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Phase field simulations of coupled microstructure solidification problems via the strong form particle difference method

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Abstract

This paper presents the development of a strong form-based collocation method called the particle difference method (PDM), capable of predicting the spatiotemporal evolution of polycrystalline material solidification through coupling of multi-phase and temperature fields. Cross coupled phase field evolution and heat transfer equations are discretized via the PDM to obtain the interface kinematics of polycrystalline boundary during solidification. A distinct feature of the PDM is its ability to represent derivative operators via a moving least-square approximation of the Taylor expansion through point-wise computations at collocation points. The method discretizes directly the strong forms using the pre-computed derivative operators at each collocation point and elegantly overcomes the topological difficulty in modeling intricate moving interfaces. To verify the efficacy of the PDM, numerical results are compared with those obtained from the conventional finite difference method for uniform and irregular distributions of the collocation points. The scalability of the parallelized PDM is tested by measuring its efficiency with increasing the number of processors. We also provide a solidification simulation with two ellipsoidal inclusions to demonstrate the capability of the PDM in complex moving interface problems with high curvature.

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Acknowledgements

The first and fifth authors acknowledge support by the Office of Naval Research (ONR) through the 2016 ONR Summer Faculty Research Fellowship and the Naval Research Laboratory’s core funding, respectively.

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Authors and Affiliations

  1. Department of Civil, Environmental and Architectural Engineering, University of Colorado at Boulder, Boulder, CO, 80309, USA

    Jeong-Hoon Song

  2. Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, Cincinnati, OH, 45220, USA

    Yao Fu

  3. Civil Infrastructure and Environmental Engineering, Khalifa University of Science and Technology, Abu Dhabi, 127788, UAE

    Tae-Yeon Kim

  4. Department of Civil Engineering, Myongji College, Seoul, 120-776, South Korea

    Yeong-Cheol Yoon

  5. Computational Multiphysics Systems Laboratory, Naval Research Laboratory, Washington, DC, 20357, USA

    John G. Michopoulos

  6. Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstrasse 15, 99423, Weimar, Germany

    Timon Rabczuk

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  1. Jeong-Hoon Song
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Song, JH., Fu, Y., Kim, TY. et al. Phase field simulations of coupled microstructure solidification problems via the strong form particle difference method. Int J Mech Mater Des 14, 491–509 (2018). https://doi.org/10.1007/s10999-017-9386-1

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