科学研究
报告题目:

A structure-preserving, upwind-SAV scheme for the degenerate Cahn-Hilliard equation with applications to simulating surface diffusion

报告人:

黄琼敖 助理教授(河南大学)

报告时间:

报告地点:

老外文楼信息与计算科学系办公室

报告摘要:

In this talk, I will introduce a structure-preserving scheme for the Cahn-Hilliard equation with degenerate mobility. First, by applying a finite volume method with upwind numerical fluxes to the degenerate Cahn-Hilliard equation rewritten by the scalar auxiliary variable (SAV) approach, we creatively obtain a bound-preserving, energy-stable and fully-discrete scheme, which, for the first time, addresses the boundedness of the classical SAV approach under $H^{-1}$-gradient flow. Then, a dimensional-splitting technique is introduced in high-dimensional cases, which greatly reduces the computational complexity while preserves original structural properties. Numerical experiments are presented to verify the bound-preserving and energy-stable properties of the proposed scheme. Finally, by applying the proposed structure-preserving scheme, we numerically demonstrate that surface diffusion can be approximated by the Cahn--Hilliard equation with degenerate mobility and Flory--Huggins potential when the absolute temperature is sufficiently low, which agrees well with the theoretical result by using formal asymptotic analysis. This talk is based on a joint work with Wei Jiang, Jerry Zhijian Yang and Cheng Yuan.