Application Of RBF Collocation Method In Inverse Problem Of Heat Conduction In Multilayer Medium

Heat conduction inverse problem is a kind of issues which inverse objects’ initial states, flow states, boundary conditions, internal heat resources and heat transfer coefficients by studying the surface or the internal temperature of objects. This kind of problems involves many interdisplinarites,such as physics, mathematics, information science and experimental technology. Now they have been widely applied to non-destructive testing(NDT), aerospace, biomedicine, metallurgical melting and nuclear engineering.Heat conduction inverse problem is an ill-pose issue,which is even a small perturbation of the input measured temperature can induce the huge errors to the compute results.The ill-posed makes the results are very sensitive to the perturbations of input data. Hence, how to overcome the ill-posed become the major goal for people who studying the heat conduction inverse problems. In recent years, researchers have developed various numerical methods. Among these methods, radius basis function(RBF) attract people’s attention. Compared with traditional numerical methods, such as finite difference method (FDM), finite element method and boundary element method, RBF has following advantages:firstly, it eliminate the dependence to the mesh; secondly, basis functions are simply in the form and unrelated to the space dimensionality; thirdly, basis functions are isotropy and the method can easily impose essential boundary conditions. All these advantages make RBF be the focus of the recent studying.In this paper, we study the effects of radial basis function(RBF) collocation method when it used in the heat conduction process of composite which is composed of materials with different thermal conductivities. The research mainly includes following parts:1. Inverse problem which heat conduction medium includes solid materials with different thermal features. We use model of the steel furnace with double-wall construction and discuss the moving boundary identification problem of two layers heat conductive solid medium. In order to obtaining temperature values used in inverse problem,we first build model for forward problem by using RBF collocation method and compute temperature distribution in problem domain. Secondly, we use forward problem’s results with random perturbation to simulate temperature values used in the inverse problem. Finally, we build model by using RBF collocation method and gain the inwall corrode boundary identification method of the steel furnace.2. Heat conduction inverse problem of multi-layer medium which made of solid and liquid. By using the model of flow tube, we establish a inverse boundary value problem. Then we transfer the inverse problem to forward problem by combining RBF collocation method with boundary control method. By doing this,we obtain a new method for solving inverse boundary value problem. To get temperature values used in the inverse problem, we still first build model of forward problem by using RBF collocation method and compute the temperature distribution in the fluid domain. Then we use forward problem’s results with random perturbation to simulate temperature values in fixed points of flow tube.3. The applications of adaptive collocation method based on the RBF in the multi-layer medium heat conduction problem. We use three layers heat conduction model which was made of different thermal conductive materials. To overcome the drawback that we required shape parameters when use RBF collocation method solving inverse problem, we generalized the adaptive greedy method to multi-layer composite medium heat conduction problem. By doing this, provide the adaptive greedy method of Cauchy problem with multi-layer composite medium.