论文标题
两相的两个磁通的有限体积近似退化cahn-hilliard模型
Finite Volume approximation of a two-phase two fluxes degenerate Cahn-Hilliard model
论文作者
论文摘要
我们研究[W. E和P. Palffy-Muhoray。物理。 Rev. E，55：R3844-R3846，1997]，并由作者在[C. Cancès，D。Matthes和F. Nabet。拱。配给。机械。肛门，233（2）：837-866，2019]。该方案被证明可以保留连续模型的关键特性，即质量保护，浓度的阳性，能量的衰减以及熵耗散率的控制。这允许建立与该方案相对应的非线性代数系统的解决方案。此外，我们表明，由于紧凑的论点，近似解决方案会收敛到连续问题的弱解决方案，因为离散参数往往$ 0 $。数值结果说明了数值模型的行为。
We study a time implicit Finite Volume scheme for degenerate Cahn-Hilliard model proposed in [W. E and P. Palffy-Muhoray. Phys. Rev. E, 55:R3844-R3846, 1997] and studied mathematically by the authors in [C. Cancès, D. Matthes, and F. Nabet. Arch. Ration. Mech. Anal., 233(2):837-866, 2019]. The scheme is shown to preserve the key properties of the continuous model, namely mass conservation, positivity of the concentrations, the decay of the energy and the control of the entropy dissipation rate. This allows to establish the existence of a solution to the nonlinear algebraic system corresponding to the scheme. Further, we show thanks to compactness arguments that the approximate solution converges towards a weak solution of the continuous problems as the discretization parameters tend to $0$. Numerical results illustrate the behavior of the numerical model.
