A numerical technique for two-dimensional grid generation with grid control at all of the boundaries

Abstract

Abstract A numerical technique is developed in the present investigation to generate grids by the use of the Poisson equations. Orthogonal grids are obtained along all of the two boundaries η = 0 and η = ηmax. The “stand-off” grid spacing between ϵ = 0 and ϵ = Δϵ and between ϵ = ϵmax − Δϵ and ϵ = ϵmax can be controlled by employing a proper grid point distribution on the boundaries η = 0 and η = ηmax Thanks to the orthogonal boundary grids, the present numerical technique is applicable to complex geometry by patching grids without slope discontinuity across the interface of the patches. This technique also allows the Poisson equations to generate coordinates for O-type grid system and for periodic turbine cascades. In the course of grid generation, the magnitudes of the required control functions might be very large in a region where clustering grids are needed. To guarantee a good numerical stability in spite of the values of the control functions, the weighting function scheme along with the SIS solver is employed. Through the examples illustrated in the present study, the negative Jacobian reported by previous investigators is shown not to arise from the use of the Poisson equations. It, indeed, comes from the truncation error of the central difference scheme used by them.