某些电磁波传播问题的格子Boltzmann方法研究

The study on the basic theory and numerical simulation are widely used in aerospace engineering, medical treatment, national defense, and etc. Lattice Boltzmann Method(LBM) is a local kinetic model that based on the basic theory of cellular automata, kinetic theory and nonequilibrium statistical physics,which is discrete of time, space and particle velocity. In addition to the description of hydrodynamics system, LBM provides a new idea for solving linear and nonlinear partial differential equation problems. There is important significant that LBM for electromagnetic waves propagation. . In this project, we would like to construct lattice Boltzmann model for Maxwell’s equations with high accuracy. Specifically, we would have chosen two problems of electromagnetic waves propagation : (1) Waveguides and cavities, (2) Dipole antenna and a half wave dipole antenna. On the one hand, we need to study the method for improving accuracy of this model, and verify the stability of this model; the other hand, we should also study the effectiveness of this model. Our proposed method is applied to study some complex problems of electromagnetic waves propagation.

电磁波传播的基本理论及数值模拟研究在航空航天、医疗、国防等高科技领域有着重要的应用前景。格子Boltzmann方法(LBM)是在元胞自动机、分子运动论和非平衡统计物理的基本理论上发展起来的时间、空间、粒子速度都完全离散的局部动理学模型。除了描述流体力学系统外，LBM为求解线性及非线性偏微分方程问题提供了新思路。研究电磁波传播的格子Boltzmann方法有着重要意义。. 本项目将对某些电磁波传播问题构造高精度Maxwell方程组的格子Boltzmann模型。特别地，我们主要选择下述两个电磁波传播问题进行研究：(1) 波导与谐振腔，(2) 偶极子天线及半波振子天线周围的辐射场。一方面，我们要研究提高模型精度的方法，验证所构造模型的稳定性；另一方面，还要研究模型计算的有效性。本项目提出的方法适用于研究电磁波传播中一些复杂问题。