Large time steps in the explicit formulation of transient heat transfer

• Published in: International journal of heat and mass transfer 2017-05, Vol.108, p.2040-2052
• Main Authors: Li, Eric, He, Z.C., Tang, Qian, Zhang, G.Y.
• Format: Article
• Language: English
• Subjects: Critical time step; Dynamic heat transfer; Flexible integration points; Numerical integration; Stability
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2017.01.065

•The stiffness and mass using MIR are formulated in dynamic heat transfer.•A much larger time step can be applied by tuning the integration point of mass.•The steady solution is identical regardless of integration point in the mass model. In this paper, a generalized formulation of stiffness and mass using modified integration rules (MIR) with flexible integration points is developed to improve the stability of transient heat transfer problems. With adjustment of integration points in the stiffness, the softening or stiffening properties of discretized model for heat transfer problems can be altered. In addition, it is found that the integration points in the mass have a great effect on the critical time step for the explicit formulation of transient heat transfer problems. With a proper selection of integration points in the mass, a much larger time step can be applied in the analysis of transient heat transfer problems. Furthermore, it is observed that the final steady solutions of transient heat transfer problems are identical regardless of locations of integration points in the mass model. Numerical experiments including 2D heat transfer problems with different boundary conditions including heat conduction, heat convection and radiation are studied to verify the properties of flexible integration points in the stiffness and mass.