2015) were performed for the competitive growth of multiple 3D columnar dendrites during directional solidification (Takaki et al. Large-scale simulations with multiple GPUs (Shimokawabe et al. In addition, the PF computation for dendrite growth is easily accelerated by GPU computing because it requires a large number of floating-point calculations per grid point. GPU computing is quite efficient for implementing discretization methods with simple calculation algorithms, such as finite difference or finite volume methods. 2011 Ohno 2012 Tourret and Karma 2015 Clarke et al. Currently, GPUs are commonly used in the PF simulations of dendritic solidification owing to their high parallel computing performance (Yamanaka et al. 2000).Ī graphics processing unit (GPU) was first used for PF computation in the early 2000s. Therefore, the PF simulations of dendrite growth were limited to the two-dimensional (2D) simulations and three-dimensional (3D) simulations of single dendrite growth until the early 2000s (Kobayashi 1994 Karma and Rappel 1998 Karma et al. However, even in a quantitative PF model, it is necessary to use a numerical grid that is several times smaller than the curvature radius of a dendrite tip. A quantitative solidification model (Ohno 2020) can be utilized to perform quantitative simulations using an interface width larger than the physical interface. However, the PF method is a diffuse interface model, which requires a finer spatial resolution compared to other simulation methods, resulting in higher calculation costs. Among these, the PF method is the most powerful because it does not require the explicit tracking of an interface and accurately expresses the free-boundary problem through the thin-interface limit. 2015), front tracking method (Juric and Tryggvason 1996 Al-Rawahi and Tryggvason 2002, 2004), and phase-field (PF) method (Gránásy et al. There are a few numerical simulation methods that can express dendrite growth, such as the cellular automaton method (Brown et al. As the solidification microstructure determines the macroscopic properties of a cast product, it is important to accurately predict the formation process of the solidification microstructure considering the competitive growth (Dantzig and Rappaz 2009 Kurz et al. Finally, weak scaling tests are performed to confirm the parallel efficiency of the developed code.Ī solidification microstructure is generally composed of equiaxed and columnar structures, which are formed by the competitive growth of a massive number of dendrites. Next, we evaluate the efficiency of dynamic load balancing by performing multiple-GPU parallel computations for three different directional solidification simulations using a moving frame algorithm. The accuracy of an AMR refinement condition is confirmed through the single-GPU computations of columnar dendrite growth during the directional solidification of a binary alloy. In the parallel GPU computation, we apply dynamic load balancing to parallel computing to equalize the computational cost per GPU. In this study, we perform a three-dimensional dendrite growth phase-field simulation in which AMR is implemented via parallel computing using multiple graphics processing units (GPUs), which provide high parallel computation performance. In such cases, the adaptive mesh refinement (AMR) method is effective for improving the computational performance.
In the phase-field simulation of dendrite growth during the solidification of an alloy, the computational cost becomes extremely high when the diffusion length is significantly larger than the curvature radius of a dendrite tip.
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