Research On Several Numerical Techniques For The Coupled Problem Of Engineering Electromagnetic Field

Many complicated engineering problem, such as the 3D eddy current field problem and the coupled problem of magnetic and flow fields, the mathematics models of which can be expressed as the partial differential equations problem for determining solution. These equations are usually nonsteady and nonlinear. Their numerical solutions not only need huge computational cost, but also involve many numerical techniques, and therefore have become a little bit hot and difficult point to which domestic and international researchers pay attention currently.In this paper, taking the 3D eddy current field problem and the coupled problem of magnetic and flow fields as examples, a series of researches on the several numerical techniques for the coupled problem analysis of the engineering electromagnetic fields have been conducted in depth. The detailed work is as follows:The 3D eddy current field problems are the main part of the coupled problem of many engineering electromagnetic field. The computation time of solving the linear algebra equations usually takes most of the whole computation time for numerically solving the problem. This paper presents two kinds of improved preconditioned conjugate gradient method for solution of large sparse symmetric ill-conditioned linear equations in 3D eddy current field analysis. First, in the premise that the coefficient matrix is symmetry definite, an improved preconditioned conjugate gradient method (PICCG1 method) with the controlling parameter is presented, which can reduce the computation time of each iterative step of the conjugate gradient method. Theoretical analysis and practical computation show that the PICCG1 method keeps the convergence rate close to the conventional ICCG method when dealing with the same equations, but it can reduce the computation time over 30% compared with the ICCG method. Secondly, in the premise that the coefficient matrix is symmetry and indefinite, an improved preconditioned conjugate gradient method (PICCG2 method) with the controlling parameters is presented, which can reduce the number of iterations of the conjugate gradient method. Theoretical analysis and practical computation show that the PICCG2 method obviously reduces the number of iterations and the computation time 60% or so compared with the ICCG method.The coupled problems of magnetic and flow fields not only include complicated space distributions and time variations, but also involve kinematic media. The numerical techniques for the questions are at the stage of being explored and developed. This paper presents a kind of directly coupled solving process for the coupled problem of magnetic and flow fields. The detailed case includes five parts as follows. First, based on the magnetohydrodynamics equations and with the proper use of the artificial nonsteady method and proceeding simplified assumption, the practical determining solution problem for the directly coupled questions of the magnetic and flow fields is obtained in this paper, and it is used for simulation of theelectromagnetic centrifugal casting. Secondly, the discretization pattern is obtained for the determining solution problem mentioned above, through using the backward difference method to time variable and the finite volume method to space variables in an annular sloving domain which is used for actual computation. Thirdly, the corresponding iterative pattern is obtained by using Newton-Laphson method for solving the discretization pattern mentioned above, and the local convergence condition is also given. Fourthly, a kind of improved triangular decomposition method is presented with the controlling parameter for non-symmetric cyclic block tridiagonal linear equations mentioned above. Numerical examples show that with the method the computation time is reduced 40% or so compared with the conventional triangular decomposition method. Lastly, the comparison of the numerical results and experiment results for the electromagnetic centrifugal casting of OCrl7Mnl4Mo2N stainless cored steel seamless tubes show that the directly coupled solving method presented in the paper is proper and valid.