Benchmarking of Massively Parallel Phase-Field Codes for Directional Solidification

TL;DR

This paper benchmarks two state-of-the-art PF implementations (GPU-PF: CUDA-based finite-difference on uniform grids; PRISMS-PF: adaptive-mesh finite element) using a unified thin-interface, anti-trapping PF model with interface width $W_0$ and related parameters. It validates predictions against NASA DECLIC-DSI-R data for Al-3wt%Cu and SCN-Camphor, showing strong agreement in dendrite morphology and primary spacing across 2D and 3D cases, while highlighting the impact of initial perturbations on chaotic regimes. Key contributions include detailed convergence and performance analyses, demonstration of cross-code quantitative agreement, and guidance on numerical choices that influence chaotic evolution. The work provides a practical reference for ICME workflows in PF modeling and makes data and codes publicly available to support reproducibility and community benchmarking.

Abstract

We present a detailed benchmark comparing two state-of-the-art phase-field implementations for simulating alloy solidification under experimentally relevant conditions. The study investigates the directional solidification of Al-3wt%Cu under additive manufacturing conditions and SCN-0.46wt% camphor under microgravity conditions from National Aeronautics and Space Administration (NASA) DECLIC-DSI-R experiments. Both codes, one employing finite-difference discretization with uniform mesh and GPU-acceleration and the other one employing finite-element discretization with adaptive-mesh and CPU-parallelization, solve the same quantitative phase-field formulation that incorporates an anti-trapping current for the solidification of dilute alloys. We evaluate the predictions of each code for dendritic morphology, primary spacing, and tip dynamics in both 2D and 3D, as well as their numerical convergence and computational performance. While existing benchmark problems have primarily focused on simplified or small-scale simulations, they do not reflect the computational and modeling challenges posed by employing experimentally relevant time and length scales. Our results provide a practical framework for assessing phase-field code performance as well as validating and facilitating their application in integrated computational materials engineering (ICME) workflows that require integration with realistic experimental data.

Figures (6)

• Figure 1: Comparison of $\phi = 0$ solid-liquid interface contours at four different time slices from two simulations: the PRISMS-PF finite element implementation (grey) and the GPU-PF finite difference code (colored dash lines). The excellent agreement confirms consistent interface evolution between the two codes at this intermediate stage.
• Figure 2: Comparison of $\phi = 0$ solid-liquid interface contours at four different time slices from two simulations: the PRISMS-PF finite element implementation (orange) and the GPU-PF finite difference code (purple). The excellent agreement confirms consistent interface evolution between the two codes at this intermediate stage.
• Figure 3: $\phi = 0$ solid-liquid interface contours at $t = 400\tau_0$ with long-wavelength perturbations ($n = 1$) for four cases: two spatial discretizations and the corresponding time steps sizes each for GPU-PF (left two) and PRISMS-PF (right two). Middle: the initial position of the perturbed interface.
• Figure 4: Comparison of 3D solid-liquid interface evolution between GPU-PF and PRISMS-PF under DECLIC-DSI-R benchmark conditions. The domain size is $(L_x,\,L_y,\,L_z)=(0.194~\mathrm{mm},\,0.194~\mathrm{mm},\,2.332~\mathrm{mm})$. (a) 3D interface contours at $t/\tau_0 = 424$. The dendrite morphologies show strong agreement across codes and discretizations. Red: GPU-PF simulation with $\Delta x/W_0 = 1.2$ and $\Delta t/\tau_0 = 5\times10^{-4}$; Green: GPU-PF simulation with $\Delta x/W_0 = 0.8$ and $\Delta t/\tau_0 = 5\times10^{-4}$; Yellow: PRISMS-PF simulation with $\Delta x/W_0 = 1.2$ and $\Delta t/\tau_0 = 5\times10^{-4}$; Grey: PRISMS-PF simulation with $\Delta x/W_0 = 0.8$ and $\Delta t/\tau_0 = 2\times10^{-4}$. (b) Temporal evolution of the GPU-PF interface with $\Delta x/W_0=1.2$, showing $\phi=0$ contours at $t/\tau_0 = 0$, $208$, and $424$. A sinusoidally perturbed planar front grows into uniformly spaced dendrites through cellular instability. (c) Cross-sectional views of the $x$–$z$ interface profile at $y=L_y/3$ for all simulations at $t/\tau_0 = 0$, $208$, and $424$. The right panel shows a zoomed-in view of the final front position at $t/\tau_0 = 424$, confirming excellent quantitative agreement across codes and discretizations. The color scheme follows that of (a).
• Figure 5: Interface contour and cross-section for both GPU-PF and PRISMS-PF simulations at $t=424~\tau_0$ using the composite initial condition defined in Eq. \ref{['eq:perturbation']}, with $\mathcal{A}_1=12.1905~W_0$, $\mathcal{A}_2=12.1905~W_0$ and $n=6$. The discretization $\Delta x/W_0=1.2$ and $\Delta t/\tau_0=5\times 10^{-4}$ was used for GPU-PF, and a comparable element size was used in PRISMS-PF.