A 2-D meshless time-domain algorithm for solving Maxwell’s equations based on Steger-Warming flux vector splitting approach

Abstract

A 2-D meshless time-domain algorithm is proposed for solving Maxwell’s equations. The spatial derivatives related to the algorithm are approximated by using an expanded Taylor series and the least square technique in each cloud of points, and then a Steger-Warming flux vector splitting approach is introduced for computing the physical flux of the governing equations. After that, an explicit four-stage Runge-Kutta scheme is employed in time-marching. Combined with solving Maxwell’s equations, the implementations of the present algorithm are described in details. Based on the proposed algorithm, bistatic radar cross sections for typical 2-D objects in different frequency regions are given, which show a good agreement with those of the series solutions. The paper ends with the presentation of the electromagnetic scattering fields for a 2-D aircraft model, which display the characteristics of the algorithm presented in dealing with time-domain problems to a certain extent.