Abstract
In numerical simulations, anisotropic meshes whose elements are
extended along a specified direction refine the efficiency and
accuracy of solutions.
However, automatic generation methods of anisotropic meshes are
not popular.
This page proposes a method of automated anisotropic mesh generation,
which is an extension of the
bubble mesh method.
This method packs ellipses in a region and then connect the center of
them by the Delaunay triangulation method.
Background
Conventional automated meshing methods generate isotropic meshes, as
the figure (a).
On the other hand, anisotropic meshes are usually generated by a
manual method, called "multi-block method".
In this method, a region must be first divided into quadrangles,
and then specified the number of division for each edge of quadrangular
regions, manually by a user.
Meshes are then generated by mapping grid on the regions.
Automated anisotropic meshing methods are desired, since the multi-block
method requires skill and labor for the division of regions.
Automated anisotropic mesh generation
In the automated method proposed in this page, a scalar field which
specifies the size of elements and a vector field which specifies
the direction and aspect ration of elements are given for a region
(see the figure (a) and (b)).
This method first packs ellipse bubbles whose size and direction are
specified by the scalar and vector field, like the figure (c).
Then the method connects the center of bubbles to form triangular
elements, like the figure (d).
The original Delaunay triangulation method does not consider of
anisotropy of meshes.
This paper shows a anisotropic Delaunay triangulation method,
which consider of a vector field in order to generate elements
along the vector.
In the original Delaunay triangulation method, adjacent two triangular
elements are selected in order, and their shared edge may be replaced
by the another diagonal line.
To determine the edge should be replaced, two circumscribed circles
of the triangular elements are first generated.
If the non-shared vertices of triangular elements are inside the circles,
the shared edge is replaced.
In the anisotropic Delaunay triangulation method, vertices of the
two triangular elements are moved along the vector, and the elements
are shrinked, before generating the circles.
This method generates elements expanded along the vector.
 To the top page of meshing project
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