Numerical dispersion and stability characteristics of time-domain methods on nonorthogonal meshes

Abstract

The familiar finite-difference time-domain method for discretizing Maxwell's curl equations on orthogonal grids has been extended to nonorthogonal grids by a number of researchers. While it is difficult to determine the dispersion and stability characteristics of these methods when applied on arbitrary grids, analysis of the idealized but representative case of a uniform skewed mesh proves to be quite tractable in 2-D. This analysis demonstrates that numerical dispersion errors are small for well-resolved spatial wavelengths and that these methods converge to the continuous-space solution in the limit as the cell and time step sizes vanish. Grid anisotropy (variations in wave propagation speed as a function of the propagation angle relative to the mesh coordinates) increases as the mesh is skewed. In spite of this, there exist some angles where waves propagate through the skewed mesh with virtually no dispersion. This analysis also provides a stability limit for the time step size in terms of geometrical mesh quantities.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>