The Finite Phase-Field Method - A Numerical Diffuse Interface Approach for Microstructure Simulation with Minimized Discretization Error

Abstract

ABSTRACTThe Phase-field method is recognized as the method of choice for space-resolved microstructure simulation. In theoretic phase-field approaches, the underlying diffuse interface representation is discussed in the sharp interface limit. Applied phase-field models, however, have to cope with interfaces of finite size. Numerical solution based on finite differences naturally implies a discretization error. This error may result in significant deviations from the analytical sharp-interface solution, especially in cases of interface-controlled growth. Benchmark simula-tions revealed a direct correlation between the accuracy of the finite-difference solution and the number of numerical cells used to resolve the finite-sized interface width. This poses a problem, because high numbers of interface cells are unfavorable for numerical performance. To enable efficient high-accuracy computations, a new Finite Phase-Field approach is proposed, which closely links phase-field modeling and numerical discretization. The approach is based on a parabolic potential function, corresponding to phase-field solutions with a sinusoidal interface pro-file. Consideration of this profile during numerical differentiation allows an exact quantification of the bias evoked by grid spacing and interface width, which then a priori can be compensated.