Differential Equations and Computational Simulations III
Electron. J. Diff. Eqns., Conf. 01, 1997, pp. 5579.
Harmonic parameterization of geodesic quardangles
on surfaces of constant curvaturess and 2D quasiisometric grids
Gennadii A. Chumakov & Sergei G. Chumakov
Abstract:
A method for the generation of quasiisometric boundaryfitted
curvilinear coordinates for arbitrary domains is developed on the
basis of the quasiisometric mappings theory and conformal
representation of spherical and hyperbolic geometries. A
oneparameter family of Riemannian metrics with some attractive
invariant properties is analytically described. We construct the
quasiisometric mapping between the regular computation domain
R and a given physical domain D that is conformal with
respect to the unique metric from the proposed oneparameter 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 oneelement airfoil and
several test domains.
Published November 12, 1998.
Mathematics Subject Classifications: 65N50, 30C30.
Key words and phrases: regular grid generation, quasiisometric
mappings, geodesic grids, curvature.
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Gennadii A. Chumakov
Sobolev Institute of Mathematics
pr. acad. Koptyuga, 4
Novosibirsk 630090, Russia
Email address: chumakov@math.nsc.ru 
 Sergei G. Chumakov
Mathematics Department
University of Wisconsin  Madison
Madison, WI 53703, U.S.A.
Email address: chumakov@math.wisc.edu 
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