High Order On Surface Radiation Boundary Conditions For Radar Cross-Section Application

Solving problems governed by two and threedimensional wave equations in exterior domains are a complex task. There are techniques to reduce the computational complexities, one such technique is On-Surface Radiation Boundary Conditions (OSRBC). There have been recent interests in revisiting this technique for two and three-dimensional problems [1]. In this paper, we explore the implementation of a new high order OSRBC based on the high order local boundary conditions introduced by [2] for two and three dimensions to solve the wave equation in unbounded domains. In most cases, it is difficult to construct exact solutions. For comparisons of numerical solutions, we use solutions obtained from large domains as approximate exact solutions. The implementation involves a two step novel approach to handle time derivatives. First, the governing equations and boundary conditions are converted to Laplace transform domain. Then, based on bilinear transformation the procedure was converted to z domain which simplified the implementation process. In particular, this process leads to higher accuracy compared to the different types of finite difference schemes used to approximate the first and second order partial derivative in the new high order OSRBC and the auxiliary functions that define the high order boundary conditions. A series of numerical tests demonstrate the accuracy and efficiency of the new high order OSRBC for two and three-dimensional problems. Both the long domain solutions as well as the new OSRBC solutions are compared for accuracies and useful results for radar cross-section calculations are presented.