ADAPTIVE-HARMONIC STRUCTURED GRID GENERATOR
ADAPTIVE-HARMONIC STRUCTURED GRID GENERATOR
At the Computing Center of the Russian Academy of Sciences
the group of researchers headed by Dr S.A.Ivanenko developes the
ADAPTIVE-HARMONIC STRUCTURED GRID GENERATOR
Grid generating algorithm, which guarantees the convexity of all grid
cells in 2D was proposed in paper [1]. It was applied to a series of
two-dimensional domains of very complex shape. Satisfactory grids were
obtained in all cases. This method is a variational generalization of the
Winslow method and solves the problem of unconditional
minimization of the functional, which depends only on the coordinates of the
grid nodes. The use of grid convexity concept in the algorithm ensures a
one-to-one discrete mapping. On the other hand, this method removes the
necessity of splitting domain into blocks, and allows to build structured
grids over the entire domain.
On the basis of this algorithm we developed interactive 2D Grid Generator
providing an easy way to construct different grids even for very complex
domains without human expense and ingenuity. The program runs under MS
Windows 3.0.
A new method of grid adaption has been developed [2]. The method is based on a
variational formulation for the problem of constructing the harmonic
coordinates on the surface - the graph of control function. The process of
grid adaptation starts with the construction of a uniform grid on
hypersurface of control function values, and then projecting this grid back
to the computational domain. This method is a generalization of method [1].
It can be proved that all cells of generated grids are convex quadrilaterals.
The generalization to the case of structured/unstructured 3D and surface grids
is under construction.
Literature
1. Ivanenko S.A. and Charakhch'yan A.A. Curvilinear grids of convex
quadrilaterals. USSR Comput.Maths.Math.Phys, vol.28, N2, pp. 126-133, 1988.
2. Ivanenko S.A. Adaptive grids and grids on surfaces. Comput. Maths. Math.
Phys. vol.33, N8, pp. 1333-1350, 1993.
Contact address:
Dr. Sergey Ivanenko
Computing Center of the Russian Academy of Sciences,
Vavilov Str. 40, Moscow 117967, Russia.
Telephone: (095) 135-2109
Fax: 007 095 135-6159
E-mail: sivan@ccas.ru
or sivan@sms.ccas.msk.su