Bluff Automotive Body

based on "Automatic Structured Grid Generation Using Gridgen (Some Restrictions Apply)" from NASA CP-3291, "Surface Modeling, Grid Generation, and Related Issues in Computational Fluid Dynamic (CFD) Solutions", proceedings of a workshop held at NASA Lewis Research Center, Cleveland, OH, 09-11 May 1995, pp. 463-476.

Gridgen is a software system for generation of 3D, multiple block, structured grids. The system is comprised of two codes: Gridgen, an interactive program that provides capabilities ranging from geometry model import through volume grid initialization and analysis software preprocessing; and Gridgen3D, a batch program for volume grid refinement. Gridgen is a monolithic program in the sense that it consists of a single process and a single graphics window. Gridgen's window, however, is repositionable and resizable. Gridgen also manages its own non-overlapping windows inside the main window. User interaction with Gridgen is directed through text - based button menus activated via the mouse or keyboard "hot keys". A 3D, graphical image of the grid is always present and may be easily panned, zoomed, rotated, and otherwise customized by the user.

The manner in which grids are constructed using Gridgen is is based on a hierarchical paradigm, beginning with the geometry model, and proceeding to curve, surface, and volume elements as shown in the adjacent figure. The geometry model, provided as input to Gridgen, serves as the foundation for the hierarchy. The user constructs curves which are in turn used to build the topological surface and volume components. The grid for each of the hierarchical components is an implicit but separate part of the component. The result of maintaining a distinction between the geometry model, the hierarchical components, and the grid allows changes to be rapidly propagated either forward or backward throughout the grid system.

Users operate Gridgen in much the same manner as a product designer operates a computer aided design (CAD) system. After importing and repairing the geometry model (database), the user draws curves (connectors), assigns a number of points to each connector, and distributes those points along the connector using a variety of distribution functions. The connectors are then selected as the boundaries of surface grids (domains). Transfinite interpolation (TFI), elliptic partial differential equation (PDE), and hyperbolic PDE methods are available for controlling the distribution of grid points on the domains. The domains are then selected as the boundaries of volume grids (blocks). Again, TFI, elliptic PDE, and hyperbolic PDE methods are available for grid point control within the blocks. Finally, the user sets boundary conditions and exports formatted data for the chosen analysis software.

From the description above it should be apparent that grid generation using Gridgen is a user - in - the - loop task. Therefore, one of the goals of the software design has been to automate as much of the grid generation minutiae and bookkeeping as possible so that the user may concentrate on topology and grid quality. This is made possible through Gridgen's data hierarchy. The data hierarchy maintains the inter-relationships between the 1D, 2D, and 3D grid components (connectors, domains, and blocks, respectively) so that the user's changes may be propagated up or down the hierarchy automatically. Some of these automation tools are described in the following sections.

Gridgen's automation features will be demonstrated in the context of grid generation for an external automotive shape. This bluff body, illustrated in the adjacent figure, was the subject of a wind tunnel test that studied its wake structure relative to the base slant angle. This vehicle was also used as the basis for an evaluation of computational fluid dynamics (CFD) software for automotive shapes. The surface grids created using Gridgen are shown in the figure below.

Database is Gridgen's term for the geometry model of the object on and around which the grid is to be generated. Gridgen's database capability is based mathematically on nth degree, rational, Bezier curve and surface geometry. The database also includes relational data such as grouping, color, names, etc. Gridgen can import the database from several industry standard file types. The bilinear database surfaces for the bluff-body grid were created from drawings and tabular data. The surfaces in this particular database were stored in two files: one containing the five surfaces for the fore- and mid-bodies, and one containing the four aft-body surfaces.

Gridgen offers several methods for placing grid points on the database including curves that may be drawn directly on the surfaces ("Line on DB" and "Curve on DB" segment types), projection of curve grids, and projection of surface grids. More importantly, Gridgen automatically maintains the adherence of grid components to the database. This relationship between the grid and the database is maintained via the database entity name. Each entity in Gridgen's database has a unique name and every grid component that adheres to the database saves the name of the entity and the database coordinates (see adjacent figure). This allows the grid to automatically adhere to the database even when the database shape changes.

When the shape modification commands (Translate, Scale, and Rotate) are applied by the user, all of the grid elements adhering to the modified entities (as determined by the data shown in the figure above) are also modified automatically. For the bluff-body example grid, this allows the base slant angle of the grid to be changed simply by importing a different database file as shown in the adjacent figure.

The curves along which grid points are to be distributed are called connectors. Each connector consists of three attributes: shape, dimension (number of grid points), and distribution (of grid points). Although each of the three attributes of a connector may be changed individually they are all coupled. This allows the user to change any one of the attributes and the other two will be updated automatically. This feature allows the user to edit the grid without reworking the entire connector definition which can make the user much more efficient. This connector updating process occurs whenever the database is modified (as described in the previous section). As shown in the adjacent figure, changes to the connectors are propagated automatically up the grid component hierarchy to domains and blocks.

Gridgen's surface grid components are called domains. Surface grid quality (smoothness, clustering, orthogonality) can be improved by application of Gridgen's elliptic PDE techniques. Specifically, Gridgen solves Poisson's equation using an explicit, point-wise, successive over relaxation (SOR) algorithm with optimal relaxation factors subject to user selected control functions. The elliptic PDE method is quite flexible and allows the user to apply a wide variety of attributes. For example, the relatively coarse grid in the adjacent figure has been refined using Gridgen's elliptic PDE methods in order to control the clustering and orthogonality of grid lines toward the right vertical boundary.

One of the most important elliptic PDE attributes is the surface shape. This attribute in combination with the control functions allows the grid points to redistribute themselves in order to obtain the desired grid qualities while also adhering to the desired shape. Of course, the most important shape that users need to maintain is the shape of surface grids constrained to the database. There are two techniques with which Gridgen can make grid points adhere to the database. As was the case for TFI, if Gridgen determines that the surface grid points lie on the database, the elliptic PDEs will be solved in the parametric space (u,v) of the database and the model space coordinates will be obtained from the known surface shape (parametric technique). The second technique for keeping grid points on the database is a simple projection (conventional technique). Each domain being run in the elliptic PDE solver maintains the database entities to project onto, and the projection orientation (which is computed automatically by Gridgen). The advantage of the parametric elliptic PDE technique is that it's much easy to set-up (no additional attributes) and it's much faster (no projections). Fortunately, Gridgen has automated the application of the database surface technique. Specifically, when Gridgen detects that all of a grid point's neighbors (those points used in the finite differences for solution of the elliptic PDEs) lie on the same database surface the code will automatically apply the parametric technique, thus making the calculation much more efficient. When domains span multiple database surfaces, only those grid points that lie on or near the seam between the surfaces will require projection. Of course, grid points may migrate across the seam from one surface to another. The figure below shows a surface grid that has been created on the surface of the bluff body database spanning two forebody surfaces with notations as to which grid points are solved parametrically and which are solved conventionally.

It is often the case that the precise shape of a surface grid's perimeter (the connector) is not a priori known by the user. This is especially true for connectors shared between two domains. Even when shape isn't important the requirement for smooth variation of grid lines across the connector is required. Rather than forcing the user to choose between 1) manually fine-tuning the connector's shape or 2) being stuck with something inadequate, Gridgen's elliptic PDE techniques provide a boundary condition that allows the connector shape to float subject to the elliptic PDE solution. The float boundary condition treats the grid points on a connector shared between two domains in the same manner as interior domain points; they move subject to the elliptic PDE solution. When the solver is done the original connector shape is replaced by a new shape defined by the refined grid points.

The user may also defined sub-domains which, as the name implies, are subsets of a domain. Subdomains may then be used with the TFI and elliptic PDE methods to restrict the effects of the methods to a small region of the grid. Subdomains may be thought of as templates that fit over the domain grid and define the region to which changes should be made. Each subdomain saves its own unique combination of elliptic PDE attributes. When grid modifications require re-application of the PDE methods (see previous sections) the user may simply invoke the PDE method without resetting attributes.

Volume grids (blocks) are created by the user's selection of the domains that comprise the block's perimeter. Any number of domains may be used on the block's perimeter but they must be arranged into six faces such that opposite faces have the same number of grid points (ie, the block must map into an IxJxK computational parallelepiped). Once the block perimeter has been defined Gridgen will automatically create the volume grid points by applying TFI.

Block modifications, including copy, translate, scale, and rotate, will result in automatic propagation of changes down Gridgen's data hierarchy (backward editing) to the domains and connectors as shown in the adjacent figure.

Gridgen has also automated one of the most cumbersome aspects of multiple block grid generation: interblock connectivity detection. As a result of Gridgen's data hierarchy, the code automatically detects and maintains both full- and partial-face interblock connections simply by noting that the same domain is used in two blocks. Changes to a domain's grid points by the PDE solver, for example, are automatically transferred to both blocks that use that domain. Changes to a domain on a block's perimeter will propagate up Gridgen's data hierarchy and cause automatic re-TFI of the volume grid points. Also, when the boundary conditions are exported for use with the analysis software the connectivity data is formatted and exported specifically for the chosen analysis software.

Gridgen also offers an interactive tool for re-dimensioning (changing the total number of grid points) the entire blocking system. This feature allows the user to select any connector in the blocking system and change its number of grid points. That change is propagated automatically throughout the system to maintain dimensional consistency (ie, maintain IxJ domains and IxJxK blocks). An example of this feature is shown in the adjacent figure.

One final automation feature deserves mention. Gridgen can import "raw" grid points (from a PLOT3D grid file, for example). When this is done, Gridgen automatically creates connectors, domains, and blocks, from the raw grid data. Therefore, the user may then avail him/herself of all of Gridgen's commands, including analysis boundary condition setting and file export. Conversely, the Gridgen user may export the grid points from any connector, domain(s), or block(s) to a PLOT3D file for use in other applications.

Various features within Gridgen have been described and their unique automatic aspects have been emphasized. These features contrast sharply with the fact that Gridgen is not an automatic grid generator where we define automatic as "create as suitable grid given a geometry model and little or no user input". Instead, Gridgen has been motivated by the desire to emphasize grid quality and software flexibility. These emphases have led to the development of a visually based, 3D, interactive application environment that automates much of the low level grid maintenance tasks, freeing the user to apply his/her judgement as to grid suitability. Gridgen's ability to automate much of the process is directly attributable to its data hierarchy in which the curve, surface, and volume grids are maintained as secondary components of connector, domain, and block topology components.