Structure / At Right Angles To The Grid Finite Volume Method In Computational Electromagnetics

Based on the concept of aerodynamic and stealth synthesis design for aircraft and missile configurations, a characteristic-based, Finite Volume method in Time Domain (FVTD), which stems from the techniques of Computational Fluid Dynamics (CFD) has been applied to computational electromagnetism (CEM) gradually during the recent decades. Grounded on plenty of literatures, this thesis has explored cell-centered, electromagnetic variables collocated FVTD algorithms while using structured and unstructured grids successively. In this thesis, a solver for simulation of propagation of planar electromagnetic wave in free or multi-medium space in 1D cases and a solver for scattering problems in 2D cases using structured grids, and a solver for scattering problems in 3D cases using adaptive Cartesian grids are developed in order. The relatively high order precision of the solvers has been validated by quantity of numerical test cases.In the structured FVTD algorithm, after left and right state variables have been obtained using the Van Leer's MUSCL scheme, flux formulation on cell interface is obtained by using Steger-Warming flux vector splitting or approximate Riemann solution, both of which are presented successively and demonstrated essential equal by numerical results. Once flux calculation are accomplished, the semi-discretization equations are cast into ordinary differential equations, which can be solved by several numerical methods including the two and four steps Runge-Kutta algorithm adopted in 1D and 2D cases respectively in this thesis.To study the dissipation and dispersion characteristics of MUSCL scheme and two, four steps Runge-Kutta integration mentioned above, stability analysis using Modified PDE and Fourier methods is performed firstly. In the next chapter, the structured algorithm is applied to simulate the propagation of planar electromagnetic wave in free or multi-medium space. The study of impact of different MUSCL schemes, grid resolution, CFL numbers and grid forms on accuracy and dissipative and dispersive features is performed and the ranges of value for corresponding parameters are discussed and suggested based on the work done in this part. Founded on the formerly work, scattering problems of several 2D perfect electrical conductors including cylinder and NACA0012 airfoil are solved. The fact that computational results of surface induced electric current and biostatic Radar Cross Section (RCS) agree quite well with theory values or results from references demonstrates that the FVTD is a high accurate method for computational electromagnetics and the solver using 2D structured grids developed is capable for the scattering problems over quite wide range from low to high frequency and also applicable to practical shape in engineering. Meanwhile, through the discussion of the numerical results of cylinder, the impacts of the parameters involved on the results are investigated and the allowable value ranges of the parameters are also suggested.The unstructured FVTD algorithm adopted is still cast in the form of semi-discretization. After left and right state variables have been obtained by the reconstruction method, approximate Riemman Solution is introduced to implement flux calculation in the space discretization part. The reconstruction method presented in this thesis is based on one order Tailor expansion and is the key to the accuracy of algorithm. In the time integration part,several solution methods for ordinary differential equations can be applied. However, reconstruction method and time integration scheme are coupled, and the whole time stepping scheme is given.In this thesis, 3D adaptive Cartesian grid based on the omni-tree, featuring easy generating, splitting, merging and powerful adaptive ability, handling complex objects ability, is adopted to implement unstructured FVTD algorithms analyzed above, and a solver for 3D perfect conductor objects scattering problems is built. To validate the accuracy and ability to handle different complex geometries, perfect electric conduct sphere, cube, and dual spheres are chosen in order for their scattering problem simulations. The numerical results of biostatic RCS are compared with theory values or results from references.