Unconditional bound-preserving and energy-dissipating finite-volume schemes for the Cahn-Hilliard equation
Unconditional bound-preserving and energy-dissipating finite-volume schemes for the Cahn-Hilliard equation
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DOI：
10.4208/cicp.oa-2023-0049
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发表时间：
2021-05
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影响因子：
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通讯作者：
Rafael Bailo;J. Carrillo;S. Kalliadasis;Sergio P. Perez
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作者：
Rafael Bailo;J. Carrillo;S. Kalliadasis;Sergio P. Perez
我们提出了Cahn-Hilliard方程的有限体积格式，该格式无条件和离散地保持了相场的有界性和自由能的耗散。我们的数值框架适用于各种自由能势，包括Ginzburg-Landau和flori - huggins，一般的润湿边界条件和简并迁移率。它的中心推力是逆风方法，我们将其与基于经典凸分裂方法的自由能项的半隐式公式相结合。由于其维度分裂的性质，将方案扩展到任意数量的维度是直接的，这允许通过简单的并行化有效地解决高维问题。通过不同尺寸、液滴与衬底之间不同接触角的各种算例对数值方案进行了验证和测试。
We propose finite-volume schemes for the Cahn-Hilliard equation which unconditionally and discretely preserve the boundedness of the phase field and the dissipation of the free energy. Our numerical framework is applicable to a variety of free-energy potentials, including Ginzburg-Landau and Flory-Huggins, to general wetting boundary conditions, and to degenerate mobilities. Its central thrust is the upwind methodology, which we combine with a semi-implicit formulation for the free-energy terms based on the classical convex-splitting approach. The extension of the schemes to an arbitrary number of dimensions is straightforward thanks to their dimensionally split nature, which allows to efficiently solve higher-dimensional problems with a simple parallelisation. The numerical schemes are validated and tested through a variety of examples, in different dimensions, and with various contact angles between droplets and substrates.