A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn–Hilliard Equation
We present a finite-volume based numerical scheme for a nonlocal Cahn–Hilliard equation which combines ideas from recent numerical schemes for gradient flow equations and nonlocal Cahn–Hilliard equations. The equation of interest is a special case of a previously derived and studied system of equati...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.265/ |
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| author | Lyons, Rainey Muntean, Adrian Nika, Grigor |
| author_facet | Lyons, Rainey Muntean, Adrian Nika, Grigor |
| author_sort | Lyons, Rainey |
| collection | DOAJ |
| description | We present a finite-volume based numerical scheme for a nonlocal Cahn–Hilliard equation which combines ideas from recent numerical schemes for gradient flow equations and nonlocal Cahn–Hilliard equations. The equation of interest is a special case of a previously derived and studied system of equations which describes phase separation in ternary mixtures. We prove the scheme is both energy stable and respects the analytical bounds of the solution. Furthermore, we present numerical demonstrations of the theoretical results using both the Flory–Huggins (FH) and Ginzburg–Landau (GL) free-energy potentials. |
| format | Article |
| id | doaj-art-a55492aa9f204c21bea9aa3df0f4dce1 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-a55492aa9f204c21bea9aa3df0f4dce12025-02-07T13:48:46ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342024-11-01352G123925010.5802/crmeca.26510.5802/crmeca.265A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn–Hilliard EquationLyons, Rainey0https://orcid.org/0000-0003-4113-0357Muntean, Adrian1Nika, Grigor2Department of Mathematics and Computer Science, Karlstad University, SwedenDepartment of Mathematics and Computer Science, Karlstad University, SwedenDepartment of Mathematics and Computer Science, Karlstad University, SwedenWe present a finite-volume based numerical scheme for a nonlocal Cahn–Hilliard equation which combines ideas from recent numerical schemes for gradient flow equations and nonlocal Cahn–Hilliard equations. The equation of interest is a special case of a previously derived and studied system of equations which describes phase separation in ternary mixtures. We prove the scheme is both energy stable and respects the analytical bounds of the solution. Furthermore, we present numerical demonstrations of the theoretical results using both the Flory–Huggins (FH) and Ginzburg–Landau (GL) free-energy potentials.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.265/Nonlocal Cahn–Hilliard equationgradient flowfinite-volume methodbound preserving energy stable schemes |
| spellingShingle | Lyons, Rainey Muntean, Adrian Nika, Grigor A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn–Hilliard Equation Comptes Rendus. Mécanique Nonlocal Cahn–Hilliard equation gradient flow finite-volume method bound preserving energy stable schemes |
| title | A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn–Hilliard Equation |
| title_full | A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn–Hilliard Equation |
| title_fullStr | A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn–Hilliard Equation |
| title_full_unstemmed | A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn–Hilliard Equation |
| title_short | A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn–Hilliard Equation |
| title_sort | bound preserving energy stable scheme for a nonlocal cahn hilliard equation |
| topic | Nonlocal Cahn–Hilliard equation gradient flow finite-volume method bound preserving energy stable schemes |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.265/ |
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