Keywords: mesh adaptation, mesh generation, metric source, anisotropic metric, control space, sizing, metric gradation.

The three-dimensioanl mesh generator developed by the authors allows the construction of meshes with varying density and anisotropic elements. The size and shape of the mesh elements created is supervised by means of a metric stored in a control space structure. In order to enable introduction, transformation and application of metric within the mesh generator, a number of metric-related operations need to be defined for discrete metric representation. The most fundamental operations for the metric given in two three-dimensional points are: interpolation of the metric between two points, intersection of two metric sources defined at the same point, comparison of two metrics defined at the same point, and a gradation control for the metric between two points. Basing on this set of elementary operations, the higher level operations are created, regarding metric processing for discrete structure of control space (i.e. in the form of an octree or background mesh) or selected remeshing procedures.

Interpolation of the metric is required in order for the meshing routines to be able to treat the sizing field stored in the discrete structure of the control space as a continuous metric field. Different interpolation procedures may be applied depending on the control space structure and metric representation. The operation of the metric intersection allows the combination of various metric data available at a given point of the domain. Depending on the source of the metric information or the phase of the meshing process, one of the two available procedures is performed. Additional metric sources may incur modification of the current control space, by supplementing sizing information in selected sub-areas of the model domain. Alternatively, in case where a set of metric sources defines an independent sizing field (e.g. resulting from the analysis of a simulation error), a separate control space structure is constructed and initialized using such set of metric sources only. Then, this separate control space is combined with the current control space using a global intersection procedure. The gradation procedure allows for the adjustment of metric information for the whole control space, enforcing some predefined parameters such as the maximum anisotropy ratio (controlling the level of allowed anisotropy in the created mesh) or metric gradation ratio (controlling the ratio of mesh density variation).

In order to facilitate the introduction of different sizing information into the meshing process, a number of metric source representations has been proposed, including continuous functions (global or defined for some local sub-domain), discrete points and simplex sources defining the metric at a point, along a segment or a triangular face with a given vicinity radius. Because of the discrete structure of the control spaces all available metric source descriptions have to be appropriately transformed into a discrete form, represented by a set of points with metric.

The procedure of control space preparation is described in the paper. The set of implemented routines includes initialising the control space structure with discrete or continuous metric sources, updating it with additional sources and adjusting for metric gradation control. The concept of extended metric sources is also presented together with the description of a procedure of introducing such sources into the discrete structure of an adaptive control space. The algorithms presented allow construction of a single control space for the discretized model, combining all sizing information in one place. The control space created provides a precise and efficient means of supervising the procedures of volume mesh construction and adaptation implemented in the developed mesh generator.

The paper describes the implementation aspects of the metric transformation procedures presented together with the methods of initialisation and updating of the control space structure.

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