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Abstract One of the long-standing problems in the phase field, namely, combining the principles of thermodynamics and capillarity with the numerical aspects of interface propagation in simulations, is re-investigated. Numerical schemes are discussed which allow for stable simulations with arbitrary driving forces, considering or excluding capillarity. We re-investigate a classical stabilization scheme that decouples interface stabilization from curvature evaluation, ensuring stable simulations even under large driving forces. A novel mathematical analysis gives a rigorous estimate for the time stepping and a numerical value of the required stabilization strength. The proposed stabilization scheme is benchmarked for three-dimensional dendritic growth under directional solidification conditions for different solidification speeds.
Uddagiri et al. (Tue,) studied this question.