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arxiv: 2602.10316 · v2 · submitted 2026-02-10 · ❄️ cond-mat.mtrl-sci · physics.comp-ph

Benchmarking of Massively Parallel Phase-Field Codes for Directional Solidification

Jiefu Tian , David Montiel , Kaihua Ji , Trevor Lyons , Jason Landini , Katsuyo Thornton , Alain Karma This is my paper

Pith reviewed 2026-05-16 01:56 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.comp-ph
keywords solidificationphase-fieldcomputationalconditionsemployingunderbenchmarkcode
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The pith

GPU-PF and PRISMS-PF phase-field codes produce consistent predictions for dendritic morphology, primary spacing, and tip dynamics in 2D and 3D simulations of alloy solidification at experimentally relevant scales.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Phase-field modeling simulates how alloys solidify by tracking the moving boundary between liquid and solid with a smooth mathematical function instead of sharp interfaces. This study tests two different computer implementations of the same model on two real-world cases: aluminum with 3 percent copper solidifying at high speed, and a camphor mixture under low-gravity conditions from NASA experiments. One code runs on graphics cards using a regular grid; the other runs on regular processors with a mesh that refines only where needed. The benchmark checks whether both codes produce matching crystal shapes, the distance between main branches, and how the tips advance. It also measures how results change when the grid is made finer and how much computer time each code requires. The chosen conditions are much closer to actual lab or space experiments than earlier simple test problems.

Core claim

Both codes solve the same quantitative phase-field formulation that incorporates an anti-trapping current for the solidification of dilute alloys and produce consistent predictions for dendritic morphology, primary spacing, and tip dynamics in both 2D and 3D.

Load-bearing premise

That the two independent implementations accurately represent the identical phase-field model without introducing significant numerical discrepancies from discretization choices or parallelization at the large time and length scales of the experiments.

Figures

Figures reproduced from arXiv: 2602.10316 by Alain Karma, David Montiel, Jason Landini, Jiefu Tian, Kaihua Ji, Katsuyo Thornton, Trevor Lyons.

Figure 1
Figure 1. Figure 1: Comparison of ϕ = 0 solid-liquid interface contours at four different time slices from two simulations: the PRISMS-PF finite element implemen￾tation (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. Courant-Friedrichs-Lewy (CFL) condition, ∆t ≤ (∆x) 2 /(2dD˜), where d is the si… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of ϕ = 0 solid-liquid interface contours at four different time slices from two simulations: the PRISMS-PF finite element implemen￾tation (orange) and the GPU-PF finite difference code (purple). The excellent agreement confirms consistent interface evolution between the two codes at this intermediate stage. The domain length is chosen large enough to capture the later stages of interface evoluti… view at source ↗
Figure 3
Figure 3. Figure 3: ϕ = 0 solid-liquid interface contours at t = 400τ0 with long￾wavelength perturbations (n = 1) for four cases: two spatial resolutions 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. influence on the subsequent morphological evolution, owing to the fact that the growth kinetics of the dendrite tip dominate … view at source ↗
Figure 4
Figure 4. 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 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Interface contour and cross-section for both GPU-PF and PRISMS-PF simulations at [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Performance comparison between GPU-PF and PRISMS-PF. (a) Runtime for a quarter-domain simulation with symmetry-reflected boundaries. Here [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
read the original 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 high-velocity solidification 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 (GPU-PF) and the other one employing finite-element discretization with adaptive-mesh and CPU-parallelization (PRISMS-PF), 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Circularity Check

0 steps flagged

No circularity: direct code-to-code benchmark against shared model and external experiments

full rationale

The paper conducts an empirical side-by-side comparison of two independently written phase-field codes (GPU-PF with uniform FD and PRISMS-PF with adaptive FE) that both implement the same established quantitative model including anti-trapping current. No derivation chain exists; the central claim is that the codes produce consistent dendritic morphology, spacing, and tip dynamics when solving identical physics at experimental scales. This is tested directly against NASA DECLIC-DSI-R data for Al-Cu and SCN alloys rather than being forced by internal fits or self-citations. The comparison is externally falsifiable via mesh-convergence studies and experimental benchmarks, with no self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a computational benchmarking study that applies an established phase-field model; no new free parameters, axioms, or invented entities are introduced.

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