The Study Of The Method For Identifying Moving Boundary Of Multilayer Medium

This paper introduces the radial basis functions (RBF) collocation method to identify a moving boundary for a heat conduction problem of furnace with two layer walls. Parts of temperature which are obtained by the finite difference method are referenced directly as a known condition. Bringing the collection points taken by collection method into the governing equations and boundary conditions. Rearranging these governing equations and boundary conditions into an appropriate matrix form, and then combining the RBF method with regularization method L-curve method and linear least square method to get the results. Then the application of dichotomy method in each direction of θ to screen those points which temperature is1, the isotherm shape formed by these points is the geometry of moving boundary. Finally, the method is improved by using the greedy technology to choice the optimum shape parameter of the radial basis function, the collection points selected by the technology can improve the accuracy of the calculation results.The structure of this paper is:The background and present situation of this research are introduced, and then instructs the content and innovation of this article in the first chapter; Chapter two introduces the basic knowledge of the radial basis function collocation method and regularization method briefly which is using in this paper; In the third chapter physical model and the numerical method are given. Simultaneously, the influence of some factors like temperature measurement error are also investigated on estimated accuracy. From temperature curve and contrast diagram of relative root mean square error to discuss the applicability and accuracy of this method. Especially the analysis of the measurement error has a positive influence on the actual production. In the fourth chapter, we improve the method of the radial basis functions (RBF) collocation method by using greedy method to select the optimum shape parameters which can improve the precision of the results.The result indicates that the estimation error of the geometry increases with increasing of the distance between measured points and inner surface, decreases with increasing of the number of measured points. The advantage of this approach is that the calculation can be obtained without the initial temperature and it is much simpler and quicker than traditional one. The experiment proves this method is applicable and high maneuverable. However, under the reasonable preset error, this method to identify a moving boundary for a heat conduction problem can obtain accurate results.