Sphere

Applies to: Volumes topologically equivalent to a sphere and having one surface.

Summary: Generates a radially-graded hex mesh on a spherical volume.

Syntax:

Volume <range> Scheme Sphere [Graded_interval <int>] [Az_interval <int>] [Bias <val>] [Fraction <val>] [Max_smooth_iterations <int=2>]

Discussion:

This scheme generates a radially-graded mesh on a spherical volume having a single bounding surface. The mesh is a straightforward generalization of the circle scheme for surfaces. The mesh consists of inner region and outer region. The inner region is a mesh of a cube and the outer region contains fronts that trasition from cube surface to sphere surface. The number of azimuthal intervals around the equator is controlled by the az_interval input parameter. The number of radial intervals in the outer region is controlled by the graded_interval input parameter. Azimuthal mesh lines in the outer portion of the sphere have constant radius. The bias parameter controls the amount of radial grading in the outer region of the mesh (default=1 gives a uniform mesh). The fraction parameter (between 0 and 1) determines what fraction of the sphere is occupied by the inner cube. The fraction is defined as ratio of cube's body diagonal to sphere's diameter. The Max_smooth_iterations determines the number of smoothing iterations. By default number of smoothing interations is set to 2. Note that even though smoothing improves the quality of the mesh, it disturbs the bias and fraction. When bias and fraction are very critical then smoothing iterations should be set to 0.

SPHERE MESH: fraction 0.3 graded_interval 6 az_interval 40 bias 0.8 max_smooth_iterations 0

BIAS (uniform): fraction 0.3 graded_interval 6 az_interval 40 bias 1.0 max_smooth_iterations 0

FRACTION: fraction 0.7 graded_interval 6 az_interval 40 bias 1.0 max_smooth_iterations 0

INTERVAL: fraction 0.7 graded_interval 9 az_interval 40 bias 1.0 max_smooth_iterations 0

SMOOTHING: fraction 0.7 graded_interval 9 az_interval 40 bias 1.0 max_smooth_iterations 2

AZIMUTHAL (mesh coarseness): fraction 0.7 graded_interval 5 az_interval 32 bias 1.0 max_smooth_iterations 2

BIAS (graded): fraction 0.9 graded_interval 9 az_interval 32 bias 1.5 max_smooth_iterations 0