On the time integration for phase field modeling of grain growth in additive manufacturing

TL;DR

This paper introduces stabilized time integration algorithms that significantly reduce computational costs in phase field simulations of grain growth during additive manufacturing by allowing larger time steps while maintaining stability.

Contribution

The study develops and analyzes a new class of stabilized time integration methods tailored for phase field models in additive manufacturing, enabling faster simulations.

Findings

Achieved at least two orders-of-magnitude larger time steps compared to explicit methods.

Confirmed energy stability and reduced computational cost in 2D and 3D simulations.

Provided a numerical framework for large-scale phase field modeling.

Abstract

Phase field simulations play a key role in the understanding of microstructure evolution in additive manufacturing. However, they have been found extremely computationally expensive. One of the reasons is the small time step requirement to resolve the complex microstructure evolution during the rapid solidification process. This paper investigates the possibility of using a class of stabilized time integration algorithms to accelerate such phase field simulations by increasing the time steps. The specific time integration formulation and theoretical analysis on energy stability were developed, based on a phase field model dedicated to simulating rapid solidification in additive manufacturing. The numerical results confirmed that the proposed method can ensure the numerical stability and a decreasing energy requirement for the phase field simulations with at least two orders-of-magnitude larger time steps over conventional explicit methods. 2D and 3D phase field simulations have been conducted with relevant physical and kinetic parameters for 316L stainless steels. This work provides a numerical framework for efficient phase field simulations and open numerous opportunities for large scale phase field modeling.