Quasi-Orthogonal Grids with Impedance Matching

Abstract

An elliptic, quasi-orthogonal grid generation system is formulated based on quasi-conformal mapping for arbitrary anisotropic (long and skinny) regions. The resulting system is a generalization of the well-known elliptic grid generation system derived from conformal mapping. Coupled with the grid generation system, the impedance-matching principle describes a methodology for preserving the discrete accuracy of the simulation, both internal to the domain and near internal geometric interfaces. Empirically, satisfying the impedance principle tends to minimize mesh effects on the solution results; meshes that are impedance-matched tend to reduce or eliminate spurious wave reflection and/or attenuation at internal interfaces. The resulting grid generation system is used to construct impedance-matched quasi-orthogonal grids on domains containing internal geometric constraints given an algebraic grid and a grid impedance function as initial conditions.