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Closing the Gap Between CAD Model and Downstream ApplicationRida T. FaroukiOver the past 25 years, the use of computeraided design, analysis, and optimization methods has grown explosively in the aerospace, automotive, electronics, and other industries concerned with complex highperformance products. The value of software tools in the specification and verification of new product designs is obvious: They can, in principle, drive automated manufacturing, assembly, and inspection operations; they provide a "virtual laboratory" for assessing performance characteristics (such as structural strength or aerodynamic drag) that otherwise require expensive and timeconsuming physical experimentation; and their systematic use culminates in a comprehensive archival design database for future reference.Virtually all computerbased design tasks commence with the use of computeraided design (CAD) systems to create detailed geometrical models. These models serve as the point of departure for diverse analysis tools, such as computational fluid dynamics (CFD), stress analysis, geophysical data exploration, and computational electromagnetics or acoustics. The models are also employed in many manufacturing processes, such as numericalcontrol machining, injection molding, and casting. The success of such downstream applications is, of course, predicated on the receipt of geometrical models that are accurate, selfconsistent, and economical in data volume. Although modern CAD systems have attained a certain degree of maturity, their efficiency, reliability, and compatibility with subsequent analysis tools fall far short of what was envisaged at their inception, some 25 years ago. At the heart of this problem lie some deep mathematical issues, concerned with the computation, representation, and manipulation of complex geometries, that have stubbornly resisted the best efforts of the research community to formulate rigorous and efficient solution procedures. To investigate the impact of this impasse on engineering analysis, an interdisciplinary workshop, Integration of CAD and CFD, was held at the University of California, Davis, April 1213, 1999. Although the deficiencies of CAD models raise issues that are common to numerous application contexts, a specific context was chosen to ensure a sharp focus for this exploratory meeting; computational fluid dynamics seemed to be a natural choice, since analysis of flows over complex shapes (e.g., aircraft, turbine blades) are of primary concern in this field. The twoday workshop was sponsored by SIAM and the Department of Mechanical and Aeronautical Engineering at UC Davis, with financial support from the National Science Foundation. The 44 workshop attendees represented a broad international spectrum of researchers, developers, and users of CAD/CFD tools from academia, industry, and national laboratories. To promote the free exchange of ideas, an experimental format was adopted: Eight invited speakers presented "position papers" (describing experiences, open problems, needs, possibilities, etc.), followed by shorter technical presentations and open discussion sessions.
Identifying the BottleneckThe overriding theme of the workshop, echoed in virtually all the position papers, was the cumbersome and errorprone process of deriving satisfactory CFD surface and volume meshes from CAD models. This problem is not the fault of the meshing algorithms, but rather of the geometrical or topological errors and inconsistencies that plague CAD models.Meshing algorithms have attained a high degree of sophistication and reliability, provided they are furnished with "correct" geometrical input. Ken Morgan of the University of Wales, Swansea, showed impressively detailed meshes (with 50 million elements) for fighter aircraft carrying full payloads; he characterized the meshing algorithm as essentially 100% reliable, provided the input CAD model is errorfree. He presented the following "typical" breakdown of the effort in a realistic CFD analysis: 14 weeks for geometry repair and preparation, 1020 minutes for surface meshing, 34 hours for volume meshing, and about 1 hour for the actual flow analysis. Similar views were expressed by Scott Gilmore (Fluent), Bill Pien (Ford), David Ferguson (Boeing), and David Marcum (Mississippi State University). Their common experience is that the task of "geometry repair, cleanup, and preparation" on CAD models, prior to meshing, is the key bottleneck in the use of CFD as a practical design tool. This laborious, manualintervention process is the rule, rather than the exception, and typically consumes up to 80% of the total time required for CFD analyses: The subsequent meshing and solution stages are relatively headachefree. The problem is common to all of the popular commercial CAD systems (e.g., CATIA, SDRC IDEAS, Pro/ENGINEER, Unigraphics). In fact, a small industry devoted to software products (such as CAD/IQ and CADfix) that attempt to identify and correct CAD model errors, by resorting to expedient heuristics, has now emerged. Scott Gilmore noted that these problems are exacerbated by the current proliferation of different CAD systems in industry. A single company may transfer CAD models between several different systems, and the dataexchange standards (IGES and STEP) that purportedly support such transfers are notoriously unreliable. This is hardly surprising, since no satisfactory mathematical theory or algorithms currently exist for some of the geometrical entitiessurface intersections in particularthat the standards attempt to communicate. Gilmore pointed out that Fluent's CFD code incorporates a basic geometrical modeling capability. Models created with the CFD code are much more reliable in meshing than those from commercial CAD systems and, moreover, do not include fine geometrical details that are superfluous or a hindrance to the CFD analysis. Nevertheless, at least 50% of Fluent users insist on using external CAD systems for other (e.g., manufacturing) reasons, and this fraction is steadily growing.
Toward a Smoother InterfaceMichael Aftosmis (NASA Ames) and Bob Haimes (MIT) described an approach for minimizing problems caused by inconsistent interpretations of data when geometrical computations are performed partially within the CAD system and partially by a standalone meshing package. Their approach employs a software interface called CAPRI (Computational Analysis Programming Interface) that allows the meshing algorithm to pass all geometrical computations to the CAD system. For implementation of this approach, the CAD system must provide an appropriate API (application programmer's interface). The method may prove too cumbersome for contexts in which very frequent communication across the API is essential. Although it cannot cure intrinsic deficiencies of the CAD system algorithms, this approach has the virtue of placing the blame where it belongs.CFD currently employs a wide variety of meshing procedures (for several grid types, including Cartesian, structured, unstructured, adaptively refined, and overlapping). The question of whether higherorder finite elements (possibly with curved boundaries) could help resolve some of the difficulties in meshing was also discussed. This does not presently seem to be a viable proposition, howeverto accurately capture complex phenomena like shocks, the high geometrical resolution of small, adaptive grid elements appears to be essential. Physical aspects of the flow problem strongly influence the type of mesh structure that is appropriate. Several talks addressed studies of the "geometry of flow"; these studies may ultimately have an important influence on this issue. The geometry of flows and the geometry of boundaries are, of course, intimately connected in solutions of boundaryvalue problems. Depending on the goal of the calculations, the degree of resolution required for the boundary varies. For example, calculations of farfield noise, pressure distribution, and skin friction all have different requirements. Thus, knowledge of the flow physics can be very useful in the CAD process, and, conversely, CAD geometry preparation plays a crucial role in the use of CFD for the design and analysis of aerodynamic configurations. An integrated approach is desirable, with knowledge of flow geometry employed to guide discretization schemes and iterative algorithms used for more accurate flow simulations. These considerations also hold in other physical simulation contexts, such as computational electromagnetics (although the surface and volume grid requirements for electromagnetic scattering simulation differ from those for CFD). Thus, in multidisciplinary studies, such as the design of stealth aircraft, educated compromises are usually necessary. Although much of the emphasis at the workshop was on "CAD geometry and repair" issues, significant problems remain in the areas of grid generation and CFD code convergence. An inadequate grid or improperly converged solution may produce "plausible" results whose inaccuracies are not apparent without a detailed inspection for consistency, satisfaction of conservation laws, etc. There are many possible culprits here: "loose" coupling of turbulence models, inadequate grids, the unsteady nature of the flow, to name just a few. Thus, while "bad" CAD geometry is a showstopper in terms of blocking the subsequent gridgeneration and flowsolution phases, a preoccupation with this problem should not blind us to the need for rigorous accuracy/consistency checks on flow solutions as an essential supplement to sophisticated color graphics.
Design OptimizationIn practical applications, CFD computations are rarely done in isolation for purely analytic purposes. Rather, they are often used as a driver for systematic design optimization procedures. In this context, in which many CFD runs are performed in succession on modified geometries, the reliability and efficiency of the CAD/CFD interface become a crucial concern.Design optimization studies were discussed at the workshop by Helmut Sobieczky (Deutsches Zentrum für Luft und Raumfahrt) and Malcolm Bloor (University of Leeds). Usually, a design is optimized with respect to a relatively small number of key geometrical parameters, which may not be explicitly expressed in the CAD model. For example, Sobieczky described standardized 11parameter descriptions of airfoil sections that are well suited to optimization. In Bloor's approach, a surface is defined by solving a PDE subject to given boundary conditions, and design optimization goals (e.g., minimization of wave drag for a ship hull) are incorporated directly into the solution. Bill Pien described a realworld case study in which the use of CAD/CFD design optimization resulted in a reduction of the drag coefficient from 0.44 to 0.24 for a nextgeneration vehicle. To achieve this result, 15 design iterations were required over a fourmonth period. The CFD meshes had 1 million surface and 16 million volume elements. Again, the main bottleneck was in geometry repair and preparation. Pien described some of the inhibitors of a smoother CAD/CFD interface: (i) too much detail in the CAD models; (ii) CFD people who are not involved in CAD; (iii) CAD people who don't understand CFD; and (iv) a profusion of different CAD systems and CFD codes (having different mesh structure requirements). Point (i) is particularly salient in a design optimization context: Relatively "coarse" models should suffice in the early stages, until one begins to approach the optimal geometry. Thus, a means for adaptively adjusting the level of detail in the CAD model would be very useful in accelerating CAD/CFD design optimization studies. Such a "hierarchical geometry model" must be carefully formulated, so as to satisfy constraints (e.g., volume) that ensure consistent flow simulations at successive levels of geometrical resolution.
Facilitating CAD/CFD IntegrationWhat can be done about this rather unsatisfactory state of affairs? As noted by Nigel Weatherill (University of Wales, Swansea), the problems are not new, althoughas computer hardware rapidly advancesthe perception that they pose a critical and intolerable bottleneck is rapidly gaining momentum. The lack of a robust solution to the surface intersection problem is the culprit behind most problems in CAD data (e.g., gaps/overlaps between abutting surfaces, topological inconsistencies). In his 1983 PhD thesis, Tom Sederberg of Brigham Young University showed that two bicubic patches (the standard type of freeform surface used to design complex shapes like wings and turbine blades) intersect in an algebraic space curve of degree 324. The exact mathematical representation of these entities is a daunting task; on the other hand, a satisfactory theory of how to approximate them (and the "trimmed surfaces" they define) in a mutually consistent manner has failed to emerge.The problem is partly cultural in nature: The development of CAD systems has been driven by productrelease deadlines and by management teams poorly versed in the fundamental mathematical difficulties; the heuristic methods implemented in CAD systems work sufficiently well to make them worthwhile tools in industry, but not without inflicting great pain and exasperation on their users in challenging contexts like the CAD/CFD interface; and the academic CAD research community has largely forsaken many of the fundamental issues and sought refuge in simpler problems that lead to easy publications. There is no simple panacea for these issues. Nevertheless, CAD and CFD are certainly here to stay as practical design tools, and during the workshop a broad consensus emerged concerning lines of further investigation that can help facilitate and streamline their integration:
The workshop was an exhilarating experience: The interaction between two ordinarily distinct fields was conducive to new ideas, and the exploratory format also encouraged a high degree of interdisciplinary communication. For many attendees, the ability to vent frustrations before an audience with similar experiences had a valuable cathartic effect. At the least, they took away a renewed impression of the importance of the CAD/CFD interface problem, and a revitalized determination to do something serious about it. A followup workshop, Mathematical Foundations of CAD, is being held at the Mathematical Sciences Research Institute, Berkeley, California, June 45, 1999 (http://www.msri.org). Those interested in the mathematical problems of CAD may also wish to consider attending the 6th SIAM Conference on Geometric Design, Albuquerque, New Mexico, November 25, 1999 (http://www.siam.org/meetings/gd99).
Rida T. Farouki is a professor of mechanical and aeronautical engineering at the University of California, Davis, and chair of the SIAM Activity Group on Geometric Design. © 1999, Society for Industrial and Applied Mathematics 


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