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

机译：雷达截面应用的高阶表面辐射边界条件

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摘要

Solving problems governed by two and three-dimensional 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.
机译：解决外部域中由二维和三维波动方程控制的问题是一项复杂的任务。存在降低计算复杂度的技术，一种这样的技术是表面辐射边界条件（OSRBC）。近来有兴趣重新研究该技术以解决二维和三维问题[1]。在本文中，我们基于[2]针对二维和三维引入的高阶局部边界条件，探索一种新的高阶OSRBC的实现，以求解无界域中的波动方程。在大多数情况下，很难构建精确的解决方案。为了比较数值解，我们使用从大域获得的解作为近似精确解。该实现涉及一种处理时间导数的两步新颖方法。首先，将控制方程和边界条件转换为拉普拉斯变换域。然后，基于双线性变换，将该过程转换为z域，从而简化了实现过程。特别地，与用于在新的高阶OSRBC和定义高阶边界条件的辅助函数中逼近一阶和二阶偏导数的不同类型的有限差分方案相比，此过程可导致更高的精度。一系列数值测试证明了针对二维和三维问题的新型高阶OSRBC的准确性和效率。比较了长域解决方案和新OSRBC解决方案的准确性，并提出了有用的雷达截面计算结果。

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