Two Dimensional Elliptic Grid Generation Based on the Laplace Equations andAlgebraic Transformations

摘要

An elliptic grid generation procedures is described to generate boundaryconforming grids in 2D physical space. The two-dimensional elliptic grid generation system is defined according to the following two principles: (1) For a domain in physical space bounded by four edges, a coordinate system is defined which only depends on the shape of the domain; (2) An algebraic transformation is used to map the computational space one-to-one onto the parameter space. The composition of these two mappings is a differentiable one-to-one mapping with nonvanishing Jacobian from computational space onto the domain in physical space. This composite mapping defines the grid point distribution in the interior of the domain. The composite mapping obeys a nonlinear elliptic Poisson system with control functions completely defined by the algebraic transformation. The solution of the Poisson system is obtained by Picard iteration and a black-box multigrid solver.