{"title":"A FFT-based phase-field framework for simulating dendritic growth in binary alloy","authors":"Arijit Sinhababu, Shyamprasad Karagadde","doi":"10.1016/j.jcp.2024.113600","DOIUrl":null,"url":null,"abstract":"<div><div>In the present study, a Fourier pseudo-spectral-based, phase-field framework is developed to simulate the binary alloy solidification using fixed grids. The motivation behind this proposition of a new model towards overcoming existing limitations is two-fold: firstly, to create a fully validated high-order phase-field model that closely aligns with LKT predictions of tip kinetics across various undercoolings and compositions, and secondly, to achieve accurate simulations using fixed Cartesian meshes with a grid size of order more than unity. In the Fourier pseudo-spectral method, the nonlinear terms of the PF equations are de-aliased using zero padding and high-order Fourier smoothing exponential filters. Accurate growth kinetics during binary alloy solidification are observed despite employing fixed mesh sizes, even when the ratio of grid size to diffuse interface thickness is 1.42. A hybrid, integrating factor (IF)-based, strongly stable third-order Runge-Kutta method (SSPRK3) is implemented to obtain improved temporal stability at high Lewis numbers. A novel scaling relationship between dimensionless tip velocity and undercooling is obtained from the growth of a four-arm equiaxed dendrite at different levels of undercooling. The growth of several randomly oriented dendrites is also accurately simulated without using any mesh refinement schemes. Likewise, the tip velocity closely matched the LKT predictions at dilute concentrations at the boundary. Furthermore, the effects of the coupling parameter and the anti-trapping term on dendritic growth kinetics are explored. Overall, the proposed FFT-based framework is expected to capture the crystals' global chemical wave features precisely with fewer points per wavelength (PPW) and has the potential to be scaled up for large-scale simulations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113600"},"PeriodicalIF":3.8000,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021999124008489","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
In the present study, a Fourier pseudo-spectral-based, phase-field framework is developed to simulate the binary alloy solidification using fixed grids. The motivation behind this proposition of a new model towards overcoming existing limitations is two-fold: firstly, to create a fully validated high-order phase-field model that closely aligns with LKT predictions of tip kinetics across various undercoolings and compositions, and secondly, to achieve accurate simulations using fixed Cartesian meshes with a grid size of order more than unity. In the Fourier pseudo-spectral method, the nonlinear terms of the PF equations are de-aliased using zero padding and high-order Fourier smoothing exponential filters. Accurate growth kinetics during binary alloy solidification are observed despite employing fixed mesh sizes, even when the ratio of grid size to diffuse interface thickness is 1.42. A hybrid, integrating factor (IF)-based, strongly stable third-order Runge-Kutta method (SSPRK3) is implemented to obtain improved temporal stability at high Lewis numbers. A novel scaling relationship between dimensionless tip velocity and undercooling is obtained from the growth of a four-arm equiaxed dendrite at different levels of undercooling. The growth of several randomly oriented dendrites is also accurately simulated without using any mesh refinement schemes. Likewise, the tip velocity closely matched the LKT predictions at dilute concentrations at the boundary. Furthermore, the effects of the coupling parameter and the anti-trapping term on dendritic growth kinetics are explored. Overall, the proposed FFT-based framework is expected to capture the crystals' global chemical wave features precisely with fewer points per wavelength (PPW) and has the potential to be scaled up for large-scale simulations.
期刊介绍:
Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries.
The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.