Electronic Journal of Differential Equations,
Conference 01 (1998), pp. 55-79.
Title: Harmonic parameterization of geodesic quadrangles on surfaces of constant Curvature and 2-D Quasi-Isometric Grids
Authors: Gennadii A. Chumakov (Sobolev Institute of Math. Novosibirsk, Russia)
Sergei G. Chumakov (Univ. of Wisconsin, Madison, WI, USA)
Abstract:
A method for the generation of quasi-isometric boundary-fitted
curvilinear coordinates for arbitrary domains is developed on the
basis of the quasi-isometric mappings theory and conformal
representation of spherical and hyperbolic geometries. A
one-parameter family of Riemannian metrics with some attractive
invariant properties is analytically described. We construct the
quasi-isometric mapping between the regular computation domain $\cal
R$ and a given physical domain $\cal D$ that is conformal with
respect to the unique metric from the proposed one-parameter class.
The identification process of the unknown parameter takes into
account the high parametric sensitivity of metrics to the parameter.
For this purpose we use a new technique for finding the geodesic
quadrangle with given angles and a conformal module on the surface
of constant curvature, which makes the method more robust. The
method allows more direct control of the grid cells size and angle
over the field as the grid is refined. Illustrations of this
technique are presented for the case of one-element airfoil and
several test domains.
Published November 12, 1998.
Math Subject Classifications: 65N50, 30C30.
Key Words: regular grid generation; quasi-isometric mappings; geodesic grids; geodesic quadrangles; surfaces of constant curvature.