Theory

The program generates the acoustic mesh with Gmsh (Geuzaine and Remacle, 2009) in three stages: surface mesh, volume mesh, and elevation to second order with the mid-edge nodes placed on the CAD surface. The element size at a point is the smallest of several limits:

this maximum;
the curvature limit of Curvature factor;
in the volume, the growth limit of Maximum element growth rate.

No limit may go below Minimum element size, equation (2).

On auto, equation (1) ties the maximum to the wavelength at the highest frequency, so the mesh follows $f_{max}$ and the gas temperature. When the medium is mapped from the flow solution, each point uses its local sound speed $c(\mathbf{x})$ , and the coldest gas (smallest $c$ ) receives the smallest elements. A typed maximum overrides this everywhere, including the temperature dependence.

The size is passed to the mesher as Mesh.MeshSizeMax (Gmsh reference manual, 2025). Delaunay elements reach up to about 1.3 times this size (mean edge length); the resolution check evaluates the mesh as built (see Elements per wavelength). If curved second-order elements fold (negative Jacobian), the program regenerates the mesh with every size multiplied by 0.75, for up to four attempts.

Equations

h_{max}(\mathbf{x}) = \frac{c(\mathbf{x})}{f_{max}\,N_\lambda} \quad \text{(auto)}

(1)

h(\mathbf{x}) = \max\!\Big(h_{min},\ \min\big(h_{max}(\mathbf{x}),\ h_{curv}(\mathbf{x}),\ h_{grow}(\mathbf{x})\big)\Big)

(2)

where	meaning	unit
$h_{max}$	Maximum element size	m
$c$	Sound speed (uniform medium: the planned value; mapped medium: local)	m/s
$f_{max}$	Highest frequency	Hz
$N_\lambda$	Elements per wavelength	-
$h$	Element size the mesher uses at a point	m
$h_{min}$	Minimum element size	m
$h_{curv}$	Size from the curvature rule	m
$h_{grow}$	Size allowed by the growth limit (volume only)	m

Default and rule

Default: auto: c / f_max / N (N = elements per wavelength)Computed by the program
Rule: Auto. Example: air at 20 °C ( $c$ = 343 m/s), $f_{max}$ = 500 Hz and $N_\lambda$ = 10 give $h_{max}$ = 68.6 mm. The Mesh step shows the resolved value.
Source: The sizing rule is the program's own: the maximum is exactly $c/(f_{max} N_\lambda)$ , with no additional safety factor. The Gmsh options are documented in the Gmsh reference manual (Gmsh reference manual, 2025).

Valid range 0 < h_max <= 10 m; above the minimum element size

Values

Above 0 and at most 10 m, and above the minimum element size (checked when the setting is saved). Displayed and entered in mm.

Typed size

A typed size that gives fewer than 5 elements per wavelength at $f_{max}$ triggers a warning on the Mesh step; the resolution check fails below 4 elements per wavelength as built.

Mapped medium

A typed size ignores the local sound speed: the whole model uses the single size.

Theory

Equations

Default and rule

Valid range 0 < h_max <= 10 m; above the minimum element size

Related 5

References 2