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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2503.23516 |
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| _version_ | 1866913766721978368 |
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| author | Sharma, Natasha S. Tierra, Giordano |
| author_facet | Sharma, Natasha S. Tierra, Giordano |
| contents | We present a numerical scheme for solving a sixth-order Cahn-Hilliard type equation that captures the dynamics of phase transitions in a ternary mixture consisting of two immiscible fluids and a surface active molecule that is amphiphilic. We show that by considering a suitable midpoint approximation for the nonlinear terms in the differential equation, we obtain an unconditionally energy-stable numerical scheme that is second-order in time. We demonstrate that our proposed numerical scheme satisfies these key properties for a wide range of physical parameters in two and three dimensions. Moreover, we present the results of a numerical study to report on the impact of each physical parameter on the behavior of the dynamics of the phase transitions, which are in agreement with the experimental observations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unconditionally Energy Stable Second Order Numerical Scheme for a Microemulsion model Sharma, Natasha S. Tierra, Giordano Numerical Analysis 35K51, 35M13, 35Q35, 65M12, 65M60 We present a numerical scheme for solving a sixth-order Cahn-Hilliard type equation that captures the dynamics of phase transitions in a ternary mixture consisting of two immiscible fluids and a surface active molecule that is amphiphilic. We show that by considering a suitable midpoint approximation for the nonlinear terms in the differential equation, we obtain an unconditionally energy-stable numerical scheme that is second-order in time. We demonstrate that our proposed numerical scheme satisfies these key properties for a wide range of physical parameters in two and three dimensions. Moreover, we present the results of a numerical study to report on the impact of each physical parameter on the behavior of the dynamics of the phase transitions, which are in agreement with the experimental observations. |
| title | Unconditionally Energy Stable Second Order Numerical Scheme for a Microemulsion model |
| topic | Numerical Analysis 35K51, 35M13, 35Q35, 65M12, 65M60 |
| url | https://arxiv.org/abs/2503.23516 |