Problem Descriptor Reference > The Sections of a Descriptor > Definitions

FlexPDE uses an adaptive initial mesh generation procedure. Cell sizes are generated to conform with local boundary feature sizes, and cell sizes will grow gradually from locales of small cell size to locales of large cell size. Cells sides always match everywhere, and there is never a mismatch between adjacent cells.

It is possible, however, to override the default cell size logic by use of the controls MESH_SPACING and MESH_DENSITY. These parameters have special meaning in controlling the initial mesh layout. They may appear in the context of a parameter definition or redefinition (ie, in the DEFINITIONS section or in a REGION), or in the context of a boundary condition. There may be more than one control active in any locale, and the control (default or explicit) resulting in the smallest mesh cells will dominate.

MESH_SPACING dictates the desired spacing between mesh nodes.

MESH_DENSITY is the reciprocal of MESH_SPACING, and dictates the desired number of mesh nodes per unit distance.

Appearing in the DEFINITIONS section, these parameters specify a global default mesh density function in the volume of the domain.

Appearing in a REGION, these parameters specify a mesh density function in the volume of the current region (in 3D they may be qualified by LAYER or SURFACE).

Appearing in the context of a boundary condition (ie, inside a path) they dictate the mesh density along the curve or sidewall surface currently being defined. In 3D they may be qualified by LAYER or SURFACE to restrict the application of the density function.

MESH_SPACING and MESH_DENSITY specifications may be any function of spatial coordinates (but not of VARIABLES).

Examples:

MESH_DENSITY = exp(-(x^2+y^2+z^2)

This will create a Gaussian density distribution around (0,0,0), with spacing ultimately overridden by the size limit implied by NGRID.

See the User Guide section "Controlling Mesh Density" for more information.

Mesh Control Parameters

Mesh Control Parameters