Decoupled, efficient and structure-preserving numerical scheme for a non-isothermal phase field sintering model

In order to investigate the impact of temperature in the selective laser sintering industrial process, we focus on developing the non-isothermal phase-field sintering model which combines the phase field equations with the thermodynamic framework. We employ a Lagrange multiplier method to handle nonlinear terms and a second-order accurate scheme is carried out using the backward differentiation formula framework. The system is transformed into linear quadratic harmonic equations. We only need to solve one nonlinear equation by Newton iteration in order to update the Lagrange multiplier. The discrete scheme is rigorously proved to follow the second law of thermodynamics. Numerical simulations are conducted to demonstrate the deformation of grains in the system under the influence of thermal driving, as well validate the stability, accuracy, and efficiency of our method.