Curvature Refinement

The Curvature refinement level (Lcur) is the maximum level to which the cells will be split during refinement of the computational mesh until the curvature of the solid/fluid interface within the cell becomes lower than the specified Curvature refinement criterion (Ccur).

The curvature refinement procedure has the following stages:

Each solid surface is triangulated: Flow Simulation gets triangles that make up the surfaces.

Note:
The performance settings do not govern the triangulation performance.
A local (for each cell) interface curvature is determined as the maximum angle between the normals to the triangles within the cell.
If this angle exceeds the specified Ccur, and the curvature refinement level is not reached then the cell is split.

The curvature refinement works in the same manner as the small solid features refinement with the difference that the critical angle between the normals can be specified by the user (in radians) as Curvature refinement criterion (Ccur). Here, the smaller the criterion, the better resolution of the solid curvature. To give more precise and descriptive explanation, the following table presents several Ccur values together with the corresponding angles between normals and the angles between planar faces.

Table 1. Influence of the curvature criterion on the solid curvature resolution.
Curvature criterion, rad	0.3491	0.5062	0.5411	0.6982	1.0472	1.5708	2.0944	3.1416
Angle between normals (α)	20°	29°	31°	40°	60°	90°	120°	180°
Angle between faces (β)	160°	151°	149°	140°	120°	90°	60°	0°

The Table 1 states that if the Ccur is equal to 0.5062 rad, then all the cells where the angle between normals to the surface-forming triangles is more than 29° will be split.

Table 2. The dependency of the solid curvature resolution on the curvature criterion.
a) Lssf = 0, Lch = 0, Lcur = 1, Ccur = 0.5411 rad (α = 31°, β = 149°)	b) Lssf = 0, Lch = 0, Lcur = 1, Ccur = 0.5062 rad (α = 29°, β = 151°)

In Table 2 you can see that the curvature criterion set to 0.5062 rad splits the cells with the 151° cog.

Note:

The curvature refinement works exactly as the small solid features refinement when the curvature criterion is equal to 2.0944 rad (120°).

However, the default curvature criterion values are small enough to resolve obtuse angles and curvature well. Increasing the curvature criterion is reasonable if you want to avoid superfluous refinement but it is recommended that you try different criteria to find the most appropriate one.

The curvature refinement is a powerful tool, so that the competent usage of it allows you to obtain proper and optimal computational mesh. Look at the illustrations in Table 3 to the curvature refinement by the example of a sphere.

You can see that the curvature criterion set to 0.317 rad and 0.1 rad splits the cells up to the first level only. In Table 3 (b) and (c) the cells with the cogs of 162° were split. In Table 3 (d) the cells with the cogs of 174° were split.

Table 3. The curvature criterion examples.
a) Lcur = 0; Total number of cells is 64.	b) Lcur = 1; Ccur = 0.317 rad (α = 18°); Total number of cells is 120.

c) Lcur = 2; Ccur = 0.317 rad (α = 18°); Total number of cells is 120.	d) Lcur = 2; Ccur = 0.1 rad (α = 6°); Total number of cells is 148.