Research On Meshless Time-domain Algorithms For Solving Electromagnetic Stealth Problems And Their Applications

Studies on numerical methods for calculating the stealth characteristics of aircrafts have been the subject of much concern in both academic and engineering circles. In the present work, some topics related to the physical optics method, the finite-volume time-domain method and the meshless time-domain method are investigated in view of improving robust, accuracy, efficiency as well as flexibility of discretization.Firstly, a physical optics algorithm is studied. The algorithm uses Ludwig integral method to deal with the computation of the integral term related to the scattering field, without using a large number of integral sampling points. According to the lighting condition combined with using the simplified depth sorting algorithm, shading judgment can be implemented, which makes the algorithm applicable and efficient. The RCS quickly obtained for the high-frequency scattering by typical objects can be agree with the theoretical solution or that of the reference.Secondly, a cell-centred finite-volume time-domain algorithm based on the unstructured grid is presented for solving any frequency scattering problem. Then, in order to improve the traditional cell-vertex based methods, a cell-vertex finite-volume time-domain algorithm based on an unstructured grid is developed for solving the time-dependent Maxwell’s equations, which results in that all physical quantities at each time step can be updated at the vertices of the same mesh cell without using auxiliary mesh like traditional methods. In this paper, the implementations of the function reconstruction based on the cell vertices are discussed in details, which include the choice of interpolation stencils and the calculation of the reconstruction coefficients. Numerical examples show that results calculated by using quadratic function reconstruction are closer to the theoretical solutions than those based on linear function reconstruction. The results also show that well-posed PML can absorb outgoing electromagnetic waves better than no reflection boundary condition when using relative small computing domain. Additionally, both the rate of convergence and the efficiency of computation of the cell-vertex algorithm are more efficient than those of the cell-centred algorithm. Furthermore, scattered fields of complicated aerodynamic bodies like a multi-element airfoil and an aircraft model are presented, which show the present algorithm has the ability to accommodate complex geometries with multi-element to a certain extent.In order to improve the ability to deal with more complicated shapes, a meshless time-domain algorithm for a solution of the Maxwell’s equations based on the situation of 2-D TM wave incidence is proposed. Clouds of points are distributed all over the computational domain, which is realized by a technique newly developed for distributing points directly and quickly. After that, a particular approximate Riemann solver on the basis of clouds of points is constructed for computing the physical flux of the governing equations. Then typical results are given to validate the algorithm. Numerical examples show that the present algorithm either based on points distributed directly or based on mesh points has an efficient rate of convergence. The results also show that the algorithm can deal with complicated situations with multi-element or multi-component due to the use of meshless points.After that, on the basis of the weighted least square technique, a meshless time-domain algorithm is proposed for solving the Maxwell’s equations based on the situation of 2-D TE wave incidence. The introduce of the weighted factor can weaken the problem which makes the matrix ill-conditioned caused by points distributed too near, and can help to improve the flexibility of distributing points. The examples show that the external store has a significant effect on the stealth characteristics of the main aircraft body. The results also show that all the factors that include the direction of the incident wave and the size of the external store as well as the relative position between the external store and the main body can affect the total electromagnetic scattered properties and the first two factors play an important role.In order to deal with 3-D practical problems, a meshless time-domain algorithm is extended on solving the 3-D Maxwell’s equations, which is based on 3-D meshless clouds of points and the weighted least square technique. Typical results are in good agreement with the series solution or that of the reference calculated by the method of moment or the exact controllability approach. After that, numerical results for more complicated geometries such as an air-intake model and a stealth aircraft model are given, which show the developed algorithm has the ability to accommodate scattering problems for 3-D practical objects.Finally, in order to improve the accuracy of the above meshless time-domain algorithm, a meshless time-domain algorithm based on WENO reconstruction for solving the Maxwell’s equations is further proposed. The stencil required for implementing third-order WENO reconstruction in the gridless cloud is obtained by setting a local coordinate in the direction of each satellite point and introducing a virtual point so as to be used for approximating the physical quantities at the midpoint between the central and satellite points of the gridless cloud by using WENO reconstruction instead of linear function reconstruction. Typical examples verify that the numerical results calculated by using WENO reconstruction are closer to the theoretical solutions than that based on linear function reconstruction. The results also show that the number of points distributed near the truncated boundary can be reduced properly so as to reduce the total calculation amount. Furthermore, the calculated bistatic RCS for a cylinder by incident waves with different frequency are all in good agreement with the series solutions, which show that the present algorithm has the ability to solve scattering problems by incident waves with any frequency. The paper ends with the simulation of scattered fields and stealth characteristics of an aircraft model, which show the present method has the ability to accommodate complicated situations with multi-element.