Development of a wavenumber-preserving scheme for solving Maxwell's equations in curvilinear non-staggered grids

摘要

In this paper a compact finite-difference solver for solving the Maxwell's equations in curvilinear coordinates is presented. The scheme formulated in time domain can theoretically preserve zero-divergence condition and scaled wavenumber characteristics in non-staggered grids. The inherent local conservation laws are also retained discretely all the time. The space and time derivative terms are approximated to yield an equal fourth-order spatial and temporal accuracy. In irregular physical domain, Maxwell's equations are recast in terms of the contravariant and covariant field variables so that the developed dual-preserving solver can be directly implemented. In addition, in curvilinear coordinates the four components in the metric tensor have been calculated under the guideline that the determinant of the transformation matrix is computed exactly. Through the computational exercises, it is demonstrated that the newly proposed solver with a fairly small numerical scaled wavenumber error in curvilinear coordinates is computationally efficient for use to get the long time accurate Maxwell's solutions in irregular physical domain.