Adaptive Quadtree-Scaled Boundary Finite Element Method For Numerical Analysis Of Heat Transfer Problems With Phase Change

Heat transfer problems with phase change widely exist in nature and engineering applications.For example,the melting and solidification of ice,food freezing and baking,growth of crystals,and melting and solidification of electrodes during welding,et al.During the process of heat transfer with phase change,its main feature is the movement of phase transition interface caused by the absorption and release of latent heat,there it is also named as moving boundary problems.Moving boundary problems have strong nonlinearity,very few special cases have analytical solutions,so the study of numerical analysis is of great significance.Generally,there are two kinds of numerical approaches to deal with moving boundary problems,i.e.front-tracking methods and fixed-domain methods.Front-tracking methods continuously trace the interface of phase change,however a continuously deforming grid remeshing is required and it is difficult to handle the mushy phase change.Fixed-domain methods merge together both solid and liquid into a continuous region where the interface condition is described via the enthalpy,effective heat capacity or heat source term,etc.,in this way the interface tracking can be avoided,and the mushy phase change problems can be handled as well.Since the enthalpy or effective heat capacity only has a sharp change in the region of phase transition interface,it is usually only necessary to use a finer FEM mesh for the reigon of phase transition interface.In order to develop a more efficient and accurate numerical method for heat transfer problems with phase change,in this paper,a new adaptive algorithm is presented for solving the phase change heat transfer problems by integrating quadtree SBFEM and smoothed effective heat capacity method.The advantage include:(1).Implicitly representing the moving boundary by the effective heat capacity,and use Sigmoid function to smooth the effective capacity.(2).The quadtree is a kind of technique suitable for adaptively generating the mesh.(3).The SBFEM can avoid the difficulties due to the ‘hanging node' by constructing arbitrary polygon element.(4).Mesh refinement is conducted within a mushy region where the effective heat capacity changes rapidly.The main contribution in this paper includes:1.An effective heat capacity model for solving heat transfer problems with phase change based on quadtree SBFEM is established;2.A new refinement criterion based on unit physical state is proposed,which can effectively determine the interface area that needs to be refined.Compared with global uniform refinement,the proposed model can significantly reduce the amount of calculation.The work of the paper provides a new numerical approach of heat transfer problems with phase change.It has a good application prospect in the analysis and design relative with phase change energy storage material,crystal growth simulation and other numerical calculations involving moving boundary problems.