FDTD in curvilinear coordinates using a rectangular FDTD formulation

Abstract

In the simplest formulation, the FDTD algorithm requires that objects follow the rectangular grid. For curved surfaces, this is a severe limitation. In this paper, an approach to modify an existing rectangular FDTD code to model structures more naturally described in another coordinate system is demonstrated. The approach is a modification to the update coefficients and does not require significant changes to an existing piece of software.

Application of the Orthogonal Curvilinear Grid to FDTD Modeling of a Deflected Wind Turbine Blade

“…Common disadvantage of the methods is that they require significant modifications to the FDTD code, sometimes even a complete rewrite of the code. More recently, a new formulation that allows implementation of curvilinear grid using standard rectangular FDTD update equations was proposed [4]. This work is based on an earlier finding [5] that a coordinate transformation in Maxwell's equations is equivalent to renormalizing the underlying material properties and µ.…”

“…Unlike previous simulations of a bent blade inside a rectangular FDTD domain, in the new implementation the entire computational domain is bent instead, so that the memory and CPU demands remain the same. As is pointed out in [4], the existing framework of the original FDTD code can be reused without modifications, because the curvature of the grid is created by changing the anisotropic material properties throughout the domain and not the underlying update equations. As such, the technique is applicable to any possible shape of the blade (or another body) without the necessity to generate a new model.…”