Tutorial 4: Gridding Two Intersecting Ellipsoids

Many cases involving grid generation require the user to create an internal surface that defines the grid angles between two intersecting tubes or joints. Examples include tubing used for cooling, flow distribution, piping inside of an automobile or aircraft, or blood vessels attached to a heart. In this tutorial we learn how to mesh such geometry that often includes sharp angles or convex corners. In Part I we will learn the basic concepts of how to mesh an idealized geometry (a mushroom shaped region formed by two intersecting ellipsoids) and will use the same principles in Part II where we will create the mesh in 3D. In Tutorial 5 we will apply what we have learned in Tutorial 4 to create a grid on an example that is more likely to appear in practice.

What you will create in Part 1:

We will make a mesh of an idealized geometry: a mushroom shaped region formed by two intersecting ellipsoids.

Introducing Singularities
Singularities are very important in understanding gridding in GridPro and will become more important downstream when the user creates grids of increasing complexity. A problematic singularity occurs when a block corner is assigned to a surface where certain local block patterns occur. The patterns are problematic when the block count is not equal to 2 on bounding surfaces, and not equal to 4 on internal surfaces. In this case, the singular pattern is composed of 5 blocks that is placed upon an internal surface (which should have two blocks on each side). To avoid this problem, we will create another layer of topology that will push the singularity away from the surface into the mushroom cap area. Singularities and their impact on the griding process will be covered in more detail in a later tutorial.

What you will learn in Part 1:

• Using an internal surface to create a grid around a convex corner.
• Introducing singularities.

What you will create in Part 2:

Choosing the Surface Normals
The positive/negative choices in the 1 sub-menu indicate the direction of the normal vectors to the boundary surfaces. In this case, those surfaces are the two ellipsoids forming the mushroom boundaries. Each ellipsoid is defined to have a positive normal direction that points away from the center. It is needed to define tangent directions along the curve of intesections for the construction of an internal surface that biscets the angles of the convex corners. For this purpose, the normals of each ellipsoid must be flipped to the negative direction. Then the average of these unit normals will point in the correct tangent directions for the creation of the new surface. This then requires the double flip as seen in the choice of (- -). If the operation does not create a cone shaped topology group as in the picture below, choose another combination as in (++) or (+-), until it is created correctly.

What you will learn in Part 2:

• Automatically creating an internal surface at the intersection of two surfaces.
• Creating surfaces from topology.
• Fitting the Cut-Plane to a group of topology.