{"title":"凝固相场模型中的界面稳定和传播:解决大驱动力问题","authors":"Murali Uddagiri, Marvin Tegeler, Ingo Steinbach","doi":"10.1088/1361-651x/ad691d","DOIUrl":null,"url":null,"abstract":"One of the long-standing problems in the phase field, namely, combining the principles of thermodynamics and capillarity with the numerical aspects of interface propagation in simulations, is re-investigated. Numerical schemes are discussed which allow for stable simulations with arbitrary driving forces, considering or excluding capillarity. We re-investigate a classical stabilization scheme that decouples interface stabilization from curvature evaluation, ensuring stable simulations even under large driving forces. A novel mathematical analysis gives a rigorous estimate for the time stepping and a numerical value of the required stabilization strength. The proposed stabilization scheme is benchmarked for three-dimensional dendritic growth under directional solidification conditions for different solidification speeds.","PeriodicalId":18648,"journal":{"name":"Modelling and Simulation in Materials Science and Engineering","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Interface stabilization and propagation in phase field models of solidification: resolving the issue of large driving forces\",\"authors\":\"Murali Uddagiri, Marvin Tegeler, Ingo Steinbach\",\"doi\":\"10.1088/1361-651x/ad691d\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"One of the long-standing problems in the phase field, namely, combining the principles of thermodynamics and capillarity with the numerical aspects of interface propagation in simulations, is re-investigated. Numerical schemes are discussed which allow for stable simulations with arbitrary driving forces, considering or excluding capillarity. We re-investigate a classical stabilization scheme that decouples interface stabilization from curvature evaluation, ensuring stable simulations even under large driving forces. A novel mathematical analysis gives a rigorous estimate for the time stepping and a numerical value of the required stabilization strength. The proposed stabilization scheme is benchmarked for three-dimensional dendritic growth under directional solidification conditions for different solidification speeds.\",\"PeriodicalId\":18648,\"journal\":{\"name\":\"Modelling and Simulation in Materials Science and Engineering\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-08-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Modelling and Simulation in Materials Science and Engineering\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-651x/ad691d\",\"RegionNum\":4,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATERIALS SCIENCE, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Modelling and Simulation in Materials Science and Engineering","FirstCategoryId":"88","ListUrlMain":"https://doi.org/10.1088/1361-651x/ad691d","RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
Interface stabilization and propagation in phase field models of solidification: resolving the issue of large driving forces
One of the long-standing problems in the phase field, namely, combining the principles of thermodynamics and capillarity with the numerical aspects of interface propagation in simulations, is re-investigated. Numerical schemes are discussed which allow for stable simulations with arbitrary driving forces, considering or excluding capillarity. We re-investigate a classical stabilization scheme that decouples interface stabilization from curvature evaluation, ensuring stable simulations even under large driving forces. A novel mathematical analysis gives a rigorous estimate for the time stepping and a numerical value of the required stabilization strength. The proposed stabilization scheme is benchmarked for three-dimensional dendritic growth under directional solidification conditions for different solidification speeds.
期刊介绍:
Serving the multidisciplinary materials community, the journal aims to publish new research work that advances the understanding and prediction of material behaviour at scales from atomistic to macroscopic through modelling and simulation.
Subject coverage:
Modelling and/or simulation across materials science that emphasizes fundamental materials issues advancing the understanding and prediction of material behaviour. Interdisciplinary research that tackles challenging and complex materials problems where the governing phenomena may span different scales of materials behaviour, with an emphasis on the development of quantitative approaches to explain and predict experimental observations. Material processing that advances the fundamental materials science and engineering underpinning the connection between processing and properties. Covering all classes of materials, and mechanical, microstructural, electronic, chemical, biological, and optical properties.