The Finite Phase-Field Method - A Numerical Diffuse Interface Approach for Microstructure Simulation with Minimized Disc
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The Finite Phase-Field Method - A Numerical Diffuse Interface Approach for Microstructure Simulation with Minimized Discretization Error Janin Eiken Access e. V., Intzestraße 5, 52072 Aachen, Germany ABSTRACT The 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 simulations 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 profile. 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. INTRODUCTION Numerical microstructure prediction has become an indispensable tool in the process of alloy and process optimization. Phase-field approaches , being based on a diffuse representation of the phase boundaries, allow space-resolved simulation of complex microstructures both during solidification and solid-state transitions [1, 2]. While early phase-field approaches were discussed in the limit of an infinitesimally small interface width, modern phase-field approaches for applied computation require finite values, adjustable for numerical convenience. The finite-size interface region and its evolution with time are described using discrete spacing and time stepping, typically based on the finite-difference (FD) method. The phase-field software MICRESS® [3] enables application-oriented microstructure simulations for technical alloys under profound consideration of multicomponent, multiphase and polycrystalline interactions [4]. The underlying model is based on a non-conserved order parameter and both addresses diffusion-controlled and interface-controlled growth. A recent study on austenite-to-ferrite transformation in mixed mode [5] revealed that the accuracy of the predicted kinetics strongly depended on the numerical resolution of the interfacial regions. As a consequence, high accuracy was found to be incompatible with efficient computational performance. To overcome the problem, a new Finite Phase-Field (FPF) model with an implicit compensation of the FD discretization error is proposed.
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