Abstract: A method that can automatically determine mesh element sizing for improved mesh quality at encroaching boundaries has been developed and is applied to geometry-constrained meshes wherein the curvilinear distance to the boundary is computed. This technique is computationally robust and requires only a relatively coarse triangular mesh on the geometry model as input. Using isotropic or anisotropic elements guarantees high-resolution meshing, especially for geometry configurations with narrow gaps. This article develops and demonstrates the application of this technique in the presence of encroaching boundaries within a B-Rep model.

In computational fluid dynamics (CFD), unstructured meshing has long been proposed as the solution to time-intensive mesh generation. Utilizing the computational geometry solid model topology for domain decomposition into mesh topology while using unstructured meshing saves time. Also, using unstructured meshes allows for local mesh size control, which is decoupled from the global sizing, as in a structured grid. Defining an optimal local mesh becomes a problem for automatic, user-independent, unstructured meshing because isotropic sizing is impractical in simulation-driven design.

An optimal mesh has many requirements, but the first and foremost is an accurate representation of the model geometry. An issue with the element sizing approach is that the geometry-constrained surface meshing requires considering size distribution in the curvilinear space. A successful approach to automating local mesh size utilizes user-prescribed goals for geometry feature-length and curvature resolution to compute element sizing on surface boundaries within a B-Rep solid model.

However, such an approach to automatic element sizing ignores important relational effects between surface boundaries. For example, narrow regions where boundary curves encroach, as in Figure 1, are insufficiently resolved in the mesh. It is desirable to specify a minimum number of spanning mesh elements in narrow regions to resolve the gap. Therefore, additional automatic element sizing tools are required to produce suitable mesh density and quality in the presence of boundary encroachment.

(a)

(b)

Figure 1. (a) Automatic mesh sizing that respects boundary curvature resolution but ignores boundary proximity results in under-resolved gap regions; (b) Automatic sizing that ignores boundary proximity results in poor mesh quality anisotropic meshing advancing fronts collide.

Boundary encroachment is a product of local boundary element size and proximity to other boundaries. For geometry-constrained meshes, proximity is defined by the minimum curvilinear distance from a location on one boundary to all other boundaries. Any method used to determine boundary proximity must be able to handle collections of surfaces defining the curved geometry. The proposed method for mesh sizing in the presence of encroaching boundaries consists of two parts:

1. Compute the curvilinear distance from a boundary to the medial axis.
2. Adjust boundary mesh sizing locally based on the local distance to the medial axis.

The DrivAer model

The DrivAer fastback configuration illustrates a CAD solid model composed of over 1,700 trimmed surfaces for the aero body alone. As Figure 2 shows, quilting (assembling neighboring trimmed surfaces into a single topological surface) reduces the model to 67 conceptual domains upon which the curvilinear distance field has been computed. Without using quilts (also known as virtual topology), automated surface meshing techniques would recover every trimmed surface boundary, and the mesh quality would be compromised.

Figure 2. DrivAer model trimmed surfaces (upper left), virtual topology quilts (upper right), and quilt curvilinear distance field (bottom).

DLR F6 configuration

As a practical aerospace example, Figure 3 shows the distance field for the DLR F6 wing body with pylon and nacelle configuration from the 2nd AIAA Drag Prediction Workshop. The close-up view of the nacelle shows encroachment of the nacelle leading edge with the pylon leading edge. The nacelle inlet lip boundary has refined element sizing to allow the advancing mesh to reach isotropy at the medial axis between the lip and the pylon. Computation of the distance field, mesh walking to discover the distance from boundary points to the nearest medial axis, and adjustment of local element sizing consumed less than 20% of the total time to complete the surface mesh.

Figure 3. DLR F6 configuration: a close-up view of the nacelle-pylon, including distance gradient vectors (top) and nacelle-pylon mesh with nacelle inlet boundary element sizing refined (red) in proximity to the pylon (bottom).

The applications mentioned above have demonstrated a method for automatically determining suitable element sizing in the presence of encroaching quilt boundaries within a B-Rep model. Computations are undertaken to determine the curvilinear distance field within a discrete representation of a quilt. The method is computationally robust and efficient, requiring only a valid, relatively coarse triangular mesh on the quilt as input. The method produces suitable mesh resolution of good quality for narrow gaps, utilizing isotropic or anisotropic elements. Future work will involve the calculation of the 3D distance field to allow the resolution of gaps between encroaching surfaces.

Reference

1. Wyman, Nicholas J., Baker, Patrick A.  “Automatic Boundary Proximity Detection and Element Sizing for B-Rep Constrained Unstructured Meshes using Distance Fields,” AIAA paper no. 2022-3490, June 2022.

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