IMEX methods for thin-film equations and Cahn-Hilliard equations with variable mobility
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909213172695040 |
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| author | Orizaga, Saulo Witelski, Thomas |
| author_facet | Orizaga, Saulo Witelski, Thomas |
| contents | We explore a class of splitting schemes employing implicit-explicit (IMEX) time-stepping to achieve accurate and energy-stable solutions for thin-film equations and Cahn-Hilliard models with variable mobility. This splitting method incorporates a linear, constant coefficient implicit step, facilitating efficient computational implementation. We investigate the influence of stabilizing splitting parameters on the numerical solution computationally, considering various initial conditions. Furthermore, we generate energy-stability plots for the proposed methods, examining different choices of splitting parameter values and timestep sizes. These methods enhance the accuracy of the original bi-harmonic-modified (BHM) approach, while preserving its energy-decreasing property and achieving second-order accuracy. We present numerical experiments to illustrate the performance of the proposed methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_19483 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | IMEX methods for thin-film equations and Cahn-Hilliard equations with variable mobility Orizaga, Saulo Witelski, Thomas Numerical Analysis Mathematical Physics We explore a class of splitting schemes employing implicit-explicit (IMEX) time-stepping to achieve accurate and energy-stable solutions for thin-film equations and Cahn-Hilliard models with variable mobility. This splitting method incorporates a linear, constant coefficient implicit step, facilitating efficient computational implementation. We investigate the influence of stabilizing splitting parameters on the numerical solution computationally, considering various initial conditions. Furthermore, we generate energy-stability plots for the proposed methods, examining different choices of splitting parameter values and timestep sizes. These methods enhance the accuracy of the original bi-harmonic-modified (BHM) approach, while preserving its energy-decreasing property and achieving second-order accuracy. We present numerical experiments to illustrate the performance of the proposed methods. |
| title | IMEX methods for thin-film equations and Cahn-Hilliard equations with variable mobility |
| topic | Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2405.19483 |