Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

• Published in: Acta mechanica Sinica 2006-04, Vol.22 (2), p.138-147
• Main Authors: Phongthanapanich, Sutthisak, Traivivatana, Suthee, Boonmaruth, Parinya, Dechaumphai, Pramote
• Format: Article
• Language: English
• Subjects: Accuracy; Computing time; Conduction heating; Conductive heat transfer; Exact solutions; Finite element analysis; Finite element method; Heat transfer; Interpolation; Mesh generation; Square plates; Steady state; Transient heat conduction; Transient heat transfer; Two dimensional analysis; 变量元; 有限元法; 流量表述; 热传递; 稳定态
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-006-0097-3

Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method, The solution accuracy is further improved by implementing an adaptive meshing technique to generaie finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems tire： （a） a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and （b） a transient heat conduction analysis in a long plate subjected to moving heat source.