Multiblock Grid Generation. Part 1. Elliptic Grid Generation Methods for211 Structured Grids

摘要

The paper is organized as follows. In Section 2, the Laplace equations, the211u001eparameter space and the algebraic transformation are presented for domains in two 211u001edimensional physical space. The resulting Poisson equations are derived together 211u001ewith the appropriate expressions of the control functions. The relationship with 211u001eother methods is explained. The discretization and solution of the nonlinear 211u001eelliptic equations is discussed and also the orghogonalization of the grid at 211u001eboundaries. Examples of grids in 2D domains are given. Surface grid generation on 211u001eminimal surface is discussed in Section 3. It is shown that grid generation on 211u001eminimal surface is in fact the same problem as grid generation in a domain in 2D 211u001ephysical space. Illustrations of grids on minimal surfaces are given. Surface 211u001egrid generation on surfaces with a prescribed shape is treated in Section 4. It 211u001eis assumed that such surfaces are parametrized and that the parametrization is a 211u001edifferentiable one-to-one mapping from a unit square onto the surface. The 211u001egenerated surface grids are independent of the parametrization. The solution 211u001emethod to generate the grids in the interior of parametrized surfaces is 211u001edifferent from that used for minimal surfaces. It is much easier to solve the two 211u001elinear elliptic partial differential equations defined by the Laplace-Beltrami 211u001eequations directly, instead of interchanging the dependent and independent 211u001evariables which leads to a nonlinear elliptic system of partial differential 211u001eequations. An inversion problem must then be solved afterwards. Such a simple 211u001esolution method is only possible for parametrized surfaces. This is due to the 211u001efact that an initial grid folding free surface grid on a parametrized surface can 211u001ebe easily generated because the given parametrization is one-to-one.