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SpectraSim Documentation
Parameter · 08 Mesh

Maximum element growth rate

acoustics.mesh.growth_rate Step 08 · Mesh

Limits how fast the acoustic elements may grow away from the walls and small features. With 1.4 the allowed element size grows by 0.4 m per metre of distance from the surface.

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Theory

The surface is meshed first; without a limit, small surface elements (at port rims, small pipes, curved walls) would be followed by a sudden jump to the large volume elements. The program limits the size at every point of the volume by the sizes of the nearby surface nodes plus a linear growth with the distance from them, equation (1).

  • The surface size hsh_s of a node is the mean length of the surface edges meeting there.
  • The minimum is taken over the 16 nearest surface nodes.
  • The limit is applied through the Gmsh mesh-size callback while the volume is meshed (Gmsh reference manual, 2025).
  • It applies inside the volume only, and the result is never below the minimum element size nor above the maximum (see Maximum element size).

A rate of 1 would carry the smallest surface element through the whole volume; a large rate lets the elements grow to the maximum size within a short distance.

Equations

hgrow(x)=min⁡s∈S16(x)[ hs+(g−1) ∣x−xs∣ ]h_{grow}(\mathbf{x}) = \min_{s \in S_{16}(\mathbf{x})} \left[\, h_s + (g - 1)\,\lvert \mathbf{x} - \mathbf{x}_s \rvert \,\right]
(1)
wheremeaningunit
hgrowh_{grow}Size allowed by the growth limit at a volume pointm
S16S_{16}The 16 surface mesh nodes nearest to the point-
hsh_sMean length of the surface edges at node ssm
ggGrowth rate-
xs\mathbf{x}_sPosition of surface node ssm

Default and rule

Default
auto: 1.4Computed by the program
Rule

Auto = 1.4.

Source

The rule and the default are the program's own; the value 1.4 is not derived from a published correlation and has not been compared with other values. On case V1 (a 2.0 m multi-chamber muffler with a perforated pipe and three absorptive packings) at curvature factor 0.3, the growth limit hardly changes the mesh (75,254 against 75,376 tetrahedra); its effect on the transmission loss has not been solved separately.

Valid range 1 < g <= 3

Values

Above 1 and at most 3 (checked when the setting is saved).

Not measured

Its effect on the acoustic result has not been measured; on the one model checked it barely changes the element count.

References 1

  1. Geuzaine, C. and Remacle, J.-F. (2025). Gmsh reference manual, version 4.15. gmsh.info. Web page