Steady and transient heat transfer analysis using a stable node-based smoothed finite element method

• A stable node based smoothed finite element method is formulated for heat transfer analysis.
• The SNS-FEM can cure the temporal instability of the original NS-FEM dealing with transient heat transfer problems.
• Present SNS-FEM has higher calculation accuracy than original NS-FEM and conventional FEM.
• Present SNS-FEM is more efficient than original NS-FEM and conventional FEM.

In order to cure the instability of NS-FEM and further improve the accuracy, a stable node-based smoothed finite element method (SNS-FEM) is formulated for steady and transient heat transfer problems using linear triangular and tetrahedron element. In present method, both smoothed temperature gradient and variance of temperature gradient in smoothing domains are considered. The accuracy, computational efficiency and stability of SNS-FEM are examined through several numerical examples with different kinds of boundary conditions. It is found that present method is more accurate and efficient than traditional finite element method (FEM) and NS-FEM. Most importantly, compared with NS-FEM, present SNS-FEM can be very stable when dealing with transient heat transfer problems.