In this article, the phase field sintering model, which is composed of a Cahn–Hilliard type equation and several Allen–Cahn type equations, has been considered. On the scalar auxiliary variable framework, we propose a theoretically efficient and stable method for solid-state sintering. In order to overcome the nonlinear issues, we define a stabilized scalar auxiliary variable method and reformulate the phase field sintering model. An efficient and accurate numerical scheme is investigated to solve our model. The scheme consist of several decoupled diffusion equations at every time step. Therefore, our scheme is easy to implement. Then we prove the numerical discrete energy is unconditionally stable. Several numerical simulations in two- and three-dimensional spaces are presented to demonstrate the robustness of our method.
|Communications in Nonlinear Science and Numerical Simulation
|Published - 2023 Dec
Bibliographical noteFunding Information:
Y.B. Li is supported by National Natural Science Foundation of China (No. 12271430 ).
© 2023 Elsevier B.V.
- Scalar auxiliary variable
- Second order accuracy
- Solid-state sintering
- Unconditional energy stability
ASJC Scopus subject areas
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics