CELERITAS SIMULATION TECHNOLOGY, LLC
The set of overlapping grids must be assembled or connected together to form a composite grid and solution where the solution results from one grid are linked to the solution values on the other overlapping component grids. The assembly of the composite grid is a multi-step process that for static application can be performed as a pre-processing application at the end of the grid generation phase. For a moving body application the grids will typically move rigidly with each body and the grid assembly process must be performed at each time step.
Figure 1: Grid system for foil overlapping with background grid.
To illustrate the process, consider the grid system shown in Figure 1 where a body conforming grid around a foil overlaps a Cartesian background grid. This simple two-dimensional grid system illustrates the addition of geometry feature such as a rudder or stabilizer to an existing geometry, such as a ship hull, represented by the Cartesian grid.
Figure 2: Overset grid system after hole cutting. Hole points are identified and marked as blue dots. Lines connected to hole points are not displayed to graphically present the active/non-hole elements.
The first step in the overset grid assembly process is the identification of points in each component grid that are outside the domain of interest. These points, called hole points, will be inside a body or behind a symmetry plane and should be excluded from the flow solver computations. Figure 2 presents the example grid system with the background grid hole points identified and marked as blue dots. The holes and their boundaries within a grid allow the solution from one overlapping grid to be coupled to the solutions on other grids to form a single composite grid and solution.
Figure 3: Grid system with hole and fringe points identified. Hole points are identified as blue points.Fringes are identified with black and red points
The grid points adjacent to the holes become intergrid boundary points called fringe points. In addition, the boundaries of each component grid that are not physical boundary conditions such as solid surfaces and overlap other component grids will also be marked as fringe points. Figure 3 includes the identification of the fringe points that will be used as boundary condition points to connect the two grids into a single composite grid. Outer boundary fringe points for the foil grid are shown in red and inner fringe points adjacent to hole points in the background mesh are shown in black. The marking of holes and the surrounding fringe boundaries form the first phase of an overset grid assembly process.
The boundary values required by the flow-field solution at the intergrid boundary fringe points are obtained by interpolating the solution from appropriate donor elements using information from other grids that overlap the region. The second phase of the overset grid assembly process is the search for candidate donor elements and the selection of appropriate donor members to be used in the interpolation of the solution on the donor grid. For a vertex or node centered solution the donor members will be the nodes of the donor element that contains the fringe point location and standard tri-linear interpolation will be used for the interpolation weights. The set of points that are marked as hole and fringe along with the donor members and their associated interpolation weights is called the domain connectivity information (DCI) for the composite grid.
Figure 4: Grid system with hole and fringe points identified after application of process to reduce the amount of overlap between component grids.
The overset composite solution quality can be improved by having the donor element, which provides the interpolated values, of comparable size to the fringe element, which is utilizing the interpolated value as a boundary condition value. While this is a goal for generating overset component grids, it is not always achieved in practice. A final and optional phase of the overset grid assembly process is an overlap minimization process that seeks to reduce the amount of overlap between component grids. The process will attempt to remove the larger elements where there are smaller elements that overlap. For a vertex centered grid assembly the size of elements connected to a grid point are averaged to provide a “grid size” at the grid point. Points larger than the candidate donor elements in the overlap region are marked as hole points, and hence removed from active flow solution. The hole points must still have fringe intergrid boundary points between the active or field solution points and the hole points. Figure 4 shows the resulting set of hole and fringe points after application of the overlap minimization process. The background grid, which has larger elements in the overlap region, has additional points marked as hole points with the result in this case of expanding the set of hole points and pushing the surrounding fringe points to near the fringe boundary of the foil grid. The minimization process leaves sufficient overlap such that no donor element contains a fringe point.