Element-Free Galerkin Meshless Method on Solidification Behavior Inside Continuous Casting Mold
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THE improvement of the casting product quality exhibits a significant dependence on an accurate understanding of temperature and solidified shell distribution, especially in the mold region. To date, mathematical modeling could describe and solve the complex physical phenomena of strand solidification process, and had been widely employed to investigate the heat transfer, fluid flow and stress deformation of cast strands, such as finite element method (FEM), finite difference method (FDM), and finite volume method (FVM).[1–3] The above methods usually rely on the discretization of the
LAIQIANG CAI, XUDONG WANG, and MAN YAO are with the School of Materials Science and Engineering, Dalian University of Technology, Dalian, 116024, P.R. China, and also with the Key Laboratory of Solidification Control and Digital Preparation Technology (Liaoning Province), Dalian University of Technology, Dalian, 116024, China. Contact e-mail: [email protected] YU LIU is with the School of Mechanical Engineering, Northeast Electric Power University, Jilin, 132012, P.R. China. Manuscript submitted October 25, 2019.
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computational domain into meshes or elements, which requires a proper pre-definition relationship among the elements. Therefore, these methods face numerous challenges when dealing with the problems such as phase transition, moving interface tracking and large deformation. For example, the phase interfaces are inconsistent with the FEM element boundaries or a generic element is filled with different phases, which will bring some accuracy problems to the numerical integration. One possible solution in solving these problems is to refine the mesh, while interactive remesh and tedious self-adaption in the simulation will undoubtedly lead to an increase in the computational cost. On the other hand, FDM heavily relies on the generation of the uniform grids, which means that it may not be very efficient when dealing with complex geometric boundaries of the computational domain. Under such a circumstance, the meshless methods have been employed to solve the aforementioned problems due to their enormous inherent potentials. Its approximation formulations construct entirely in terms of nodes, without connectivity concept involved between the meshes.[4] Hence, it provides convenience in adding or deleting nodes when handing the moving boundaries and self-adaption problem. Over the past three decades, meshless numerical methods have performed remarkable progress in solid mechanics, heat transfer, fluid–solid coupling problem, and vibration analysis.[5]
However, in the field of continuous casting, a few studies prove that the research foundation still needs to be further improved. Some heat transfer studies have been carried out using the Local Radial Basis Function Collocation Method (LRBFCM)[6] and Finite Point method (FPM).[7–9] A few thermomechanical models have been devolved employing Meshless Local PetrovGalerkin (MLPG) Method[10] and Element-free Galerkin (EFG) method.[11] Then, the fluid flow model ha
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