An analysis framework based on three-sub-step composite implicit time integration method for transient heat conduction problem

In this study, a novel three-sub-step composite implicit time integration method for transient heat conduction analysis is proposed. The algorithmic procedure for heat conduction problem is presented. The effects of algorithmic parameters on accuracy and stability are determined analytically. With adjustable parameters, the proposed method can achieve enhanced computation accuracy, controllable numerical dissipation, and unconditional stability. The truncation error analysis demonstrates that the proposed method has at least second-order accuracy and can reach at most third-order accuracy. Numerical examples demonstrate the effectiveness of the proposed method for linear and nonlinear heat conduction problems.