Theory

Curvature sizing. $N$ sets the mesher's curvature threshold resolveFeatureAngle, equation (1). A cell of size $h$ on a wall of radius $r$ sees the surface turn by about $h/r$ radians; the mesher keeps refining a wall cell while the surface inside it turns by more than the threshold, up to the wall's finest level $h_0/8$ (OpenFOAM user guide, 2026). Refinement therefore stops at $h \approx 2r/N = D/N$ , i.e. about $N$ cells across each pipe's own diameter $D$ , equation (2). A small pipe gets small cells and a large shell keeps large ones. Each inlet and outlet face is put on the level that fits $N$ cells across its own hydraulic diameter $D_h = 4A/P$ , never coarser than the finest wall level (see Mesh sizing). The threshold is limited to 5-30°: below $N \approx 4$ it stays at 30°, and above $N \approx 23$ it stays at 5°, so values above 23 refine the curved walls no further.

Uniform sizing. The finest cell is the smallest port's hydraulic diameter divided by $N$ , equation (3), and every surface is refined to that cell size. On a large muffler with one small port this puts the small port's cell on every wall.

Both modes. The refinement targets of narrow internal pipes (uniform sizing: at least $12N/16$ cells across their own diameter) and of the jet cylinders at the inlets (cells at most $D/(10N/16)$ ) scale with $N$ , so changing $N$ refines the whole mesh in proportion; both were tuned at $N = 16$ .

In uniform mode a mesh independence study varies $N$ (11, 16, 22), because that is the setting that changes the wall cell there; a fineness study is refused in that mode. In curvature mode the study varies the fineness instead, which scales every level-driven size by the same ratio (Celik et al., 2008).

Equations

\theta_r = \min\!\left(30^\circ,\ \max\!\left(5^\circ,\ \frac{2}{N}\ \mathrm{rad}\right)\right)

(1)

\frac{h}{r} \le \theta_r \ \Rightarrow\ \frac{D}{h} \ge \frac{2}{\theta_r} = N, \qquad h \ge \frac{h_0}{8}

(2)

where	meaning	unit
$\theta_r$	`resolveFeatureAngle` (curvature sizing; 30° in uniform sizing)	°
$N$	Cells across a diameter	-
$h$	Wall cell size reached by curvature refinement	m
$r$	Local radius of the wall	m
$D$	Diameter of the pipe, $2r$	m
$h_0$	Background cell size	m

h_w = \frac{D_{h,min}}{N}

(3)

where	meaning	unit
$h_w$	Wall cell size in uniform sizing	m
$D_{h,min}$	Smallest hydraulic diameter, $4A/P$ , of all inlets and outlets	m

Default and rule

Default

8

Rule

8 (preset "default"), i.e. $\theta_r = 14.3°$ with curvature sizing. A user-defined value is rounded to a whole number between 4 and 80.

Source

Validation meshes of case V1 (a 2.0 m multi-chamber muffler with a perforated pipe and three absorptive packings; the mesher cases set up with the curvature rule):

threshold 30° ( $N \approx 4$ ): 577,357 cells in 249 s;
threshold 14.3° ( $N = 8$ ): 1,184,789 cells, layer coverage 96.1 %, maximum non-orthogonality 70.0°;
threshold 7.2° ( $N = 16$ ): did not finish within about 35 min.

The default of 8 is the program's choice based on these meshes; it has not been confirmed by a mesh independence study. With uniform sizing, a 90° pipe elbow gave pressure drops of 398, 473 and 451 Pa at 12, 16 and 24 cells across the diameter: the result is not monotonic, so a single mesh is no proof of a mesh-independent result. The threshold relation $h/r$ is the geometry of a chord on a circle; how the mesher applies the angle is described in its documentation (OpenFOAM user guide, 2026).

Valid range 4 to 80 (whole numbers); presets 4, 8, 12, 16, 24

Values

4 to 80 cells (checked when the setting is saved). Presets: 4 coarse, 8 default, 12 fine, 16 very fine, 24 reference for a mesh independence check.

Cost

Uniform sizing: the wall cells grow as $N^2$ . Curvature sizing: only the curved walls are refined further, so the growth is smaller (V1: $N$ 4 to 8 doubled the cells). With curvature sizing above $N = 23$ the curved walls are not refined further: the 5° floor of the threshold applies.

Not a convergence proof

Check the pressure drop with a mesh independence study before relying on it.

Cells across a pipe diameter

Theory

Equations

Default and rule

Valid range 4 to 80 (whole numbers); presets 4, 8, 12, 16, 24

References 2

Theory

Equations

Default and rule

Valid range 4 to 80 (whole numbers); presets 4, 8, 12, 16, 24

Related 4

References 2