The stabilized-trigonometric scalar auxiliary variable approach for gradient flows and its efficient schemes
DC Field | Value | Language |
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dc.contributor.author | Yang, Junxiang | - |
dc.contributor.author | Kim, Junseok | - |
dc.date.accessioned | 2022-02-26T22:40:49Z | - |
dc.date.available | 2022-02-26T22:40:49Z | - |
dc.date.created | 2022-01-20 | - |
dc.date.issued | 2021-08 | - |
dc.identifier.issn | 0022-0833 | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/137064 | - |
dc.description.abstract | We develop a trigonometric scalar auxiliary variable (TSAV) approach for constructing linear, totally decoupled, and energy-stable numerical methods for gradient flows. An auxiliary variable r based on the trigonometric form of the nonlinear potential functional removes the bounded-from-below restriction. By adding a positive constant greater than 1, the positivity preserving property of r can be satisfied. Furthermore, the phase-field variables and auxiliary variable r can be treated in a totally decoupled manner, which simplifies the algorithm. A practical stabilization method is employed to suppress the effect of an explicit nonlinear term. Using our proposed approach, temporally first-order and second-order methods are easily constructed. We prove analytically the discrete energy dissipation laws of the first- and second-order schemes. Furthermore, we propose a multiple TSAV approach for complex systems with multiple components. A comparison of stabilized-SAV (S-SAV) and stabilized-TSAV (S-TSAV) approaches is performed to show their efficiency. Two-dimensional numerical experiments demonstrated the desired accuracy and energy stability. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | SPRINGER | - |
dc.subject | PHASE-FIELD MODELS | - |
dc.subject | FINITE-DIFFERENCE SCHEME | - |
dc.subject | NUMERICAL SCHEME | - |
dc.subject | SAV APPROACH | - |
dc.subject | CONVERGENCE ANALYSIS | - |
dc.subject | ENERGY | - |
dc.subject | 2ND-ORDER | - |
dc.subject | EQUATION | - |
dc.subject | SYSTEM | - |
dc.title | The stabilized-trigonometric scalar auxiliary variable approach for gradient flows and its efficient schemes | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Kim, Junseok | - |
dc.identifier.doi | 10.1007/s10665-021-10155-x | - |
dc.identifier.scopusid | 2-s2.0-85112024883 | - |
dc.identifier.wosid | 000683336700001 | - |
dc.identifier.bibliographicCitation | JOURNAL OF ENGINEERING MATHEMATICS, v.129, no.1 | - |
dc.relation.isPartOf | JOURNAL OF ENGINEERING MATHEMATICS | - |
dc.citation.title | JOURNAL OF ENGINEERING MATHEMATICS | - |
dc.citation.volume | 129 | - |
dc.citation.number | 1 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Engineering | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Engineering, Multidisciplinary | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Interdisciplinary Applications | - |
dc.subject.keywordPlus | PHASE-FIELD MODELS | - |
dc.subject.keywordPlus | FINITE-DIFFERENCE SCHEME | - |
dc.subject.keywordPlus | NUMERICAL SCHEME | - |
dc.subject.keywordPlus | SAV APPROACH | - |
dc.subject.keywordPlus | CONVERGENCE ANALYSIS | - |
dc.subject.keywordPlus | ENERGY | - |
dc.subject.keywordPlus | 2ND-ORDER | - |
dc.subject.keywordPlus | EQUATION | - |
dc.subject.keywordPlus | SYSTEM | - |
dc.subject.keywordAuthor | Energy stability | - |
dc.subject.keywordAuthor | Gradient flows | - |
dc.subject.keywordAuthor | S-TSAV approach | - |
dc.subject.keywordAuthor | Stabilization technique | - |
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