly in their architecture and utilization, as discussed in the literature [2]. The most important differences are in the approach to computations and their memory. A single GPU contains a large quantity of cores, enabling it to perform with a much higher throughput than a CPU, but execution requires a different approach. GPU codes execute instructions using the Single-Instruction Multiple-Thread (SIMT) approach in which a single instruction is used for groups of threads called warps. A warp typically consists of 32 threads which must execute the same set of instructions, although on separate threads. Alternately, a CPU has far fewer cores that are much more flexible in their operation, excelling at quickly performing more complex serial computations. This is why GPUs have greater throughput when properly utilized. The second important difference is seen when comparing their memory spaces. Limited memory allocations and CPU–GPU communications cause a significant bottleneck in GPU-accelerated programs. Further study was required to properly take advantage of GPU resources. A comprehensive analysis of code performance and the model-specific features of turbulence constitutes the core of this work. In this study, a DNS simulation of HFIR channel turbulence was performed with the finite volume CFD code OpenFOAM v2112 and CUDA v11.0 on Red Hat Enterprise Linux v8.2. The OpenFOAM installation had AMGx integrated to enable GPU acceleration and utilizes the PETSc4FOAM library. The computational resources and the problem size were scaled on CPU and CPU + GPU architectures to gain a better understanding of the performance of a DNS problem on modern computing hardware. The study aimed to analyze the scaling of the code exclusively on CPUs and then to examine the scaling of the codes with GPU acceleration enabled. Scaling studies included CPU and GPU acceleration on a mesh of varying resolution to analyze the impact of problem size relative to computational resources. In the course of preparing the GPU configuration on Summit, mainly using the AMGX solvers, difficulties were encountered stemming from constant changes resulting from extensive ongoing development activities and the changing environment. This resulted in the inability to complete the GPU portion of the work. The code was compiled and tested, but production runs to assess acceleration were not performed because the used discretional compute time allocation expired as year-end approached. The Summit HPC platform is scheduled for decommissioning in 2024, making it unattractive for future use with Nvidia-based GPUs. Therefore, the work will be moved onto NERSC machines in FY24. An application was prepared and submitted, and sufficient node-hours were awarded to continue the research in the next calendar year. This report summarizes work performed thus far, which mostly focused on CPU OpenFOAM computing.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS1993

Simplified jet-A kinetic mechanism for combustor application

Successful modeling of combustion and emissions in gas turbine engine combustors requires an adequate description of the reaction mechanism. For hydrocarbon oxidation, detailed mechanisms are only available for the simplest types of hydrocarbons such as methane, ethane, acetylene, and propane. These detailed mechanisms contain a large number of chemical species participating simultaneously in many elementary kinetic steps. Current computational fluid dynamic (CFD) models must include fuel vaporization, fuel-air mixing, chemical reactions, and complicated boundary geometries. To simulate these conditions a very sophisticated computer model is required, which requires large computer memory capacity and long run times. Therefore, gas turbine combustion modeling has frequently been simplified by using global reaction mechanisms, which can predict only the quantities of interest: heat release rates, flame temperature, and emissions. Jet fuels are wide-boiling-range hydrocarbons with ranges extending through those of gasoline and kerosene. These fuels are chemically complex, often containing more than 300 components. Jet fuel typically can be characterized as containing 70 vol pct paraffin compounds and 25 vol pct aromatic compounds. A five-step Jet-A fuel mechanism which involves pyrolysis and subsequent oxidation of paraffin and aromatic compounds is presented here. This mechanism is verified by comparing with Jet-A fuel ignition delay time experimental data, and species concentrations obtained from flametube experiments. This five-step mechanism appears to be better than the current one- and two-step mechanisms.

Lee, Chi-Ming↗

NASA NTRS2002

Progress in the Development of a Nozzle Design Methodology for Pulsed Detonation Engines

The Johns Hopkins University Applied Physics Laboratory (JHU/APL), in support of the NASA Glenn Research Center (NASA GRC), is investigating performance methodologies and system integration issues related to Pulsed Detonation Engine (PDE) nozzles. The primary goal of this ongoing effort is to develop design and performance assessment methodologies applicable to PDE exit nozzle(s). APL is currently focusing its efforts on a common plenum chamber design that collects the exhaust products from multiple PDE tubes prior to expansion in a single converging-diverging exit nozzle. To accomplish this goal, a time-dependent, quasi-one-dimensional analysis for determining the flow properties in and through a single plenum and exhaust nozzle is underway. In support of these design activities, parallel modeling efforts using commercial Computational Fluid Dynamics (CFD) software are on-going. These efforts include both two and three-dimensional as well as steady and time-dependent computations to assess the flow in and through these devices. This paper discusses the progress in developing this nozzle design methodology.

Leary, B. A.↗

NASA NTRS2004

Computation of Sensitivity Derivatives of Navier-Stokes Equations using Complex Variables

Accurate computation of sensitivity derivatives is becoming an important item in Computational Fluid Dynamics (CFD) because of recent emphasis on using nonlinear CFD methods in aerodynamic design, optimization, stability and control related problems. Several techniques are available to compute gradients or sensitivity derivatives of desired flow quantities or cost functions with respect to selected independent (design) variables. Perhaps the most common and oldest method is to use straightforward finite-differences for the evaluation of sensitivity derivatives. Although very simple, this method is prone to errors associated with choice of step sizes and can be cumbersome for geometric variables. The cost per design variable for computing sensitivity derivatives with central differencing is at least equal to the cost of three full analyses, but is usually much larger in practice due to difficulty in choosing step sizes. Another approach gaining popularity is the use of Automatic Differentiation software (such as ADIFOR) to process the source code, which in turn can be used to evaluate the sensitivity derivatives of preselected functions with respect to chosen design variables. In principle, this approach is also very straightforward and quite promising. The main drawback is the large memory requirement because memory use increases linearly with the number of design variables. ADIFOR software can also be cumber-some for large CFD codes and has not yet reached a full maturity level for production codes, especially in parallel computing environments.

Vatsa, Veer N.↗

NASA NTRS2011

Technique for Calculating Solution Derivatives With Respect to Geometry Parameters in a CFD Code

A solution has been developed to the challenges of computation of derivatives with respect to geometry, which is not straightforward because these are not typically direct inputs to the computational fluid dynamics (CFD) solver. To overcome these issues, a procedure has been devised that can be used without having access to the mesh generator, while still being applicable to all types of meshes. The basic approach is inspired by the mesh motion algorithms used to deform the interior mesh nodes in a smooth manner when the surface nodes, for example, are in a fluid structure interaction problem. The general idea is to model the mesh edges and nodes as constituting a spring-mass system. Changes to boundary node locations are propagated to interior nodes by allowing them to assume their new equilibrium positions, for instance, one where the forces on each node are in balance. The main advantage of the technique is that it is independent of the volumetric mesh generator, and can be applied to structured, unstructured, single- and multi-block meshes. It essentially reduces the problem down to defining the surface mesh node derivatives with respect to the geometry parameters of interest. For analytical geometries, this is quite straightforward. In the more general case, one would need to be able to interrogate the underlying parametric CAD (computer aided design) model and to evaluate the derivatives either analytically, or by a finite difference technique. Because the technique is based on a partial differential equation (PDE), it is applicable not only to forward mode problems (where derivatives of all the output quantities are computed with respect to a single input), but it could also be extended to the adjoint problem, either by using an analytical adjoint of the PDE or a discrete analog.

Mathur, Sanjay↗

NASA NTRS1990

Multi-blocking strategies for the INS3D incompressible Navier-Stokes code

With the continuing development of bigger and faster supercomputers, computational fluid dynamics (CFD) has become a useful tool for real-world engineering design and analysis. However, the number of grid points necessary to resolve realistic flow fields numerically can easily exceed the memory capacity of available computers. In addition, geometric shapes of flow fields, such as those in the Space Shuttle Main Engine (SSME) power head, may be impossible to fill with continuous grids upon which to obtain numerical solutions to the equations of fluid motion. The solution to this dilemma is simply to decompose the computational domain into subblocks of manageable size. Computer codes that are single-block by construction can be modified to handle multiple blocks, but ad-hoc changes in the FORTRAN have to be made for each geometry treated. For engineering design and analysis, what is needed is generalization so that the blocking arrangement can be specified by the user. INS3D is a computer program for the solution of steady, incompressible flow problems. It is used frequently to solve engineering problems in the CFD Branch at Marshall Space Flight Center. INS3D uses an implicit solution algorithm and the concept of artificial compressibility to provide the necessary coupling between the pressure field and the velocity field. The development of generalized multi-block capability in INS3D is described.

Gatlin, Boyd↗